Generalized Ehrenfest Relations,Deformation Quantization,and the Geometry of Inter-model Reduction

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 \(\hbar \rightarrow 0\), 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.     

Open quantum dots: II. Probing the classical to quantum transition

Open quantum dots provide a natural system in which to study both classical and quantum features of transport. From the classical point of view these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. An important question concerns the manner in which these classical states evolve into the set of quantum states that populate the dot in the quantum limit. In the reverse direction, the manner in which the quantum states evolve to the classical world is governed strongly by Zurek's decoherence theory. This was discussed from the quantum perspective in an earlier review?(Ferry et?al 2011 Semicond. Sci. Technol. 26 043001). Here, we discuss the nature of the various classical states, how they are formed, how they progress to the quantum world, and the signatures that they create in magnetotransport and general conductance studies of these dots.     

On an Algebraic Property of the Disordered Phase of the Ising Model with Competing Interactions on a Cayley Tree

It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains.     

Confined quantum time of arrivals

We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For the spatially confined particle, we show that the problem admits a solution in the form of an eigenvalue problem of a compact and self-adjoint time of arrival operator derived by a quantization of the classical time of arrival, which is canonically conjugate with the Hamiltonian in a closed subspace of the Hilbert space.     

Generation of entangled coherent states for two cavity modes via resonant interaction with a V-type three-level atom

This paper proposes a scheme for the generation of entangled coherent states for two cavity modes. In the scheme a V-type three-level atom is sent through a two-mode cavity filled with a coherent field. After the atom cavity interaction and detection of the atomic state the cavity modes may evolve to a superposition of two-mode coherent states. As the scheme is based on resonant atom-cavity interaction, the required interaction time is short, which is important in view of the decoherence. Moreover, additional classical pulses are unnecessary before and after the atom-cavlty interaction.     

Dynamics of Quantum Discord in Asymmetric and Local Non-Markovian Environments

The non-Markovian decoherence of quantum and classical correlationsis analytically obtained when two qubits are asymmetrically subjected to the bit flip channel and phase flip channel. For one class of initial mixed states, quantum correlations quantified by quantum discord decay synchronously with classical correlations. The discovery that the decaying rates of quantum and classical correlations suddenly change at the characteristic time is physically interpreted by the distance from quantum state to the closest classical states. In a large time interval, quantum correlations are greater than classical correlations. The quantum and classical correlations can be preserved over a longer period of time via the kernel characterizing the environment memory effects.     

A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field

Yangian Y(sl(2)) is realized in the bi-spin system coupled with a time-dependent external magnetic field. It is shown that Y(sl(2)) generators can describe the transitions between the "spin triplet" and the "spin singlet" that evolve with time. Furthermore, new transition operators between the states with Berry phase factor and those between the states of nuclear magnetic resonance are presented.     

The Weyl representation in classical and quantum mechanics

The position representation of the evolution operator in quantum mechanics is analogous to the generating function formalism of classical mechanics. Similarly, the Weyl representation is connected to new generating functions described by chords and centres in phase space. Both classical and quantal theories relie on the group of translations and reflections through a point in phase space. The composition of small time evolutions leads to new versions of the classical variational principle and to path integrals in quantum mechanics. The strong resemblance between the two theories allows a clear derivation of the semiclassical limit in which observables evolve classically in the Weyl representation. The restriction of the motion to the energy shell in classical mechanics is the basis for a full review of the semiclassical Wigner function and the theory of scars of periodic orbits. By embedding the theory of scars in a fully uniform approximation, it is shown that the region in which the scar contribution is oscillatory is separated from a decaying region by a caustic that touches the shell along the periodic orbit and widens quadratically within the energy shell.     

Persistence of microstructural evolution in irradiated metals and its consequences at high radiation exposure

Abstract

A review is presented of a very general aspect of the response of all metals subjected to displacive irradiation. This aspect is referred to as «persistence» and describes the tendency of both radiation-induced microstructural evolution and the associated changes in material properties or dimensional stability to evolve to saturation states that resist further change upon continued irradiation. It is shown that new persistent states can develop on a longer time frame associated with the late-term loss of existing microstructural components or the gain of new components, especially when transmutation and/or segregation occurs. The persistent states are often dependent on the irradiation conditions, and if these are changed, the material usually adjusts to form the persistent state characteristic of the new conditions, with the memory of the former state often lost, and sometimes leaving no visible record of the former state in the new microstructure. Depending on the microstructural components involved, the transition toward the new persistent state can occur quickly or very slowly.     

Multi-soliton complexes in mode-locked fiber lasers

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers in the normal dispersion domain. In the distributed mathematical model (complex cubic-quintic Ginzburg–Landau equation), we observe a discrete family of soliton pairs with equidistantly increasing peak separation. We show that stabilization of previously unstable bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time. Furthermore, we investigate the parameter domain where the region of stable bound states does not shrink to zero for vanishing absorber recovery time corresponding to a laser with an instantaneous saturable absorber. For a certain domain of the small-signal gain, we obtain a robust first level bound state with almost constant separation where the phase of the two pulses evolves independently. Moreover, their phase difference can evolve either periodically or chaotically depending on the small signal gain. Interestingly, higher level bound states exhibit a fundamentally different dynamics. They represent oscillating solutions with a phase difference alternating between zero and π.     

A geometrical interpretation of the Pauli exclusion principle in classical field theory

It is shown that classical Dirac fields with the same couplings obey the Pauli exclusion principle in the following sense: If at a certain time two Dirac fields are in different states, they can never reach the same one. This is geometrically interpreted as analogous to the impossibility of crossing of trajectories in the phase space of a dynamical system. An application is made to a model in which extended particles are represented as solitary waves of a set of several fundamental, confined nonlinear Dirac fields, with the result that the same mechanism accounts both for fermion and boson behaviors.     

Modulated amplitude waves and the transition from phase to defect chaos

The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We describe periodic coherent structures of the CGLE, called modulated amplitude waves (MAWs). MAWs of various periods P occur in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures evolve towards defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.     

Semi-quantum Dialogue Based on Single Photons

In this paper, we propose two semi-quantum dialogue (SQD) protocols by using single photons as the quantum carriers, where one requires the classical party to possess the measurement capability and the other does not have this requirement. The security toward active attacks from an outside Eve in the first SQD protocol is guaranteed by the complete robustness of present semi-quantum key distribution (SQKD) protocols, the classical one-time pad encryption, the classical party’s randomization operation and the decoy photon technology. The information leakage problem of the first SQD protocol is overcome by the classical party’ classical basis measurements on the single photons carrying messages which makes him share their initial states with the quantum party. The security toward active attacks from Eve in the second SQD protocol is guaranteed by the classical party’s randomization operation, the complete robustness of present SQKD protocol and the classical one-time pad encryption. The information leakage problem of the second SQD protocol is overcome by the quantum party’ classical basis measurements on each two adjacent single photons carrying messages which makes her share their initial states with the classical party. Compared with the traditional information leakage resistant QD protocols, the advantage of the proposed SQD protocols lies in that they only require one party to have quantum capabilities. Compared with the existing SQD protocol, the advantage of the proposed SQD protocols lies in that they only employ single photons rather than two-photon entangled states as the quantum carriers. The proposed SQD protocols can be implemented with present quantum technologies.     

Zwitters: Particles between quantum and classical

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics.     

Epistemic Entanglement due to Non-generating Partitions of Classical Dynamical Systems

Quantum entanglement relies on the fact that pure quantum states are dispersive and often inseparable. Since pure classical states are dispersion-free they are always separable and cannot be entangled. However, entanglement is possible for epistemic, dispersive classical states. We show how such epistemic entanglement arises for epistemic states of classical dynamical systems based on phase space partitions that are not generating. We compute epistemically entangled states for two coupled harmonic oscillators.     

Resonances,Unstable Systems,and Irreversibility: Matter Meets Mind

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-time oriented semigroups is open to question. One possible role for these latter states and semigroups is as an abstract representation of mental systems as opposed to material systems. The beginnings of this interpretation will be sketched.     

Classical Mechanics Is not the ħ, → 0 Limit of Quantum Mechanics

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have a common part but there exist tomograms of classical states which are not admissible in quantum mechanics and, vice versa, there exist tomograms of quantum states which are not admissible in classical mechanics. The role of different transformations of reference frames in the phase space of classical and quantum systems (scaling and rotation) determining the admissibility of tomograms as well as the role of quantum uncertainty relations are elucidated. The union of all admissible tomograms of both quantum and classical states is discussed in the context of interaction of quantum and classical systems. Negative probabilities in classical and quantum mechanics corresponding to tomograms of classical and quantum states are compared with properties of nonpositive and nonnegative density operators, respectively. The role of the semigroup of scaling transforms of the Planck's constant is discussed.     

Quantum to classical correspondence for the Fermi-acceleration model

A quantum particle which is confined to the interior of a box with infinitely high but periodically oscillating walls can have an unusual semiclassical limit: For the special case of a one-dimensional linear wall motion we show that the semiclassical domain corresponds to a classical motion in phase space where the initial momentum depends on the particle's position in the box. Another result is that quantum states which correspond to classical cycle-1 fixed points have maximum stability against the boundary induced perturbation (caused by the moving wall). Higher cycle-n fixed points are calculated by numerical bookkeeping up to n = 20. The classical motion is marginally stable. We show how a slight change in the boundary condition will lead to chaotic motion.     

A probabilistic model of quantum states for classical data security

The phenomenal progress of quantum information theory over the last decade has substantially broadened the potential to simulate the superposition of states for exponential speedup of quantum algorithms over their classical peers. Therefore, the conventional and modern cryptographic standards (encryption and authentication) are susceptible to Shor’s and Grover’s algorithms on quantum computers. The significant improvement in technology permits consummate levels of data protection by encoding classical data into small quantum states that can only be utilized once by leveraging the capabilities of quantum-assisted classical computations. Considering the frequent data breaches and increasingly stringent privacy legislation, we introduce a hybrid quantum-classical model to transform classical data into unclonable states, and we experimentally demonstrate perfect state transfer to exemplify the classical data. To alleviate implementation complexity, we propose an arbitrary quantum signature scheme that does not require the establishment of entangled states to authenticate users in order to transmit and receive arbitrated states to retrieve classical data. The consequences of the probabilistic model indicate that the quantum-assisted classical framework substantially enhances the performance and security of digital data, and paves the way toward real-world applications.     

Phase particle integrations of the nuclear vlasov equation

The non-linear Vlasov equation, describing the time development of the one-body Wigner distribution function, is integrated as an initial value problem by following the trajectories of notional phase particles which evolve along its hamiltonian characteristic curves. Initial conditions are generated by galilean transformations of the self-consistent solutions of the static equation obtained assuming a Thomas-Fermi form for the Wigner distribution.Fusion, deep inelastic collisions and fragmentation are all exhibited depending on the bombarding energy per nucleon, in qualitative agreement with the results of comparable TDHF calculations. A simple criterion for determining the boundaries between these phenomena, based on classical penetration of the collective mean field by the phase particles, is found not to be accurate, presumably due to an inadequate allowance for the effects of self-consistency.