相关论文: Time evolution of the classical and quantum mechan…
The integral Wigner - Liouwille equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte-Carlo procedure and molecular dynamics methods. The strong…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
Using operator ordering techniques based on BCH-like relations of the su(1,1) Lie algebra and a time-splitting approach,we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial…
The creation of quantum coherences requires a system to be anharmonic. The simplest such continuous 1D quantum system is the Kerr oscillator. It has a number of interesting symmetries we derive. Its quantum dynamics is best studied in phase…
Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a…
We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…
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…
Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium ($\chi^{(3)}$ non-linearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schr\"odinger equation and the classical position and momentum variables solving Hamilton's equations. Here…
The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…
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…
Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix…
In this article the time evolution operator of two interacting quantum oscillators, whose Hamiltonian is an element of the complex $\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$ algebra, is analyzed using the Feynman time ordering operator…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master…