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We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian. [ABSTRACT FROM AUTHOR]

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R (t) ) representing another observable. In the language of physics, the information carried by R (t) ≠ R † (t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ (t) . From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ (t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the "kinematical input" operator R (t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a (t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R (t) mimicking the birth of the Universe ("Big Bang") at t = 0 . [ABSTRACT FROM AUTHOR]

Using the thin-layer quantization, we formulate the problem of a Schrödinger particle constrained to move along a coordinate surface of the bi-spherical coordinate system. In three-dimensional space, the free Schrödinger equation is not separable in this coordinate system. However, when we consider the equation for a particle constrained to a given surface, there are only two degrees of freedom. One has to introduce a geometrical potential to attach the particle to the surface. This well-known potential has two contributions: one from Gauss' curvature and the other from the mean curvature. The Schrödinger equation leads to a general Heun equation. We solve it exactly and present the eigenfunctions and plots of the probability densities, and, as an application of this methodology, we study the problem of an electric charge propagating along these coordinate surfaces in the presence of a uniform magnetic field. [ABSTRACT FROM AUTHOR]

An approach of the proper quantization rule to find exact solution of radial Schrödinger equation for non-polynomial potentials, which are quasi exactly solvable, is developed in this work. Using this rule, the determination of the energy spectrum En for non-pollynomialy potentials is somewhat impossible and limited, which provides their energy at ground state only. To overcome this difficulty, we devised in this approach the potential into two potentials: an exact potential Ve(r) and a non-linear extension Va(r), the potential will be expressed as:V (r) = Ve(r)+Va(r), then calculate the energy level εn and the ground state ε0 energy for exactly solvable potential Ve(r) using the proper quantization rule, from which an analytical expression of energie En for non-polynomial potential V (r) related with the ground level energy E0 is found easily. We conclude that the study of non-exactly potential remain to the study of the first exactly solvable potential. [ABSTRACT FROM AUTHOR]

The helical edge states of two-dimensional topological insulators (TIs) experience appreciable quantum mechanical scattering in narrow channels when the width changes abruptly. The interference of the geometry scattering in narrow-wide-narrow waveguide structures is shown to give rise to the strong suppression of transmission when the incident energy is barely above the propagation threshold. Periodic resonant transmission takes place in this high reflection regime while the length of the wide section is varied. The resonance condition is governed by the transverse confinement in the wide section, where the form of quantization is manifested to differ for the two orthogonal directions. The confined energy levels in TI quantum dots are derived based on this observation. In addition, the off-diagonal spin-orbit term is found to produce an anomalous resonance state, which merges with the bottom ordinary resonance state to annihilate. [ABSTRACT FROM AUTHOR]

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter t (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed. [ABSTRACT FROM AUTHOR]

In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show that it generates the exact quantization condition for all conventional potentials. We also prove that this correction is related to the previously proven exactness of SWKB for these potentials. • We introduced a generalized Langer correction for all conventional potentials. • We demonstrated that this correction regularizes the wave functions near singularities. • We proved that the generalized Langer correction generates the exact quantization condition for all conventional potentials. • We demonstrated a connection between the exactness of WKB with generalized Langer corrections and SWKB. [ABSTRACT FROM AUTHOR]

Abstract We explain how stochastic TQFT supersymmetry can be made compatible with space supersymmetry. Taking the case of N = 2 supersymmetric quantum mechanics, (the proof would be the same for the Wess–Zumino model), we determine the kernels that ensure the convergence of the stochastic process toward the standard path integral, under the condition that they are covariant under supersymmetry. They depend on a massive parameter M that can be chosen at will and modifies the course of the stochastic evolution, but the infinite stochastic time limit of the correlation functions is in fact independent on the choice of M. [ABSTRACT FROM AUTHOR]

Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two-level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamiltonian. As a result, we would expect that the quantum dynamics of the two-photon JCM in terms of the CK Hamiltonian is qualitatively different from that of the usual one-photon case. We analytically calculate the explicit form of the atom-field entangled state and numerically evaluate the dynamics of its physical properties. The degree of entanglement, atomic population as well as sub-Poissonian statistics and quadrature squeezing of the field are analyzed. We adjust the latter evolved parameters by appropriately tuning the damping parameter within the CK Hamiltonian and detuning factor. Finally, we report a field detuning asymmetry in the collective statistical behavior. [ABSTRACT FROM AUTHOR]

This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of topological string theory. The method can be applied to traditional spectral problems governed by the Schrödinger equation, where it both reproduces and extends the results of well-established approaches, such as the exact WKB method. It can be also applied to spectral problems based on the quantization of mirror curves, where it leads to new results on the trans-series structure of the spectrum. Various examples are discussed, including the modified Mathieu equation, the double-well potential and the quantum mirror curves of local P2 and local F0. In all these examples, it is verified in detail that the trans-series obtained with this new method correctly predict the large-order behavior of the corresponding perturbative sectors. [ABSTRACT FROM AUTHOR]

Abstract In a recent article, a generic optimal control problem was studied from a physicist's point of view (Contreras et al. 2017). Through this optic, the Pontryagin equations are equivalent to the Hamilton equations of a classical constrained system. By quantizing this constrained system, using the right ordering of the operators, the corresponding quantum dynamics given by the Schrödinger equation is equivalent to that given by the Hamilton–Jacobi–Bellman equation of Bellman's theory. The conclusion drawn there were based on certain analogies between the equations of motion of both theories. In this paper, a closer and more detailed examination of the quantization problem is carried out, by considering three possible quantization procedures: right quantization, left quantization, and Feynman's path integral approach. The Bellman theory turns out to be the classical limit ħ → 0 of these three different quantum theories. Also, the exact relation of the phase S (x , t) of the wave function Ψ (x , t) = e i ħ S (x , t) of the quantum theory with Bellman's cost function J + (x , t) is obtained. In fact, S (x , t) satisfies a 'conjugate' form of the Hamilton–Jacobi–Bellman equation, which implies that the cost functional J + (x , t) must necessarily satisfy the usual Hamilton–Jacobi–Bellman equation. Thus, the Bellman theory effectively corresponds to a quantum view of the optimal control problem. Highlights • Optimal Control theory. • Pontryagin's equations and Hamilton–Jacobi–Bellman equation. • Dirac's constrained systems method. • Quantum Mechanics. [ABSTRACT FROM AUTHOR]

We consider the relationship between the unitary quantization scheme and the para-Fermi statistics of order 2. We propose an appropriate generalization of Green’s ansatz, which has made it possible to transform bilinear and trilinear commutation relations for the creation and annihilation operators for two different para-Fermi fields φa and φb into identities. We also propose a method for incorporating para-Grassmann numbers ξk into the general unitary quantization scheme. For the parastatistics of order 2, a new fact has been revealed: the trilinear relations containing both para-Grassmann variables ξk and field operators ak and bm are transformed under a certain reversible mapping into unitary equivalent relations in which commutators are replaced by anticommutators, and vice versa. It is shown that this leads to the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green’s components of operators ak and bm is constructed in explicit form, which enabled us to reduce the initial commutation rules for the components to the normal commutation relations for ordinary Fermi fields. We have analyzed a nontrivial relationship between the trilinear commutation relations of the unitary quantization scheme and the so-called Lie supertriple system. The possibility of incorporating the Duffin-Kemmer-Petiau theory into the unitary quantization scheme is discussed briefly. [ABSTRACT FROM AUTHOR]

Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. We first take a look at the algebraic description of both classical and quantum observables in terms of Jordan-Lie algebras and show how the two algebraic structures are the precise mathematical manifestation of the twofold role of observables. Then, we turn to the geometric reformulation of quantum kinematics in terms of Kähler manifolds. A key achievement of this reformulation is to show that the twofold role of observables is the constitutive ingredient defining what an observable is. Moreover, it points to the fact that, from the restricted point of view of the transformational role of observables, classical and quantum kinematics behave in exactly the same way. Finally, we present Landsman’s general framework of Poisson spaces with transition probability, which highlights with unmatched clarity that the crucial difference between the two kinematics lies in the way the two roles of observables are related to each other. [ABSTRACT FROM AUTHOR]

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. [ABSTRACT FROM AUTHOR]

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime”. We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics. [ABSTRACT FROM AUTHOR]

Examples of many-body Hamiltonians are identified which yield time-evolutions, having the property that the projection of an arbitrary orbit in phase space onto configuration space is periodic with a period independent of initial data (“isochrony”), while the evolution in phase space is not periodic. These include a variation on the harmonic oscillator as well as a Hamiltonian yielding the “goldfish” equations of motion. We then investigate a one-body version in the complex plane of this goldfish Hamiltonian. Its quantization is studied, and it is shown that the spectrum is continuous and infinitely degenerate; the general solution of the time-dependent Schrödinger equation in the position representation is not time-periodic, but its square modulus does evolve isochronously. [ABSTRACT FROM AUTHOR]

These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularities and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterparts are also presented, in the viewpoint of the inverse question: from the quantum mechanical spectrum, can one recover the classical system? [ABSTRACT FROM AUTHOR]

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit ħ→0, and, on the other, a certain generalization of Ehrenfest’s Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models. [ABSTRACT FROM AUTHOR]

The temporal evolution of a quantum spherical spin in contact with a thermal bath is studied by solving the exact Redfield equation, in order to evaluate the effect of the frequently used Lindblad approximation. This simple model can be used as a starting point for the study of more complex open quantum systems. Significant discrepancies are observed for short times. In the equilibrium state both models give identical results, as expected. [ABSTRACT FROM AUTHOR]

In this paper, we give a correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the torus T2. To achieve this, we use the correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the complex plane and a relation between the Berezin-Toeplitz quantization of a periodic symbol on the real phase space R2 and the Berezin-Toeplitz quantization of a symbol on the torus T2. [ABSTRACT FROM AUTHOR]

The use of the quantizer–dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an appropriate quantizer–dequantizer system. If this manifold of states is invariant with respect to some unitary evolution, the quantizer–dequantizer system provides a classical-like realization of such dynamics, which in general is non linear. Integrability properties are also discussed. Weyl systems and generalized coherent states are used as a simple illustration of these ideas. [ABSTRACT FROM AUTHOR]

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise. [ABSTRACT FROM AUTHOR]

The symplectic analysis, initiated by Faddeev and Jackiw, is applied to the first-order (Palatini) form of the Einstein-Hilbert action in 1 + 1 dimensions. The constraints that arise are shown to result in the same gauge transformations that follow from the first-class constraints occurring when the Dirac constraint formalism is applied to this action. Problems associated with gauge fixing are discussed. [ABSTRACT FROM AUTHOR]

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). [ABSTRACT FROM AUTHOR]

The interaction between particles in the mean-field approximation of the many-body theory is often taken into account with the use of the semiclassical description of the particle motion. However, quantization of a part of the degrees of freedom becomes essential in certain cases. In this work, two such cases where nonlinear wave equations appear have been considered: electrons in a quantum well and excitons in a trap. In the case of indirect excitons in an annular trap, the one-dimensional Gross-Pitaevskii equation permits an analytical solution and it turns out that there can be no bound state in a one-dimensional symmetric potential well. This makes the problem qualitatively different from a similar one-body problem. In the case of electrons in a quantum well, the nonlinear integro-differential equation does not have an exact solution and the allowed energy levels have been found by the direct variational method. [ABSTRACT FROM AUTHOR]

Quantum computers by their nature are many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization. [ABSTRACT FROM AUTHOR]

Generic higher derivative theories are believed to be fundamentally unphysical because they contain Ostrogradsky ghosts. We show that within complex classical mechanics it is possible to construct higher derivative theories that circumvent the Ostrogradsky theorem and have a real energy spectrum that is bounded from below. The complex theory can be canonically quantised. The resulting quantum theory does not suffer from the kinetic instability and maintains the usual probabilistic interpretation without violating the correspondence principle. As a proof of concept, we construct a class of stable interacting complex higher derivative theories and present a concrete example. This consistent and canonical framework allows us to analyse the previous attempts to avoid ghosts that use non-canonical quantisation schemes, such as the Lee–Wick theories, Dirac–Pauli quantisation or PT -symmetric quantum mechanics. The key to understand the would-be ghosts in any kinetically stable higher derivative theory is to accept the complex system behind it. [ABSTRACT FROM AUTHOR]

For a particle of mass μ moves on a 2 D surface f ( x ) = 0 embedded in 3 D Euclidean space of coordinates x , there is an open and controversial problem whether the Dirac's canonical quantization scheme for the constrained motion allows for the geometric potential that has been experimentally confirmed. We note that the Dirac's scheme hypothesizes that the symmetries indicated by classical brackets among positions x and momenta p and Hamiltonian H c remain in quantum mechanics, i.e., the following Dirac brackets [ x , H c ] D and [ p , H c ] D holds true after quantization, in addition to the fundamental ones [ x , x ] D , [ x , p ] D and [ p , p ] D . This set of hypotheses implies that the Hamiltonian operator is simultaneously determined during the quantization. The quantum mechanical relations corresponding to the classical mechanical ones p / μ = [ x , H c ] D directly give the geometric momenta. The time t derivative of the momenta p ˙ = [ p , H c ] D in classical mechanics is in fact the generalized centripetal force law for particle on the 2 D surface, which in quantum mechanics permits both the geometric momenta and the geometric potential. [ABSTRACT FROM AUTHOR]

This paper collects and extends the lectures I gave at the 'XXIV International Fall Workshop on Geometry and Physics' held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (-) algebraic formulation of quantum theories. [ABSTRACT FROM AUTHOR]

In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation. [ABSTRACT FROM AUTHOR]

The ordering problem has been one of the long standing and much discussed questions in quantum mechanics from its very beginning. Nowadays, there is more or less a consensus among physicists that the right prescription is Weyl’s rule, which is closely related to the Moyal–Wigner phase space formalism. We propose in this report an alternative approach by replacing Weyl quantization with the less well-known Born–Jordan quantization. This choice is actually natural if we want the Heisenberg and Schrödinger pictures of quantum mechanics to be mathematically equivalent. It turns out that, in addition, Born–Jordan quantization can be recovered from Feynman’s path integral approach provided that one used short-time propagators arising from correct formulas for the short-time action, as observed by Makri and Miller. These observations lead to a slightly different quantum mechanics, exhibiting some unexpected features, and this without affecting the main existing theory; for instance quantizations of physical Hamiltonian functions are the same as in the Weyl correspondence. The differences are in fact of a more subtle nature; for instance, the quantum observables will not correspond in a one-to-one fashion to classical ones, and the dequantization of a Born–Jordan quantum operator is less straightforward than that of the corresponding Weyl operator. The use of Born–Jordan quantization moreover solves the “angular momentum dilemma”, which already puzzled L. Pauling. Born–Jordan quantization has been known for some time (but not fully exploited) by mathematicians working in time–frequency analysis and signal analysis, but ignored by physicists. One of the aims of this report is to collect and synthesize these sporadic discussions, while analyzing the conceptual differences with Weyl quantization, which is also reviewed in detail. Another striking feature is that the Born–Jordan formalism leads to a redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution reducing interference effects. [ABSTRACT FROM AUTHOR]

We study the semiclassical mechanics of systems with second-class constraints. We assume that the quantum mechanics of such a system is constructed by the Batalin-Fradkin-Tyutin method, where some additional coordinates and momenta are introduced and second-class constraints are converted into firstclass constraints. We also assume that the algebraic quantization method is used to quantize the extended system. To construct the semiclassical approximation, we use the Maslov complex germ theory. We study the semiclassical states of a system with second-class constraints, their scalar product, and the action of semiclassical observables in the first order of the semiclassical expansion. We consider the transformation of semiclassical states in the course of evolution. [ABSTRACT FROM AUTHOR]

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space-time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity. [ABSTRACT FROM AUTHOR]

Everettian quantum mechanics faces the challenge of how to make sense of probability and probabilistic reasoning in a setting where there is typically no unique outcome of measurements. Wallace has built on a proof by Deutsch to argue that a notion of probability can be recovered in the many worlds setting. In particular, Wallace argues that a rational agent has to assign probabilities in accordance with the Born rule. This argument relies on a rationality constraint that Wallace calls state supervenience . I argue that state supervenience is not defensible as a rationality constraint for Everettian agents unless we already invoke probabilistic notions. [ABSTRACT FROM AUTHOR]

In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary. [ABSTRACT FROM AUTHOR]

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in q 3 ( q 3 denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness. [ABSTRACT FROM AUTHOR]

The standard time-of-arrival distribution cannot reproduce both the temporal and the spatial profile of the modulus squared of the time-evolved wave function for an arbitrary initial state. In particular, the time-of-arrival distribution gives a non-vanishing probability even if the wave function is zero at a given point for all values of time. This poses a problem in the standard formulation of quantum mechanics where one quantizes a classical observable and uses its spectral resolution to calculate the corresponding distribution. In this work, we show that the modulus squared of the time-evolved wave function is in fact contained in one of the degenerate eigenfunctions of the quantized time-of-arrival operator. This generalizes our understanding of quantum arrival phenomenon where particle detection is not a necessary requirement, thereby providing a direct link between time-of-arrival quantization and the outcomes of the two-slit experiment. [ABSTRACT FROM AUTHOR]

Rather than consider space-time as an a priori arena in which events take place, it is a construction of our mind making possible a particular kind of ordering of events. As quantum entanglement is a property of states independent of classical distances, the notion of space and time has to be revised to represent the holistic interconnectedness of quanta. We also speculate about various forms of reprogramming, or reconfiguring, the propagation of information for multipartite statistics and in quantum field theory. [ABSTRACT FROM AUTHOR]

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications. [ABSTRACT FROM AUTHOR]

Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl–Wigner formalism. Besides reproducing the magnetic field aspect of a Zeeman-like effect, the momentum space NC parameter introduces mutual information properties quantified by the quantum purity related to the relevant coordinates of the corresponding Hilbert space. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified. [ABSTRACT FROM AUTHOR]

The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with non-commuting coordinates. This demonstrates that the algebraic extension keeps the simple structure of Quantum Mechanics, while it also introduces an effective quite involved structure in the 4-dimensional sub-space. The first steps to pseudo-complex Quantum Mechanics in 1-dimension are outlined, awaiting still the interpretation of some new emerging structures. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We describe the behavior of a quantum particle in a random medium using the Green's function in the functional integral representation and propose methods for evaluating it. We calculate the localization length in the case of motion in a disordered medium and in a medium described by a random Gaussiantype potential. We consider the motion of the quantum particle in the quantized-field vacuum and show the difference between the relativistic and nonrelativistic approaches. [ABSTRACT FROM AUTHOR]

In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to Oβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length. [ABSTRACT FROM AUTHOR]

We investigate the behavior of an ensemble ofnon-interacting, identical atoms excited by a laser. In general, the-th atom sees a Rabi frequency, an initial position dependent laser phase, and a motion induced Doppler shift of. Whenoris distinct for each atom, the system evolves into a superposition ofintercoupled states, of which there aresymmetric andasymmetric collective states. For a collective state atomic interferometer (COSAIN), we recently proposed, it is important to understand the behavior of all the collective states under various conditions. In this paper, we show how to formulate the properties of these states under various non-idealities, and use this formulation to understand the dynamics thereof. We also consider the effect of treating the center of mass degree of freedom of the atoms quantum mechanically on the description of the collective states, illustrating that it is indeed possible to construct a generalized collective state, as needed for the COSAIN, when each atom is assumed to be in a localized wave packet. The analysis presented in this paper is important for understanding the dynamics of the COSAIN, and will help advance the analysis and optimization of spin squeezing in the presence of practically unavoidable non-idealities as well as in the domain where the center of mass motion of the atoms is quantized. [ABSTRACT FROM AUTHOR]

In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and emphasize the analogies between Hamiltonian flows and quantum propagators; this allows us to verify G. Mackey's observation that quantum mechanics (in its Weyl formulation) is a refinement of Hamiltonian mechanics. We discuss in detail the metaplectic representation, which very explicitly shows the close relationship between classical mechanics and quantum mechanics; the latter emerging from the first by lifting Hamiltonian flows to the double covering of the symplectic group. We also give explicit formulas for the factorization of Hamiltonian flows into simpler flows, and prove a quantum counterpart of these results. [ABSTRACT FROM AUTHOR]

We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian in order to treat electronic and nuclear degrees of freedom (dofs) within a consistent dynamic framework. We introduce an efficient symplectic integration scheme, the MInt algorithm, for numerical time evolution of the phase space variables and monodromy matrix under the non-separable MMST Hamiltonian. We then calculate the probability of transmission through a curve crossing in model two-level systems and show that MQC-IVR reproduces quantum-limit semiclassical results in good agreement with exact quantum methods in one limit, and in the other limit yields results that are in keeping with classical limit semiclassical methods like linearized IVR. Finally, exploiting the ability of the MQC-IVR to quantize different dofs to different extents, we present a detailed study of the extents to which quantizing the nuclear and electronic dofs improves numerical convergence properties without significant loss of accuracy. [ABSTRACT FROM AUTHOR]

We report for the first time a quantum mechanical simulation study of gate capacitance components in aggressively scaled InAs Nanowire Tunnel Field-Effect Transistors. It will be shown that the gate-drain capacitance exhibits the same functional dependence over the whole V gs range as the total gate capacitance, albeit with smaller values. However, as opposed to the previous capacitance estimations provided by semiclassical TCAD tools, we find that the gate capacitance exhibits a non-monotonic behavior vs. gate voltage, with plateaus and bumps related with energy quantization and subband formation determined by the device cross-sectional size, as well as with the position of channel-conduction subbands relative to the Fermi level in the drain contact. From this point of view, semiclassical TCAD tools seem to be inaccurate for capacitance estimation in aggressively-scaled TFET devices. [ABSTRACT FROM AUTHOR]

Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG)-like Whitham behavior. We show that at the Argyres–Douglas (AD) point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory. [ABSTRACT FROM AUTHOR]