Related papers: Classical harmonic oscillator with quantum energy …
We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system…
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…
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…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
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…
We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a…
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…
The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
It is shown that response properties of a quantum harmonic oscillator are in essence those of a classical oscillator, and that, paradoxical as it may be, these classical properties underlie all quantum dynamical properties of the system.…
Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…
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…