相关论文: A New Look at the Arcsine Law and "Quantum-Classic…

In the present paper we discuss how to generalize ``Quantum-Classical Correspondence'' by means of the notion of interacting Fock spaces, which associates algebraic probability theory and the theory of orthogonal polynomials of probability…

We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…

In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…

Using Stein's method for the Beta distributions and a recent technique by Goldstein and Reinert of comparing the Stein characterization of the target distribution with that of the approximating distribution we prove a rate of convergence in…

Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a…

Interacting Fock space connects the study of quantum probability theory, classical random variables, and orthogonal polynomials. It is a pre-Hilbert space associated with creation, preservation, and annihilation processes. We prove that if…

We show that the Schr\"{o}dinger equation for the quantum harmonic oscillator can be derived as an approximation to the Newtonian mechanics of a classical harmonic oscillator subject to a random force for time intervals $O( m / \hbar)$,…

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 study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to a system of two harmonic oscillators for some characteristic time interval. We show that, for the case where the…

In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…

We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of…

An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We…

Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…

Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…

A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass…

We derive a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011),…

Classical systems of coupled harmonic oscillators are studied using the Carati-Galgani model. We investigate the consequences for Einstein's conjecture by considering that the exchanges of energy, in molecular collisions, follows the L\'evy…

We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…