289 results on '"Mathematical physics"'
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2. From classical to quantum, from physics to philosophy: Benjamin H. Feintzeig: The classical-quantum correspondence. Cambridge Elements in the philosophy of physics. Cambridge: Cambridge University Press, 2022, 97 pp, $22 PB.
- Author
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Chua, Eugene Y. S.
- Subjects
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QUANTUM field theory , *PHYSICS , *PLANCK'S constant , *C*-algebras , *MATHEMATICAL physics , *QUANTUM theory , *BANACH algebras , *QUANTUM groups - Abstract
"The Classical-Quantum Correspondence" by Benjamin H. Feintzeig is a comprehensive exploration of the classical-quantum correspondence using C* algebras and quantization theory. The book is aimed at researchers interested in the foundations of quantum physics and covers topics such as the 0-limit, classical-quantum structural continuity, and the interpretation of particle concepts in quantum field theories. It assumes a strong mathematical background but is a good starting point for those familiar with the algebraic approach to quantum theories. The book also applies the formal framework to philosophical considerations, including the reduction of classical to quantum physics and the explanation of classical physics using quantum physics. It discusses the concept of quantization theory, the interpretation of Planck's constant, and the continuity of structure in the transition from classical to quantum physics. The text concludes by discussing the heuristic role of quantization in constructing quantum theories and its potential implications for interpretative questions in quantum mechanics. [Extracted from the article]
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- 2024
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3. A second-quantised Shannon theory
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Kristjánsson, Hlér and Chiribella, Giulio
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Physics ,Quantum computing ,Quantum information ,Theoretical computer science ,Quantum communication ,Quantum physics ,Theoretical physics ,Quantum theory ,Mathematical physics ,Computer science - Abstract
Shannon's theory of information laid the groundwork for the rapid developments in information and communications technologies over the last century. Yet, it assumed that information carriers were described by the laws of classical physics, whilst at the most fundamental level, nature obeys the laws of quantum physics. Quantum Shannon theory, which describes information carriers as quantum states, has led to a new era of possibilities, such as perfectly secure cryptography without pre-established keys. Yet, there is a sense in which this transition from classical to quantum is incomplete. Traditionally, quantum Shannon theory has focused on scenarios where the internal states of information carriers are quantum, whilst their trajectories in spacetime have still been assumed to be classical. This work presents a second level of quantisation where both the information itself and its propagation in spacetime are treated in a quantum fashion. The second-quantised Shannon theory describes the possibility of a single particle being simultaneously transmitted through multiple communication channels in a quantum superposition. The framework is developed using the tools of higher-order transformations and quantum resource theories, formally quantifying the resources required for communication between a sender and receiver in this setting. The advantages of the second-quantised theory are illustrated in a series of examples, showcasing various counterintuitive phenomena that occur when information is simultaneously transmitted through multiple communication channels. In particular, when a single particle travels in a quantum superposition through two alternative transmission lines, the noisy processes in the two lines can destructively interfere, leading to a cleaner communication channel overall. Various different scenarios are encompassed in the framework, including transmission through a superposition of both independent and correlated channels, as well as through large-scale communication networks. This work concludes with a study of the robustness of these protocols to errors and a discussion of recent experimental demonstrations of their associated communication advantages.
- Published
- 2022
4. Author index.
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YANG-Mills theory , *TOPOLOGICAL entropy , *CONSERVATION laws (Mathematics) , *VERTEX operator algebras , *MATHEMATICAL physics , *VON Neumann algebras , *QUANTUM theory , *SECOND law of thermodynamics - Published
- 2023
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5. -modular transformation of the superconformal algebra characters.
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Bahraminasab, M. R. and Ghominejad, M.
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ALGEBRA , *THETA functions , *SUPERSTRING theories , *MATHEMATICAL physics , *QUANTUM theory - Abstract
The superconformal algebra characters have to exhibit modular invariance in order to be appropriately applied in quantum superstring theories. The nonunitary characters are given by higher-level Appell functions and different kinds of Jacobi theta functions are involved within their algebraic structures. Evaluating their -modular invariance appears to be quite simple, but verifying their -modular invariance entails a serious mathematical physics exploration. In this regard, we use a new vocabulary for Jacobi theta functions, namely "spectral theta functions," which allows us to come up with the -modular transformation of nonunitary (nontrivial) characters for the central charge , where is a pair of coprime positive integers. [ABSTRACT FROM AUTHOR]
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- 2023
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6. Indistinguishable entangled fermions: basics and future challenges.
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Majtey, Ana P., Valdés-Hernández, Andrea, and Cuestas, Eloisa
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QUANTUM information theory , *FERMIONS , *MATHEMATICAL physics , *INFORMATION resources , *QUANTUM theory , *DIRAC function - Abstract
The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of exploiting quantum indistinguishability as a resource in quantum information theory. Impressive theoretical and experimental advances have been made in the last decades that bring us closer to a deeper comprehension and to a better control of entanglement. Yet, when it involves composites of indistinguishable quantum systems, the very meaning of entanglement, and hence its characterization, still finds controversy and lacks a widely accepted definition. The aim of the present paper is to introduce, within an accessible and self-contained exposition, the basic ideas behind one of the approaches advanced towards the construction of a coherent definition of entanglement in systems of indistinguishable particles, with focus on fermionic systems. We also inquire whether the corresponding tools developed for studying entanglement in identical-fermion systems can be exploited when analysing correlations in distinguishable-party systems, in which the complete information of the individual parts is not available. Further, we open the discussion on the broader problem of constructing a suitable framework that accommodates entanglement in the presence of generalized statistics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'. [ABSTRACT FROM AUTHOR]
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- 2023
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7. Emergence and identity of quantum particles.
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Dieks, Dennis
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QUANTUM field theory , *MATHEMATICAL physics , *QUANTUM theory , *QUANTUM mechanics , *CLASSICAL mechanics - Abstract
According to classical physics, particles are basic constituents of the physical world. Quantum theory is much less friendly to particles; in particular, relativistic quantum field theory (RQFT) creates serious obstacles for the idea that particles are fundamental. Apparently, when moving from the domain of RQFT to that of classical mechanics (CM), particles have to emerge at some stage. It is standard to assume that this emergence has been completed at the level of quantum mechanics, halfway between RQFT and CM, even though particles of the same kind in many-particle quantum mechanics have the curious feature of being 'entities without identity'. Against this 'Received View' about the nature of quantum particles we outline and defend an Alternative View (AV), in which the emergent character of particles is emphasized. According to this AV, the step to a particle theory has not yet been made in quantum mechanics: conditions have still to be satisfied in order to make the particle concept applicable. If these conditions are met, the quantum particles that emerge are distinguishable individuals possessing physically defined identities, in stark contrast to what the Received View asserts. We will compare and contrast the two Views, both from a physical and a logical/conceptual point of view. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'. [ABSTRACT FROM AUTHOR]
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- 2023
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8. Teichmüller Theory: Classical, Higher, Super and Quantum.
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TEICHMULLER spaces ,MATHEMATICAL physics ,PHYSICAL sciences ,QUANTUM theory ,MATHEMATICS conferences - Abstract
Teichmüller spaces play a major role in many areas of mathematics and physical science. The subject of the conference was recent developments of Teichmüller theory with its different ramifications that include the classical, the higher, the super and the quantum aspects of the theory. [ABSTRACT FROM AUTHOR]
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- 2023
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9. Göran Lindblad in Memoriam.
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Bengtsson, Ingemar
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MATHEMATICAL physics ,STATISTICAL physics ,QUANTUM entropy ,QUANTUM theory ,INFORMATION theory - Published
- 2023
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10. Free Choice in Quantum Theory: A p -adic View.
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Anashin, Vladimir
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QUANTUM theory , *MATHEMATICAL physics , *ENTROPIC uncertainty , *RATIONAL numbers , *QUANTUM mechanics , *MEASUREMENT errors - Abstract
In this paper, it is rigorously proven that since observational data (i.e., numerical values of physical quantities) are rational numbers only due to inevitably nonzero measurements errors, the conclusion about whether Nature at the smallest scales is discrete or continuous, random and chaotic, or strictly deterministic, solely depends on experimentalist's free choice of the metrics (real or p-adic) he chooses to process the observational data. The main mathematical tools are p-adic 1-Lipschitz maps (which therefore are continuous with respect to the p-adic metric). The maps are exactly the ones defined by sequential Mealy machines (rather than by cellular automata) and therefore are causal functions over discrete time. A wide class of the maps can naturally be expanded to continuous real functions, so the maps may serve as mathematical models of open physical systems both over discrete and over continuous time. For these models, wave functions are constructed, entropic uncertainty relation is proven, and no hidden parameters are assumed. The paper is motivated by the ideas of I. Volovich on p-adic mathematical physics, by G. 't Hooft's cellular automaton interpretation of quantum mechanics, and to some extent, by recent papers on superdeterminism by J. Hance, S. Hossenfelder, and T. Palmer. [ABSTRACT FROM AUTHOR]
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- 2023
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11. Construction of Solitary Wave Solutions to the (3 + 1)-Dimensional Nonlinear Extended and Modified Quantum Zakharov–Kuznetsov Equations Arising in Quantum Plasma Physics.
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Areshi, Mounirah, Seadawy, Aly R., Ali, Asghar, AlJohani, Abdulrahman F., Alharbi, Weam, and Alharbi, Amal F.
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PLASMA physics , *QUANTUM plasmas , *QUANTUM theory , *ION acoustic waves , *MATHEMATICAL physics , *PLASMA waves , *KADOMTSEV-Petviashvili equation , *NONLINEAR evolution equations - Abstract
Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The derived results via the MEAEM method, ESE method, and modified F-expansion have been retrieved and will be expedient in the future to illuminate the collaboration between lower nonlinear ion-acoustic waves. For the physical behavior of the models, some solutions are plotted graphically in 2D and 3D by imparting particular values to the parameters under the given condition at each solution. Hence explored solutions have profitable rewards in the field of mathematical physics. [ABSTRACT FROM AUTHOR]
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- 2023
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12. An Intensional Probability Theory: Investigating the Link between Classical and Quantum Probabilities †.
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Milovanović, Miloš and Saulig, Nicoletta
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MATHEMATICAL physics , *QUANTUM theory , *STATISTICAL models , *QUANTUM states - Abstract
The link between classical and quantum theories is discussed in terms of extensional and intensional viewpoints. The paper aims to bring evidence that classical and quantum probabilities are related by intensionalization, which means that by abandoning sets from classical probability one should obtain quantum theory. Unlike the extensional concept of a set, the intensional probability is attributed to the quantum ensemble, which is contextually dependent. The contextuality offers a consistent realization of the measurement problem, which should require the existence of the time operator. The time continuum by Brouwer has satisfied such a requirement, which makes it fundamental to mathematical physics. The statistical model it provides has been proven tremendously useful in a variety of applications. [ABSTRACT FROM AUTHOR]
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- 2022
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13. New trends in quantum integrability: recent experiments with ultracold atoms.
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Guan, Xi-Wen and He, Peng
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ATOMIC physics , *MATHEMATICAL physics , *MANY-body problem , *QUANTUM theory , *ATOMS , *ULTRACOLD molecules , *YANG-Baxter equation - Abstract
Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang–Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga–Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology. [ABSTRACT FROM AUTHOR]
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- 2022
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14. State Of The Quantum Vacuum, The: Casimir Physics In The 2020's
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Kimball A Milton and Kimball A Milton
- Subjects
- Mathematical physics, Vacuum polarization--Mathematical models, Quantum theory, Casimir effect--Mathematical models
- Abstract
This review volume is intended to survey the field of quantum fluctuational phenomena induced by material bodies, which is commonly encompassed under the name of Casimir physics. H B G Casimir first discovered that zero-point fluctuations in the electromagnetic field caused an attractive force between closely separated metallic plates. Now — 75 years later — the field is burgeoning, with numerous experimental verifications and applications to practical devices starting to emerge.In this book, new ideas about Casimir physics are brought to bear on such diverse subjects as cosmology, where the Casimir energy may explain the dark energy that causes the cosmic repulsion, and nonstatic regimes, such as Casimir or quantum friction. Unsolved problems, including divergences in Casimir self-energies, the meaning of local energy densities in inhomogeneous backgrounds, and discrepancies between theory and experiment, are treated in some detail. It is hoped that this collection of papers will serve as an introduction to the field for newcomers to the subject, and that it will inspire a new burst of research into the nature of the quantum vacuum.
- Published
- 2023
15. Lógica cuántica, Nmatrices y adecuación, I.
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Jorge, Juan Pablo and Holik, Federico
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SEMANTICS , *QUANTUM logic , *LOGIC , *MATHEMATICAL physics , *QUANTUM theory , *STRUCTURAL analysis (Engineering) , *LATTICE theory - Abstract
In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent of the number of truth values involved, generalizing previous works. We also show the failure of the adequacy of every Nmatrix that is a model of the non-distributive lattice of quantum propositions. [ABSTRACT FROM AUTHOR]
- Published
- 2022
16. The Un(solv)able Problem.
- Author
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Cubitt, Toby S., Pérez-García, David, and Wolf, Michael
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QUANTUM theory , *MATHEMATICAL physics , *QUANTUM logic - Abstract
The article describes an unsolvable problem in physics: the undecidability of the spectral gap. Particular focus is given to how this relates to 20th-century mathematical results by Kurt Gödel and Alan Turing and quantum physics. Other topics discussed include further details on the mathematics of quantum mechanics, the work of the German mathematician David Hilbert, and how the work of the author gives mathematical proof that one of the basic questions of quantum physics cannot be solved in general.
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- 2018
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17. Universe Without Things : Physics in an Intangible Reality
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Jan-Markus Schwindt and Jan-Markus Schwindt
- Subjects
- Mathematical physics, Physics, Quantum theory
- Abstract
Physics is written in the language of mathematics, and its findings are based on thousands of experiments. But what kind of picture does physics paint of the world? What do theories like relativity or quantum mechanics contribute to it? How complete is this picture? This book sheds light on how the'things'these theories are about relate to our everyday things, and points out what questions remain unanswered and what problems are involved.In this book, the author presents how physics works, what it can and cannot do. In doing so, he describes the surprising answers that physics provides to many of our questions about the nature of'things'and the world; answers that challenge our intuition in many ways.This book is a translation of the original German 1st edition Universum ohne Dinge by Jan-Markus Schwindt, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
- Published
- 2022
18. Is biological randomness just noise?
- Author
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Longo, Giuseppe
- Subjects
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QUANTUM theory , *HAMILTONIAN operator , *MATHEMATICAL physics , *PROBABILITY theory , *MATHEMATICAL symmetry - Published
- 2022
19. Mathematical Models In Science
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Olav Arnfinn Laudal and Olav Arnfinn Laudal
- Subjects
- General relativity (Physics), Quantum theory, Mathematical physics, Geometry, Algebraic
- Abstract
Mathematical Models in Science treats General Relativity and Quantum Mechanics in a non-commutative Algebraic Geometric framework.Based on ideas first published in Geometry of Time-Spaces: Non-commutative Algebraic Geometry Applied to Quantum Theory (World Scientific, 2011), Olav Arnfinn Laudal proposes a Toy Model as a Theory of Everything, starting with the notion of the Big Bang in Cosmology, modeled as the non-commutative deformation of a thick point. From this point, the author shows how to extract reasonable models for both General Relativity and Quantum Theory. This book concludes that the universe turns out to be the 6-dimensional Hilbert scheme of pairs of points in affine 3-space. With this in place, one may develop within the model much of the physics known to the reader. In particular, this theory is applicable to the concept of Dark Matter and its effects on our visual universe.Hence, Mathematical Models in Science proves the dependency of deformation theory in Mathematical Physics and summarizes the development of physical applications of pure mathematics developed in the twentieth century.
- Published
- 2021
20. Don't Be Afraid of Physics : Quantum Mechanics, Relativity and Cosmology for Everyone
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Ross Barrett, Pier Paolo Delsanto, Ross Barrett, and Pier Paolo Delsanto
- Subjects
- Cosmology, Physics--Popular works, Mathematical physics, Quantum theory
- Abstract
With the aid of entertaining short stories, anecdotes, lucid explanations and straight-forward figures, this book challenges the perception that the world of physics is inaccessible to the non-expert. Beginning with Neanderthal man, it traces the evolution of human reason and understanding from paradoxes and optical illusions to gravitational waves, black holes and dark energy. On the way, it provides insights into the mind-boggling advances at the frontiers of physics and cosmology. Unsolved problems and contradictions are highlighted, and contentious issues in modern physics are discussed in a non-dogmatic way in a language comprehensible to the non-scientist. It has something for everyone.
- Published
- 2021
21. Comment on 'Backflow in relativistic wave equations'.
- Author
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Barbier, Maximilien, Fewster, Christopher J, Goussev, Arseni, Morozov, Gregory V, and Srivastava, Shashi C L
- Subjects
- *
WAVE equation , *MATHEMATICAL physics , *QUANTUM theory , *QUANTUM mechanics , *DIMENSIONLESS numbers - Published
- 2023
- Full Text
- View/download PDF
22. Some Unusual Topics in Quantum Mechanics
- Author
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Pankaj Sharan and Pankaj Sharan
- Subjects
- Particles (Nuclear physics), Quantum theory, Mathematical physics, Quantum field theory
- Abstract
In this book, the author addresses selected topics in quantum mechanics that are not usually covered in books, but which are very helpful in developing a student's interest in, and a deeper understanding of the subject. The topics include two different ways of looking at quantum mechanics; three clarifying topics that students often find confusing; one classic theorem never proved in the classroom; and a discussion on whether there can be a non-linear quantum mechanics. The book can be used as supporting material for graduate-level core courses on quantum mechanics.
- Published
- 2020
23. Classical and Quantum Dynamics : From Classical Paths to Path Integrals
- Author
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Walter Dittrich, Martin Reuter, Walter Dittrich, and Martin Reuter
- Subjects
- Physics, Quantum theory, Mathematical physics, Nuclear physics, Field theory (Physics)
- Abstract
Graduate students seeking to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger's source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann's (Einstein's) ideas on space and time and their philosophical implications are discussed.
- Published
- 2020
24. Developments in Mathematical and Conceptual Physics : Concepts and Applications for Engineers
- Author
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Harish Parthasarathy and Harish Parthasarathy
- Subjects
- Mechanics, Quantum theory, Physics--Textbooks, Mathematical physics, Field theory (Physics)
- Abstract
This book presents concepts of theoretical physics with engineering applications. The topics are of an intense mathematical nature involving tools like probability and random processes, ordinary and partial differential equations, linear algebra and infinite-dimensional operator theory, perturbation theory, stochastic differential equations, and Riemannian geometry. These mathematical tools have been applied to study problems in mechanics, fluid dynamics, quantum mechanics and quantum field theory, nonlinear dynamical systems, general relativity, cosmology, and electrodynamics. A particularly interesting topic of research interest developed in this book is the design of quantum unitary gates of large size using the Feynman diagrammatic approach to quantum field theory. Through this book, the reader will be able to observe how basic physics can revolutionize technology and also how diverse branches of mathematical physics like large deviation theory, quantum field theory, general relativity, and electrodynamics have many common issues that provide the starting point for unifying the whole of physics, namely in the formulation of Grand Unified Theories (GUTS).
- Published
- 2020
25. Unstable Systems
- Author
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Lawrence Horwitz, Yosef Strauss, Lawrence Horwitz, and Yosef Strauss
- Subjects
- Mathematical physics, Quantum theory, Mechanics, Stability, Quantum systems, Dynamics
- Abstract
This book focuses on unstable systems both from the classical and the quantum mechanical points of view and studies the relations between them. The first part deals with quantum systems. Here the main generally used methods today, such as the Gamow approach, and the Wigner-Weisskopf method, are critically discussed. The quantum mechanical Lax-Phillips theory developed by the authors, based on the dilation theory of Nagy and Foias and its more general extension to approximate semigroup evolution is explained.The second part provides a description of approaches to classical stability analysis and introduces geometrical methods recently developed by the authors, which are shown to be highly effective in diagnosing instability and, in many cases, chaotic behavior. It is then shown that, in the framework of the theory of symplectic manifolds, there is a systematic algorithm for the construction of a canonical transformation of any standard potential model Hamiltonian to geometric form, making accessible powerful geometric methods for stability analysis in a wide range of applications.
- Published
- 2020
26. A Cost-Efficient Approach towards Computational Fluid Dynamics Simulations on Quantum Devices.
- Author
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Jóczik, Szabolcs, Zimborás, Zoltán, Majoros, Tamás, and Kiss, Attila
- Subjects
QUANTUM theory ,FINITE element method ,MATHEMATICAL physics ,REDUCED-order models ,MATHEMATICAL models ,COMPUTATIONAL fluid dynamics - Abstract
Numerical simulations of physical systems are found in many industries, as they currently play a crucial role in product development. There are many numerical methods for solving differential equations that describe the underlying physics behind the mathematical models in the simulation, among which, the finite element method (FEM) is one of the most commonly used. Although in many applications the FEM seems to provide an acceptable solution to the problem, there are still many complex real-life processes that can be challenging to simulate numerically due to their complexity and large size. Recently, there has been a shift in research towards efficiently applying quantum algorithms in finite element analysis (FEA), as the potential and speedup that they could offer have been shown, but little to no effort has been made towards the applicability and cost efficiency of these algorithms in real-world quantum devices. In this paper, we propose a cost-efficient method for applying quantum algorithms in FEA for industrial problems post-processed by classical algorithms in order to address the limitations of available quantum hardware and their cost when accessing them through different cloud-based services. We carry this out by approximating the solution of the initially large system with a suitable quantum algorithm and using the obtained solutions to generate a set of reduced-order models (ROMs) that are much smaller in complexity and size than the original model. This allows the simulation of the original model with different parameter sets and excitations to be run efficiently on classical computers without having the need to access quantum subroutines again. This way, we have reduced the usage of quantum hardware (and thus the development cost) while still taking advantage of its quantum speedup. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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27. LINEARISED COHERENT STATES FOR NON-RATIONAL SUSY EXTENSIONS OF THE HARMONIC OSCILLATOR.
- Author
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CONTRERAS-ASTORGA, ALONSO, FERNÁNDEZ C., DAVID J., and MURO-CABRAL, CÉSAR
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MATHEMATICAL physics ,HYPERGEOMETRIC functions ,COHERENT states ,HARMONIC oscillators ,MATHEMATICAL functions ,QUANTUM theory ,GROUND state energy ,QUANTUM mechanics - Published
- 2022
28. Recuperando la memoria del matemático, científico e ingeniero Esteban Terradas e Illa.
- Author
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PASTOR SAAVEDRA, MARÍA ASUNCIÓN
- Subjects
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MATHEMATICIANS , *TELEPHONE networks , *EDUCATIONAL change , *MATHEMATICS , *ENGINEERS , *PHYSICS , *MATHEMATICAL physics , *SPECIAL relativity (Physics) , *QUANTUM theory , *AERONAUTICS - Abstract
The article presents the life and work of Esteban Terradas e Illa, a Spanish mathematician, scientist, and engineer. Terradas was recognized for his contributions in mathematics and physics, as well as his involvement in educational reform in Catalonia. He held academic positions at universities in Zaragoza and Barcelona, and was a member of the Royal Academy of Exact, Physical and Natural Sciences. Additionally, he played an important role in the construction of the telephone network and secondary railways in Catalonia, as well as in projects related to aeronautics in Argentina. The article provides links to online sources that contain additional biographical information about Terradas Illa. [Extracted from the article]
- Published
- 2022
29. From Random Walks to Random Matrices
- Author
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Jean Zinn-Justin and Jean Zinn-Justin
- Subjects
- Quantum field theory, Renormalization (Physics), Mathematical physics, Field theory (Physics), Physics, Quantum theory, Statistical physics
- Abstract
Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models, and in consequence develops our understanding of the fundamental nature of the universe. This books offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic and develops the discussion in a self-contained manner. At the same time the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes are renormalization group, fixed points, universality, and continuum limit, which open and conclude the work. The development of modern theoretical physics has required important concepts and novel mathematical tools, examples discussed in the book include path and field integrals, the notion of effective quantum or statistical field theories, gauge theories, and the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations, and summation of perturbative series.
- Published
- 2019
30. Old Problems and New Horizons in World Physics
- Author
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Volodymyr Krasnoholovets and Volodymyr Krasnoholovets
- Subjects
- Quantum theory, Mathematical physics
- Abstract
In the frame of the new explanatory theoretic models, matter and energy may be different characteristics of a physical system and “equivalence” between matter and energy becomes not so obvious. Quantum Mechanics was developed based on the assumption that electron mass is constant. Variable electron mass automatically rules out the entirety of quantum mechanics. Electron mass can change during chemical and biological processes and then other characteristics modify correspondingly. It is accepted that the Special Theory of Relativity (STR) does not contradict quantum mechanics, but in reality, the opposite is true. Even for a non-rocket scientist, this contradiction becomes evident with the simplest analysis of energy mass and energy equivalence formula. In simple words, the formula assumes that if energy is quantized, mass must be quantized too. How do atomic particles know how much mass to convert into energy and keep the same proportion in the conversion? Maybe one proton or one neutron converts more mass than his neighbor does!
- Published
- 2019
31. A Mathematical Companion to Quantum Mechanics
- Author
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Shlomo Sternberg and Shlomo Sternberg
- Subjects
- Quantum theory, Mathematical physics
- Abstract
This original 2019 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Its intended audience is students of mathematics at the senor university level and beginning graduate students in mathematics and physics. Early chapters address such topics as the Fourier transform, the spectral theorem for bounded self-joint operators, and unbounded operators and semigroups. Subsequent topics include a discussion of Weyl's theorem on the essential spectrum and some of its applications, the Rayleigh-Ritz method, one-dimensional quantum mechanics, Ruelle's theorem, scattering theory, Huygens'principle, and many other subjects.
- Published
- 2019
32. Quantum Mechanics : A Fundamental Approach
- Author
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K. Kong Wan and K. Kong Wan
- Subjects
- Chemistry, Physical and theoretical, Quantum theory, Mathematical physics, Physics--Data processing
- Abstract
The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning, which makes it difficult to appreciate the mathematical formalism and understand quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. This book is divided into four parts. Part I is a brief review of the general properties of classical and quantum systems. A general discussion of probability theory is also included which aims to help in understanding the probability theories relevant to quantum mechanics. Part II is a detailed study of the mathematics for quantum mechanics. Part III presents quantum mechanics in a series of postulates. Six groups of postulates are presented to describe orthodox quantum systems. Each statement of a postulate is supplemented with a detailed discussion. To make them easier to understand, the postulates for discrete observables are presented before those for continuous observables. Part IV presents several illustrative applications, which include harmonic and isotropic oscillators, charged particle in external magnetic fields and the Aharonov–Bohm effect. For easy reference, definitions, theorems, examples, comments, properties and results are labelled with section numbers. Various symbols and notations are adopted to distinguish different quantities explicitly and to avoid misrepresentation. Self-contained both mathematically and physically, the book is accessible to a wide readership, including astrophysicists, mathematicians and philosophers of science who are interested in the foundations of quantum mechanics.
- Published
- 2019
33. ON CLASSES OF q-AL-OBOUDI TYPE HARMONIC FUNCTIONS.
- Author
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L., DILEEP and NANDINI, P.
- Subjects
QUANTUM theory ,MATHEMATICAL physics ,UNIVALENT functions ,ANALYTIC functions ,HARMONIC functions - Abstract
The theory of q-analysis has many applications in various sub-fields of mathematics and quantum physics. In this paper, we define and investigate the classes of complex valued harmonic functions using the q-Al-Oboudi difierential operator D
k λ,q : For functions belonging to these classes, we obtain some coeficient conditions, distortion bounds and other interesting properties. [ABSTRACT FROM AUTHOR]- Published
- 2021
34. Quantum Foundations, Probability and Information
- Author
-
Andrei Khrennikov, Bourama Toni, Andrei Khrennikov, and Bourama Toni
- Subjects
- Mathematical physics, Probabilities, Quantum theory
- Abstract
Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory.Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.
- Published
- 2018
35. Lost in Math : How Beauty Leads Physics Astray
- Author
-
Sabine Hossenfelder and Sabine Hossenfelder
- Subjects
- Mathematical physics, Cosmology, Quantum theory
- Abstract
In this'provocative'book (New York Times), a contrarian physicist argues that her field's modern obsession with beauty has given us wonderful math but bad science.Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades.The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these'too good to not be true'theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.
- Published
- 2018
36. Special issue in honour of the life and work of Fritz Haake.
- Author
-
Gnutzmann, Sven, Guhr, Thomas, Schomerus, Henning, and Życzkowski, Karol
- Subjects
- *
MATHEMATICAL physics , *STATISTICAL physics , *QUANTUM theory , *DECOHERENCE (Quantum mechanics) , *QUANTUM superposition - Abstract
Rev.Lett.86 2913 Strunz W T, Haake F and Braun D 2003 Universality of decoherence for macroscopic quantum superpositionsPhys. Rev.Lett.93 014103 Müller S, Heusler S, Braun P, Haake F and Altland A 2005 Periodic-Orbit theory of universality in quantum chaosPhys. Petr, who was a full professor in St Petersburg, became a frequent guest of Fritz since the 1990s, and later indeed joined the University of Essen. Rev.Lett.41 1685 HaakeF1979TheoryofSuperfluorescence (SpringerSeriesinOpticalSciences,LaserSpectroscopy IV)vol 21 (Berlin: Springer) [4] BraunD,BraunPAandHaake F1999 Semiclassicsforadissipativequantum mapPhys.D131265 Braun D, Braun P A and Haake F 2000 Long-lived quantum coherence between macroscopically distinct states in superradianceOpt. [Extracted from the article]
- Published
- 2021
- Full Text
- View/download PDF
37. Foundations of Quantum Theory : From Classical Concepts to Operator Algebras
- Author
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Klaas Landsman and Klaas Landsman
- Subjects
- Algebra, Mathematical physics, Physics, Matrix theory, Quantum theory
- Abstract
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C•-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its'spontaneous'breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.This book is Open Access under a CC BY licence.
- Published
- 2017
38. Operational Symmetries : Basic Operations in Physics
- Author
-
Heinrich Saller and Heinrich Saller
- Subjects
- Quantum theory, Symmetry (Physics), Mathematical physics
- Abstract
This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato's and Kepler's symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations.
- Published
- 2017
39. Lectures on Hyperhamiltonian Dynamics and Physical Applications
- Author
-
Giuseppe Gaeta, Miguel A. Rodríguez, Giuseppe Gaeta, and Miguel A. Rodríguez
- Subjects
- Symplectic manifolds, Hamiltonian systems, Physics, Quantum theory, Mathematical physics
- Abstract
This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of Hamiltonian mechanics, in which the role of the symplectic structure is taken by a hyperkähler one (thus there are three Kähler/symplectic forms satisfying quaternionic relations). This has proved to be of use in the description of physical systems with spin, including those which do not admit a Hamiltonian formulation. The book is the first monograph on the subject, which has previously been treated only in research papers.
- Published
- 2017
40. Structure of Space and the Submicroscopic Deterministic Concept of Physics
- Author
-
Volodymyr Krasnoholovets and Volodymyr Krasnoholovets
- Subjects
- Mathematical physics, Quantum theory
- Abstract
This book, Structure of Space and the Submicroscopic Deterministic Concept of Physics, completely formalizes fundamental physics by showing that all space, which consists of objects and distances, arises from the same origin: manifold of sets. A continuously organized mathematical lattice of topological balls represents the primary substrate named the tessellattice. All fundamental particles arise as local fractal deformations of the tessellattice. The motion of such particulate balls through the tessellattice causes it to deform neighboring cells, which generates a cloud of a new kind of spatial excitations named ‘inertons'. Thus, so-called'hidden variables'introduced in the past by de Broglie, Bohm and Vigier have acquired a sense of real quasiparticles of space.This theory of space unambiguously answers such challenging issues as: what is mass, what is charge, what is a photon, what is the wave psi-function, what is a neutrino, what are the nuclear forces, and so on. The submicroscopic concept uncovers new peculiar properties of quantum systems, especially the dynamics of particles within a section equal to the particle's de Broglie wavelength, which are fundamentally impossible for quantum mechanics. This concept, thoroughly discussed in the book, allows one to study complex problems in quantum optics and quantum electrodynamics in detail, to disclose an inner world of particle physics by exposing the structure of quarks and nucleons in real space, and to derive gravity as the transfer of local deformations of space by inertons which in turn completely solves the problems of dark matter and dark energy. Inertons have revealed themselves in a number of experiments carried out in condensed media, plasma, nuclear physics and astrophysics, which are described in this book together with prospects for future studies in both fundamental and applied physics.
- Published
- 2017
41. Finite and Profinite Quantum Systems
- Author
-
Apostolos Vourdas and Apostolos Vourdas
- Subjects
- Computer science--Mathematics, Quantum computers, Physics, Mathematical physics, Quantum optics, Quantum theory
- Abstract
This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits'and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and quantum computing, two-dimensional electron systems in magnetic fields and the magnetic translation group, the quantum Hall effect, other areas in condensed matter physics, and Fast Fourier Transforms. The monograph combines ideas from quantum mechanics with discrete mathematics, algebra, and number theory. It is suitable for graduate students and researchers in quantum physics, mathematics and computer science.
- Published
- 2017
42. Numerical Simulation of Free Dissipative Open Quantum System and Establishment of a Formula for π.
- Author
-
Agasti, Souvik
- Subjects
- *
MATHEMATICAL physics , *QUANTUM theory , *UNITARY transformations , *COMPUTER simulation - Abstract
We transform the system/reservoir coupling model into a one-dimensional semi-infinite discrete chain with nearest neighbor interaction through a unitary transformation, and, simulate the dynamics of free dissipative open quantum system. We investigate the consequences of such modeling, which is observed as finite size effect causing the recurrence of particle from the end of the chain. Afterwards, we determine a formula for π in terms of the matrix operational form, which indicates a robustness of the connection between quantum physics and basic mathematics. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
43. The Butterfly in the Quantum World : The Story of the Most Fascinating Quantum Fractal
- Author
-
Indubala I Satija and Indubala I Satija
- Subjects
- Quantum theory, Fractals, Mathematical physics
- Abstract
Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the'Hofstadter butterfly', a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today.The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.
- Published
- 2016
44. Probability And Randomness: Quantum Versus Classical
- Author
-
Andrei Yu Khrennikov and Andrei Yu Khrennikov
- Subjects
- Probabilities, Quantum theory, Mathematical physics
- Abstract
Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level.
- Published
- 2016
45. Quantum Algebras and Poisson Geometry in Mathematical Physics
- Author
-
M. V. Karasev and M. V. Karasev
- Subjects
- Mathematical physics, Quantum theory, Commutation relations (Quantum mechanics), Poisson manifolds, Symplectic manifolds
- Abstract
This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.
- Published
- 2016
46. Effective Evolution Equations From Quantum Dynamics
- Author
-
Niels Benedikter, Marcello Porta, Benjamin Schlein, Niels Benedikter, Marcello Porta, and Benjamin Schlein
- Subjects
- Quantum theory, Mathematical physics
- Abstract
These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.
- Published
- 2016
47. Chiral soliton solutions of perturbed chiral nonlinear Schrödinger equation with its applications in mathematical physics.
- Author
-
Cheemaa, N., Chen, S., and Seadawy, A. R.
- Subjects
- *
MATHEMATICAL physics , *PLASMA physics , *SCHRODINGER equation , *NUCLEAR physics , *NONLINEAR Schrodinger equation , *QUANTUM mechanics , *QUANTUM theory - Abstract
In this article, we have discussed the analytical treatment of perturbed chiral nonlinear Schrödinger equation with the help of our newly developed method extended modified auxiliary equation mapping method (EMAEMM). By using this newly proposed technique we have found some quite general and new variety of exact traveling wave solutions, which are collecting some kind of semi half bright, dark, bright, semi half dark, doubly periodic, combined, periodic, half hark, and half bright via three parametric values, which is the primary key point of difference of our technique. These results are highly applicable to develop new theories of quantum mechanics, biomedical problems, soliton dynamics, plasma physics, nuclear physics, optical physics, fluid dynamics, biomedical problems, electromagnetism, industrial studies, mathematical physics, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions using Mathematica 10.4 to get complete understanding in a more efficient manner to observe the behavior of different new dynamical shapes of solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
48. Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 2.
- Author
-
Khrennikov, Andrei, Raedt, Hans de, Plotnitsky, Arkady, and Polyakov, Sergey
- Subjects
- *
QUANTUM theory , *MATHEMATICAL physics , *QUANTUM entropy , *CLASSICAL mechanics , *GROUND state energy - Abstract
This volume is the second of the two volumes presenting theoretical and experimental viewpoints on foundational problems of quantum physics that are directly related to quantum information and technology. Related problematics are discussed, from a general historical and philosophical perspective of fundamental principles of quantum theory, in Plotnitsky's "A matter of principle: The principles of quantum theory, Dirac's equation, and quantum information". [Extracted from the article]
- Published
- 2020
- Full Text
- View/download PDF
49. Road to Reality with Roger Penrose
- Author
-
Eckstein, Michał, Szybka, Sebastian J., McCabe, Gordon, Ladyman, James, Presnell, Stuart, Eckstein, Michał, Szybka, Sebastian J., McCabe, Gordon, Ladyman, James, and Presnell, Stuart
- Subjects
- Mathematical physics, Quantum theory, Realism
- Abstract
Where does the road to reality lie? This fundamental question is addressed in this collection of essays by physicists and philosophers, inspired by the original ideas of Sir Roger Penrose, the English mathematical physicist and philosopher of science. The topics range from black holes and quantum information to the very nature of mathematical cognition itself. [Subject: Philosophy, Physics, Mathematics, Cosmology]
- Published
- 2015
50. Testing Quantum Contextuality : The Problem of Compatibility
- Author
-
Jochen Szangolies and Jochen Szangolies
- Subjects
- Quantum theory, Mathematical physics, Physics
- Abstract
Jochen Szangolies contributes a novel way of dealing with the problem of the experimental testability of the Kochen-Specker theorem posed by realistic, that is, noisy, measurements. Such noise spoils perfect compatibility between successive measurements, which however is a necessary requirement to test the notion of contextuality in usual approaches. To overcome this difficulty, a new, extended notion of contextuality that reduces to Kochen-Specker contextuality in the limit of perfect measurement implementations is proposed by the author, together with a scheme to test this notion experimentally. Furthermore, the behaviour of these tests under realistic noise conditions is investigated.
- Published
- 2015
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