Related papers: On Quantum - Classical Correspondence for Baker's …
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
We point out a correspondence between classical and quantum states, by showing that for every classical distribution over phase--space, one can construct a corresponding quantum state, such that in the classical limit of $\hbar\to 0$ the…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
Motivated by various systems in which quantum effects occur in classical backgrounds, we consider the dynamics of a classical particle as described by a coherent state that is coupled to a quantum bath via bi-quadratic interactions. We…
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
We introduce a family of models for quantum mechanical, one-dimensional random walks, called quantum multibaker maps (QMB). These are Weyl quantizations of the classical multibaker models previously considered by Gaspard, Tasaki and others.…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…
This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
We study classical and quantum phases in the adiabatic Born-Oppenheimer context. These include a classical astronomical case, the general dual description of the phases, a new "Paradox" connected to scattering Berry phase and its resolution…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…