1,475 results on '"QUANTUM theory"'
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2. 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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3. -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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4. 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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5. 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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6. 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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7. 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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8. 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]
- Published
- 2022
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9. 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]
- Published
- 2022
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10. Lógica cuántica, Nmatrices y adecuación, I.
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Jorge, Juan Pablo and Holik, Federico
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SEMANTICS , *QUANTUM logic , *MATHEMATICAL physics , *QUANTUM theory , *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
11. Is biological randomness just noise?
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Longo, Giuseppe
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QUANTUM theory , *HAMILTONIAN operator , *MATHEMATICAL physics , *PROBABILITY theory , *MATHEMATICAL symmetry - Published
- 2022
12. Comment on 'Backflow in relativistic wave equations'.
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Barbier, Maximilien, Fewster, Christopher J, Goussev, Arseni, Morozov, Gregory V, and Srivastava, Shashi C L
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WAVE equation , *MATHEMATICAL physics , *QUANTUM theory , *QUANTUM mechanics , *DIMENSIONLESS numbers - Published
- 2023
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13. The Un(solv)able Problem.
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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.
- Published
- 2018
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14. Special issue in honour of the life and work of Fritz Haake.
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Gnutzmann, Sven, Guhr, Thomas, Schomerus, Henning, and Życzkowski, Karol
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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
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15. Numerical Simulation of Free Dissipative Open Quantum System and Establishment of a Formula for π.
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Agasti, Souvik
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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
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16. Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 2.
- Author
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Khrennikov, Andrei, Raedt, Hans de, Plotnitsky, Arkady, and Polyakov, Sergey
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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
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17. On the Tension Between Physics and Mathematics.
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Rédei, Miklós
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MATHEMATICAL physics , *MATHEMATICIANS , *PHYSICISTS , *QUANTUM theory , *PHYSICS - Abstract
Because of the complex interdependence of physics and mathematics their relation is not free of tensions. The paper looks at how the tension has been perceived and articulated by some physicists, mathematicians and mathematical physicists. Some sources of the tension are identified and it is claimed that the tension is both natural and fruitful for both physics and mathematics. An attempt is made to explain why mathematical precision is typically not welcome in physics. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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18. Solitary wave and elliptic function solutions of sinh-Gordon equation and its applications.
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Lu, Dianchen, Seadawy, Aly R., and Arshad, M.
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ELLIPTIC functions , *WAVE functions , *DIFFERENTIAL geometry , *NONLINEAR differential equations , *MATHEMATICAL physics , *PARTIAL differential equations , *QUANTUM theory , *SINE-Gordon equation - Abstract
The sinh -Gordon model is an important model in special nonlinear partial differential equations (PDEs) which is arising in solid-state physics, mathematical physics, fluid dynamics, fluid flow, differential geometry, quantum theory, etc. The exact solutions in the type of solitary wave and elliptic functions solutions are created of sinh -Gordon model by employing modified direct algebraic scheme. Moments of a few solutions are also depicted graphically. These solutions helps the physicians and mathematicians to understand the physical phenomena of this model. This technique can be utilized on other models to launch further exclusively novel solutions for other categories of nonlinear PDEs occurring in mathematical Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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19. Hohenberg–Kohn Theorems for Interactions, Spin and Temperature.
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Garrigue, Louis
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STATISTICAL physics , *MATHEMATICAL physics , *TEMPERATURE , *QUANTUM theory , *DENSITY of states - Abstract
We prove Hohenberg–Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain the information of the interactions and of the external potentials. Then, in the presence of the Zeeman interaction, a strong constraint on external fields is derived for systems having the same ground state densities and magnetizations. Also, we provide a counterexample in a setting involving non-local potentials. Next, we prove that the density and the entropy of a ground state contain the information of both the imposed external potential and temperature. Eventually, we conclude that at positive temperature, Hohenberg–Kohn theorems generically hold, in particular they hold in the classical case. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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20. Nonadiabatic couplings in the collisional removal of O2(b 1Σg+,v) by O2.
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Dayou, F., Hernández, M. I., Campos-Martínez, J., and Hernández-Lamoneda, R.
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POTENTIAL energy surfaces , *MATHEMATICAL physics , *QUANTUM theory , *ENERGY levels (Quantum mechanics) , *RELAXATION methods (Mathematics) , *GEOMETRIC modeling - Abstract
The effect of nonadiabatic couplings on the collisional removal of O2(b 1Σg+,v) by O2(X 3Σg-, v=0) is investigated. Two-dimensional adiabatic and quasidiabatic potential energy surfaces for the excited dimer states and the corresponding nonadiabatic radial couplings have been computed by means of ab initio calculations. Alternately, a two-state theoretical model, based on the Landau–Zener and Rosen–Zener–Demkov assumptions, has been employed to derive analytical forms for the nonadiabatic couplings and an adiabatic-to-diabatic transformation only depending on a reduced set of adiabatic energy terms. Compared to the ab initio results, the predictions of the model are found to be highly accurate. Quantum dynamics calculations for the removal of the first ten vibrational states of O2(b 1Σg+,v) indicate a clear dominant contribution of the vibration-electronic relaxation mechanism relative to the vibration-translation energy transfer. Although the present reduced-dimensionality model precludes any quantitative comparison with experiments, it is found that the removal probabilities for v=1–3 are qualitatively consistent with the experimental observations, once the vibrational structure of the fragments is corrected with spectroscopical terms. Besides, the model served to show how the computation of the adiabatic PESs just at the crossing seam was sufficient to describe the nonadiabatic dynamics related to a given geometrical arrangement. This implies considerable savings in the calculations which will eventually allow for larger accuracy in the ab initio calculations as well as higher dimensional treatments. [ABSTRACT FROM AUTHOR]
- Published
- 2010
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21. Quantum mechanical simulation of nanosized metal-oxide-semiconductor field-effect transistor using empirical pseudopotentials: A comparison for charge density occupation methods.
- Author
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Jiang, Xiang-Wei, Deng, Hui-Xiong, Li, Shu-Shen, Luo, Jun-Wei, and Wang, Lin-Wang
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METAL oxide semiconductor field-effect transistors , *PSEUDOPOTENTIAL method , *CHARGE density waves , *QUANTUM theory , *MATHEMATICAL physics , *EIGENFUNCTIONS - Abstract
The atomistic pseudopotential quantum mechanical calculations are used to study the transport in million atom nanosized metal-oxide-semiconductor field-effect transistors. In the charge self-consistent calculation, the quantum mechanical eigenstates of closed systems instead of scattering states of open systems are calculated. The question of how to use these eigenstates to simulate a nonequilibrium system, and how to calculate the electric currents, is addressed. Two methods to occupy the electron eigenstates to yield the charge density in a nonequilibrium condition are tested and compared. One is a partition method and another is a quasi-Fermi level method. Two methods are also used to evaluate the current: one uses the ballistic and tunneling current approximation, another uses the drift-diffusion method. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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22. Calculation of the capacitances of conductors: Perspectives for the optimization of electronic devices.
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Kopp, Thilo and Mannhart, Jochen
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CAPACITORS , *QUANTUM theory , *ELECTRIC charge , *MATHEMATICAL physics , *ELECTRODES - Abstract
The equation describing the capacitance of capacitors is determined. It is shown that by optimizing the material of the conducting electrodes, the capacitance of capacitors reaching the quantum regime can be substantially enhanced or reduced. Dielectric capacitors with negative total capacitances are suggested and their properties analyzed. Resulting perspectives to enhance the performance of electronic devices are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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23. Joule heating in single-walled carbon nanotubes.
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Ragab, Tarek and Basaran, Cemal
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CARBON nanotubes , *ENERGY transfer , *PHONONS , *THERMODYNAMICS , *QUANTUM theory , *MATHEMATICAL physics - Abstract
Joule heating in single-walled carbon nanotubes (CNTs) using a quantum mechanical approach is presented in this paper. The modeling is based on the energy transfer between the electrons and both acoustic and optical phonons. In this formulation, only the knowledge of the full energy dispersion relation, phonon dispersion relation, and the electron-phonon coupling potential is required for the calculations. For verification of the proposed model, the current-voltage relation for extremely long nanotubes is calculated and the results are compared with the experimental data. The electric field dependence of the amount of energy generated by Joule heating is plotted. Moreover the effect of the thermal environment on the behavior of Joule heating is studied. The formulation proposed in this paper can also be used for structures other than CNTs. Computations indicate that, contrary to popular opinion, metallic CNT does not follow Joule’s law of P=IV. Joule heating in CNT is significantly less than what is predicted with Joule law (P=IV), which would make it a perfect candidate to replace copper as interconnect material in electronics. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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24. Monte-Carlo-based spectral gain analysis for terahertz quantum cascade lasers.
- Author
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Jirauschek, Christian and Lugli, Paolo
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TERAHERTZ spectroscopy , *MONTE Carlo method , *TRANSPORT theory , *PHONON scattering , *ELECTRON scattering , *QUANTUM theory , *MATHEMATICAL physics - Abstract
Employing an ensemble Monte Carlo transport simulation, we self-consistently analyze the spectral gain for different terahertz quantum cascade laser structures, considering bound-to-continuum as well as resonant phonon depopulation designs. In this context, we investigate temperature dependent gain broadening, affecting the temperature performance of terahertz structures. Furthermore, we discuss the influence of the individual scattering mechanisms, such as electron-electron, impurity and interface roughness scattering. A comparison of the simulation results to experimental data yields good agreement. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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25. Photo-oxidation effects of light-emitting porous Si.
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Tamura, Tomoyuki and Adachi, Sadao
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POROUS silicon , *NANOCRYSTALS , *PHOTON emission , *QUANTUM theory , *MATHEMATICAL physics , *PHOTOOXIDATIVE stress - Abstract
The effects of light illumination on porous silicon (PSi) properties have been studied using photoluminescence (PL), PL excitation (PLE), and x-ray photoelectron spectroscopy (XPS) measurements. The PL spectrum evolution in PSi sample under light illumination at various wavelengths indicates that the photo-oxidation occurs and causes a decrease in its intensity with increasing illumination time t. The decrease in the PL intensity IPL can be written as logarithmic expression, namely, the Elovich equation IPL∝-α ln t, where α is the quenching rate of the PL intensity associated with the native oxide growth. The α value is dependent on the illuminated photon energy Epo in a manner α=0.050Epo. Each PL spectrum can be deconvoluted into four Gaussian peaks. The higher the PL peak energy, the larger its photo-oxidation-induced blueshift. This fact and XPS results support that the light emission in a porous sample is due to the quantum-size effect, i.e., relaxation of the momentum conservation at and above the indirect absorption edge (supra-indirect-gap emission). The PLE spectra suggest that the surface hydrogen termination should influence the highly excited carrier dynamics in nanocrystalline PSi materials. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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26. Hydrostatic pressure effects on electron states in GaAs–(Ga,Al)As double quantum rings.
- Author
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Culchac, F. J., Porras-Montenegro, N., and Latgé, A.
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HYDROSTATICS , *QUANTUM theory , *ELECTRONS , *MAGNETIC fields , *EXCITON theory , *HOLES (Electron deficiencies) , *MATHEMATICAL physics , *MASS measurement - Abstract
Here we address a theoretical analysis of the effects of applied hydrostatic pressure on electron states in concentric GaAs–(Ga,Al)As double quantum rings, under axial magnetic fields. Emphasis is put on the dependence of such effects on the system geometry confinement described within a hard potential model and following an effective-mass approximation. The energy of the ground and excited electronic states were found to decrease with the applied hydrostatic pressure, due mainly to an effective reduction in the barrier potential confinement. Also, while the increase in the magnetic field opens the electron states degeneracy with different angular momenta, the increase in the applied hydrostatic pressure does not alter significantly the energy of these states. For both symmetric and asymmetric double quantum rings, one found that the electron-heavy hole transition energies augment with the applied hydrostatic pressure, mainly due to the increase in the GaAs gap. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
27. Molecular theory of barycentric velocity: Monatomic fluids.
- Author
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Byung Chan Eu
- Subjects
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FLUID mechanics , *INERTIA (Mechanics) , *QUANTUM theory , *SEMICONDUCTOR doping , *PHYSICAL & theoretical chemistry , *MATHEMATICAL physics - Abstract
The notion of barycentric velocity appears in irreversible thermodynamics and fluid mechanics, in which it is a field variable obeying the hydrodynamic equations or, more specifically, the momentum balance equation, which is coupled to the rest of hydrodynamic equations. Therefore, its behavior is not known until the hydrodynamic equations are solved for the flow problem of interest. Unlike diffusion fluxes, heat fluxes, or stresses, it does not have its own constitutive relation similar to Fick’s law, Fourier’s law, and Newton’s law of viscosity. In this work, the constitutive equation is derived for it. In parallel to the phenomenological notion of barycentric velocity, the notion of mean fluid velocity appears in statistical mechanics of irreversible dynamic processes according to the theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)], and plays the same role of the phenomenological counterpart. In this work, we investigate the statistical mechanical meanings of the mean fluid velocity of a fluid in flow beyond its formal connection with the barycentric velocity. We show that it consists of two components; the center-of-gravity velocity of the packet of fluid molecules, which may be identified with the barycentric velocity in the phenomenological theory, and the diffusive contribution of its collective modes relative to the center of gravity. If the fluid is uniform in space or if the packet of fluid mass is rigid, the diffusive component vanishes. The statistical mechanical (molecular theory) formula for the mean fluid velocity provides the constitutive relation for it in terms of density and temperature gradients present in the fluid in flow. The constitutive relation obtained for the mean fluid velocity can be an important component in the theory of transport processes in liquids. Its significance to fluid mechanics is briefly discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2008
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28. Active-space coupled-cluster methods through connected quadruple excitations.
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Peng-Dong Fan and So Hirata
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EXCITON theory , *QUANTUM theory , *TRANSPORT theory , *HYDRIDES , *HYDROGEN , *MATHEMATICAL physics - Abstract
Coupled-cluster methods that include just a subset of all connected triple, quadruple, or both excitation amplitudes, according to the ansatz of and Adamowicz co-workers [Int. Rev. Phys. Chem. 12, 339 (1993); J. Chem. Phys. 99, 1875 (1993); 100, 5792 (1994)] and Piecuch et al. [J. Chem. Phys. 110, 6103 (1999)], have been implemented into parallel execution programs. They are applicable to closed- and open-shell species and they take advantage of real Abelian point-group symmetry. A symbol manipulation program has been invoked to automate the implementation. These methods have been applied to the singlet-triplet separations of five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+) with consideration of scalar relativistic effects. They have been shown to be remarkably effective with errors arising from the use of a very small subset of higher-order excitations being no more than a few tenths of 1 kcal/mol. [ABSTRACT FROM AUTHOR]
- Published
- 2006
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29. Incorporation of nonadiabatic transition into wave-packet dynamics.
- Author
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Mil'nikov, Gennady V., Zou, Shiyang, and Nakamura, Hiroki
- Subjects
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WAVE packets , *ADIABATIC invariants , *MATHEMATICAL physics , *QUANTUM theory , *PHOTONS , *EXCITON theory - Abstract
Nonadiabatic wave-packet dynamics is factorized into purely adiabatic propagation and instantaneous localized nonadiabatic transition. A general formula is derived for the quantum-mechanical local nonadiabatic operator which is implemented within the framework of the R-matrix method. The operator can be used for incorporating the nonadiabatic transition in semiclassical wave-packet dynamics. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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- View/download PDF
30. Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules.
- Author
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Schaefer, Patricia, Riccardi, Demian, and Qiang Cui
- Subjects
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QUANTUM theory , *BOUNDARY value problems , *COMPLEX variables , *MATHEMATICAL physics , *INITIAL value problems , *DIRICHLET problem - Abstract
A robust approach for dealing with electrostatic interactions for spherical boundary conditions has been implemented in the QM/MM framework. The development was based on the generalized solvent boundary potential (GSBP) method proposed by Im et al. [J. Chem. Phys. 114, 2924 (2001)], and the specific implementation was applied to the self-consistent-charge density-functional tight-binding approach as the quantum mechanics (QM) level, although extension to other QM methods is straightforward. Compared to the popular stochastic boundary-condition scheme, the new protocol offers a balanced treatment between quantum mechanics/molecular mechanics (QM/MM) and MM/MM interactions; it also includes the effect of the bulk solvent and macromolecule atoms outside of the microscopic region at the Poisson–Boltzmann level. The new method was illustrated with application to the enzyme human carbonic anhydrase II and compared to stochastic boundary-condition simulations using different electrostatic treatments. The GSBP-based QM/MM simulations were most consistent with available experimental data, while conventional stochastic boundary simulations yielded various artifacts depending on different electrostatic models. The results highlight the importance of carefully treating electrostatics in QM/MM simulations of biomolecules and suggest that the commonly used truncation schemes should be avoided in QM/MM simulations, especially in simulations that involve extensive conformational samplings. The development of the GSBP-based QM/MM protocol has opened up the exciting possibility of studying chemical events in very complex biomolecular systems in a multiscale framework. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
31. Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations.
- Author
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Noid, W. G. and Loring, Roger F.
- Subjects
- *
QUANTUM theory , *THERMODYNAMICS , *NONLINEAR theories , *MATHEMATICAL analysis , *MATHEMATICAL physics , *ENERGY transfer - Abstract
The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting h→0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
32. Nucleation of ordered solid phases of proteins via a disordered high-density state: Phenomenological approach.
- Author
-
Pan, Weichun, Kolomeisky, Anatoly B., and Vekilov, Peter G.
- Subjects
- *
NUCLEATION , *MATHEMATICAL physics , *HEMOGLOBIN polymorphisms , *BLOOD proteins , *THERMODYNAMICS , *QUANTUM theory - Abstract
Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
33. A simple method for the preparation of pseudopure states in nuclear magnetic resonance quantum information processing.
- Author
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Fung, B. M. and Ermakov, Vladimir L.
- Subjects
- *
NUCLEAR magnetic resonance , *QUANTUM theory , *QUANTUM logic , *MATHEMATICAL physics , *RESONANCE , *MAGNETIC fields - Abstract
The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of pseudopure states (POPS) as a basis for QIP is very convenient because of the simplicity in experimental execution. It is now further demonstrated that the product of the NMR spectra corresponding to two sets of POPS that share a common pseudopure state has the same peak frequencies as those of the common (single) pseudopure state. Examples of applying two different quantum logic gates to a 5-qubit system are given. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
34. Incoherent noise and quantum information processing.
- Author
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Boulant, N., Emerson, J., Havel, T. F., Cory, D. G., and Furuta, S.
- Subjects
- *
HAMILTONIAN systems , *QUANTUM theory , *INFORMATION processing , *PERTURBATION theory , *MATHEMATICAL physics , *EIGENVALUES - Abstract
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modeled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
35. Exponentially localized magnetic fields for single-spin quantum logic gates.
- Author
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Lidar, D.A. and Thywissen, J.H.
- Subjects
- *
MAGNETIC fields , *FIELD theory (Physics) , *QUANTUM logic , *QUANTUM theory , *MATHEMATICAL physics , *SUPERCONDUCTORS - Abstract
An infinite array of parallel current-carrying wires is known, from the field of neutral particle optics, to produce an exponentially localized magnetic field when the current direction is antiparallel in adjacent wires. We show that a finite array of several tens of superconducting Nb nanowires can produce a peak magnetic field of 10 mT that decays by a factor of 104 over a length scale of 500 nm. Such an array is readily manufacturable with current technology, and is compatible with both semiconductor and superconducting quantum computer architectures. A series of such arrays can be used to individually address single single-spin or flux qubits spaced as little as 100 nm apart, and can lead to quantum logic gate times of 5 ns. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
36. A Bohmian total potential view to quantum effects. I. Methodology and simple model systems.
- Author
-
González, Javier, Bofill, Josep Maria, and Giménez, Xavier
- Subjects
- *
WAVE packets , *QUANTUM theory , *SCHRODINGER equation , *MATRICES (Mathematics) , *GEOMETRIC quantization , *MATHEMATICAL physics - Abstract
The coherent-state wave packet dynamics of several model systems is analyzed in terms of Bohm's total potential. The quantum dynamics has been obtained by solving the time-dependent Schrödinger equation, and a method for obtaining the total potential from it, involving just matrix algebra, has been proposed. Contrary to what one may expect, it is shown that the time- and state-dependent features of the total potential admit a rationale, classical-like description of quantum effects, leading to a unified picture of them, which is not critically dependent, as for the key features, on the classical potential. An outstanding feature is found to be the relation of the state system's density amplitude and sharpness (in its dependence with position) with quantum effects. Sharp density profiles and low densities cause the total potential to strongly depart from the classical value, in both time regimes and position ranges, which provide a clearer, more deterministic view to quantum dynamics. Free motion as well as scattering processes by square and Eckart barriers have been analyzed by means of careful inspection of several time dependent snapshots. The result is an insightful picture of processes involving tunneling and antitunneling, including their dynamical variants, as well as resonances and quantization. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
37. Paul Busch 1955–2018.
- Author
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Gudder, S., Lahti, P., and Sozzo, S.
- Subjects
- *
MATHEMATICAL physics , *QUANTUM measurement , *QUANTUM theory , *QUANTUM mechanics , *ROLE models - Published
- 2021
- Full Text
- View/download PDF
38. QUANTUM WEIRDNESS IT'S ALL IN YOUR MIND.
- Author
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Von Baeyer, Hans Christian
- Subjects
- *
QUANTUM theory , *QUANTUM information theory , *MATHEMATICAL models , *MATHEMATICAL physics , *PARADOX , *QUANTUM mechanics , *WAVE functions , *BAYESIAN analysis , *PROBABILITY theory - Abstract
In this article the author discusses a version of quantum theory that removes the paradoxes of the microscopic world making quantum information a figment of the imagination. Topics include some bizarre paradoxes of quantum mechanics, such as the appearance of particles in two places at the same time, the development of a model in 2001 by a team of physicists that eliminates quantum paradoxes by combining quantum theory with probability theory and reimaging the wave function, called Quantum Bayesianism (QBism), physicists' use of the wave function to calculate the probability that a particle will have a certain property, and some criticisms of QBism, such as its inability to explain complex macroscopic phenomena in microscopic terms.
- Published
- 2013
- Full Text
- View/download PDF
39. PHYSICS.
- Author
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Greene, Brian, Webb, Richard, Jamieson, Valerie, Battersby, Stephen, Bekenstein, Jacob, Clarkson, Chris, Clark, Stuart, Tegmark, Max, Chalmers, Matthew, Wilczek, Frank, Randall, Lisa, Conrad, Janet, and Brooks, Michael
- Subjects
- *
PHYSICS , *MATHEMATICAL physics , *GENERAL relativity (Physics) , *MATHEMATICAL models , *QUANTUM theory , *METAPHYSICAL cosmology , *LARGE Hadron Collider , *DARK matter , *DARK energy , *INFLATIONARY universe - Abstract
The article presents an introduction to a special issue on unanswered questions in the field of theoretical physics. Particular focus is given to the importance of mathematics in theoretical physics, noting physicist Albert Einstein's focus on mathematical equations in the development of his theory of general relativity. Also discussed is the potential application of quantum mechanics mathematics to the concept of a multiverse. Other topics include planned projects for the Large Hadron Collider, the existence of dark matter and dark energy, and the theory of universal inflation. INSET: SIX ROUTES TO AN ULTIMATE THEORY.
- Published
- 2013
40. THE QUANTUM SIMS.
- Author
-
Brooks, Michael
- Subjects
- *
COMPUTER simulation , *QUANTUM theory , *SIMULATION methods & models , *MATHEMATICAL physics , *MAGNETISM , *HIGGS bosons - Abstract
The article discusses quantum simulation. The author notes that conventional computers have difficulty solving or modeling quantum problems, adding that an idea by U.S. physicist Richard Feynman called quantum simulation can overcome the restrictions of conventional computers. Topics include quantum simulation experiments by Martin Zwierlein and colleagues at the Massachusetts Institute of Technology (MIT), the Higgs boson, and the use of quantum simulation for studying magnetism.
- Published
- 2013
- Full Text
- View/download PDF
41. Slippage of initial conditions for the Redfield master equation.
- Author
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Gaspard, P. and Nagaoka, M.
- Subjects
- *
EQUATIONS , *QUANTUM theory , *MATHEMATICAL physics - Abstract
Examines the general form of the slippage to be applied to the initial conditions of the Redfield master equation for a slow open quantum subsystem. Non-Markovian dynamics of the subsystem; Preservation of possitivity by the Redfield equation after the slippage superoperator has been applied to the initial density matrix of the subsystem; Reduction of the Redfield equation to the Lindblad equation.
- Published
- 1999
- Full Text
- View/download PDF
42. Cryptanalysis and Improvement of a Multiparty Quantum Direct Secret Sharing of Classical Messages with Bell States and Bell Measurements.
- Author
-
Liu, Xiao-Fen
- Subjects
- *
CRYPTOGRAPHY , *QUANTUM information theory , *QUANTUM states , *QUANTUM theory , *MATHEMATICAL physics - Abstract
Recently, a multiparty quantum direct secret sharing protocol with Bell states was presented (Song et al., Int. J Theor. Phys. 57, 1559, 2018). In this protocol, the secret message of the dealer is directly encoding into the transmitted particles. All agents obtain their pieces of secret by making Bell state measurement on their receiving particles, then cooperate to recover the dealer's secret. However, as we show, this protocol is insecure, because an outside attacker or two special dishonest agents can eavesdrop the secret fully. Furthermore, an improved version of this protocol is proposed, which can stand against the presented attacks. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
43. Quantum minds.
- Author
-
Buchanan, Mark
- Subjects
- *
QUANTUM logic , *QUANTUM theory , *LOGIC , *FUZZY logic , *THOUGHT & thinking , *MATHEMATICAL physics - Abstract
The article discusses how quantum theory might apply to the way humans think. He notes that human thinking often fails in respect to the principles of classical logic, such as making systematic errors when reasoning with probabilities, but that those errors make sense within the context logic based on quantum mathematics. Topics include why quantum mathematics is better than classical mathematics in understanding the fuzzy and flexible ways humans use ideas, the emerging field of quantum interaction, which explores how quantum theory can be used in non-physics areas, such as human language and cognition, biology, and economics, and experiments investigating flexible logic in the human mind.
- Published
- 2011
- Full Text
- View/download PDF
44. Conventional Bell Basis in PT-symmetric Quantum Theory.
- Author
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Zhu, Xiang-yu and Tao, Yuan-hong
- Subjects
- *
ORTHOGONAL functions , *HAMILTONIAN mechanics , *QUANTUM theory , *QUANTUM information theory , *MATHEMATICAL physics - Abstract
Theories defined by non-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected properties at the classical as well as at the quantum level. In this paper the conventional Bell basis is discussed using the CPT-inner product for a general two-state system in PT-symmetric quantum theory. The conventional Bell basis has many applications in quantum information theory because of the mutual orthogonality, normlization, and maximally entangled degree of each vector in the basis. This paper analyzes four properties of the Bell basis in PT-symmetric quantum theory: CPT-orthogonality, CPT-norm, CPT-entanglement degree and CPT-mutual unbiased property with other maximally entangled bases. The conventional Hermitian Bell states are not CPT-normalized and are not maximally entangled states in PT-symmetric quantum theory. The orthogonality still holds for four of the six pairs of Bell states under the CPT-inner product. Furthermore, the mutually unbiased property with another maximally entangled basis is preserved at the level of twenty five percent. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
45. New Symmetries for the Uq(slN) 6-j Symbols from the Eigenvalue Conjecture1.
- Author
-
Morozov, A. and Sleptsov, A.
- Subjects
- *
EIGENVALUES , *REGGE trajectories , *REGGE theory , *MATHEMATICAL physics , *RACAH coefficients , *QUANTUM theory - Abstract
In the present paper, we discuss the eigenvalue conjecture, suggested in 2012, in the particular case of Uq(slN) 6-j The eigenvalue conjecture provides a certain symmetry for Racah coefficients and we prove that the eigenvalue conjecture is provided by the Regge symmetry for Uq(slN) 6-j, when three representations coincide. This in perspective provides us a kind of generalization of the Regge symmetry to arbitrary Uq(slN) 6-j. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
46. A general framework for quantum splines.
- Author
-
Abrunheiro, L., Camarinha, M., Clemente-Gallardo, J., Cuchí, J. C., and Santos, P.
- Subjects
- *
SPLINES , *QUANTUM theory , *DENSITY matrices , *MATHEMATICAL physics , *MATHEMATICAL models , *HILBERT space - Abstract
Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on 𝔲 ∗ ( n ) which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
47. The unavoidable information flow to environment in quantum measurements.
- Author
-
Haapasalo, Erkka, Heinosaari, Teiko, and Miyadera, Takayuki
- Subjects
- *
QUANTUM measurement , *QUANTUM theory , *QUANTUM information theory , *QUANTUM states , *MATHEMATICAL physics - Abstract
One of the basic lessons of quantum theory is that one cannot obtain information on an unknown quantum state without disturbing it. Hence, by performing a certain measurement, we limit the other possible measurements that can be effectively implemented on the original input state. It has been recently shown by two of the authors of the present article [T. Heinosaari and T. Miyadera, Phys. Rev. A 91, 022110 (2015)] that one can implement sequentially any device, either channel or observable, which is compatible with the first measurement. In this work, we prove that this can be done, apart from some special cases, only when the succeeding device is implemented on a larger system than just the input system. This means that some part of the still available quantum information has been flown to the environment and cannot be gathered by accessing the input system only. We characterize the size of the post-measurement system by determining the class of measurements for the observable in question that allow the subsequent realization of any measurement process compatible with the said observable. We also study the class of measurements that allow the subsequent realization of any observable jointly measurable with the first one and show that these two classes coincide when the first observable is extreme. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
48. Spectral Equations for the Modular Oscillator.
- Author
-
Kashaev, Rinat M. and Sergeev, Sergey M.
- Subjects
- *
TOPOLOGICAL algebras , *MATHEMATICAL physics , *MIRROR symmetry , *ENUMERATIVE geometry , *QUANTUM theory - Abstract
Motivated by applications for non-perturbative topological strings in toric Calabi–Yau manifolds, we discuss the spectral problem for a pair of commuting modular conjugate (in the sense of Faddeev) Harper type operators, corresponding to a special case of the quantized mirror curve of local ℙ 1 × ℙ 1 and complex values of Planck’s constant. We illustrate our analytical results by numerical calculations. In memory of Ludwig Faddeev [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
49. The Nature of Representation in Feynman Diagrams.
- Author
-
Dorato, Mauro and Rossanese, Emanuele
- Subjects
- *
FEYNMAN diagrams , *MATHEMATICAL physics , *MATHEMATICAL models , *QUANTUM field theory , *QUANTUM electrodynamics , *QUANTUM theory - Abstract
The article discusses the alleged nature of representation of Feynman diagrams (FDs) in quantum field theory, particularly in quantum electrodynamics (QED). Topics include an illustration of the formalism of FDs, an explanation of why certain FD features can lead to the mistaken belief that they can act as a pictorial representation of physical processes occurring in spacetime, and the main problems encountered by the claim that FDs are pictures of the physical processes they model.
- Published
- 2018
- Full Text
- View/download PDF
50. How Do Feynman Diagrams Work?
- Author
-
Brown, James Robert
- Subjects
- *
FEYNMAN diagrams , *MATHEMATICAL models , *MATHEMATICAL physics , *QUANTUM theory , *QUANTUM electrodynamics , *QUANTUM chromodynamics - Abstract
The article explores the role of Feynman diagrams (FD) in physics. Topics include some of the questions involved in understanding FDs such as how they evolve to become useful in quantum electrodynamics (QED), a number of rules for constructing FDs in QED, and the symbols used to depict QED processes. Also mentioned are the principle philosophical issues involving Feynman diagrams, including whether FD pictures are of physical reality and whether they represent any physical processes.
- Published
- 2018
- Full Text
- View/download PDF
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