Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Far East Journal of Dynamical Systems

SIGN SOLVED PROPAGATOR OF TWO COUPLED AND FORCED OSCILLATORS WITH COUPLING OF THE FORM

Emmanouil George Thrapsaniotis

Published Mar 25, 2008• 0 citations
Publisher

Abstract

In the present paper we derive in an exact closed form the sign solved propagator of a general time dependent system of two coupled and forced harmonic oscillators with coupling of the form The method is based on the use of the central limit theorem in the phase of the path expression. The result is applied on the time evolution of the Wigner distribution of the present system.

DOI
10.17654/0972111808002

Related papers

Path integral methods via the use of the central limit theorem and application

Emmanouil George Thrapsaniotis

We consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x 1 x α 2 and we derive the relevant sign solved propagator.

Journal of Physics A Mathematical and Theoretical•Apr 24, 2008•6 citations

DYNAMICS EVOLUTION FOR TIME-DEPENDENT COUPLED OSCILLATORS

Xiao Wang

By means of the time-dependent quantum transformation theory,we derive the exact solution for the time-dependent coupled oscillators.Based on this result,for the given initial states,the dynamics evolutions of Fock state and coherent state are discussed.

Diwen wuli xuebao•Jan 1, 2008•0 citations

Exact solution of a time-dependent quantal harmonic oscillator with damping and a perturbative force

Dinkar C. Khandekar, S. V. Lawande

The problem of a quantal harmonic oscillator with damping and a time-dependent frequency acted on by a time-dependent perturbative force is exactly solved. The wavefunctions are found in Schrödinger representation using the theory of explicitly time-dependent invariants and also by an expansion of the Feynman propagator. The propagator is obtained in exactly closed form by an explicit path integration of the classical Lagrangian. It is found that the wavefunctions and the propagator depend only on the solution of classical damped oscillator through a single function ρ (t). The function ρ (t) itself may be obtained as a solution of a second order nonlinear differential equation under the appropriate set of initial conditions.

Journal of Mathematical Physics•Sep 1, 1979•85 citations

The propagator of the time-dependent forced harmonic oscillator with time-dependent damping

Bin Kang Cheng

By using the Caldirola–Kanai Hamiltonian and by applying Feynman polygonal paths, exact evaluation of the propagator of one-dimensional time-dependent forced and damped harmonic oscillator, based on the work of Montroll in deriving the propagator of the harmonic oscillator with time-dependent frequency, is possible. The results are compared with previously found results.

Journal of Mathematical Physics•Jan 1, 1986•11 citations

Path Integral for a Harmonic Oscillator with Time-Dependent Mass and Frequency

Surarit Pepore, P. Winotai, Tanakorn Osotchan +1 more

The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.

•Jan 1, 2006•6 citations

Path integral approach to the general driven time-dependent harmonic oscillator and squeezed state

Jing‐Bo Xu, ZHANG XUN-SHENG, Shangbin Li

The time evolution of the general driven time-dependent harmonic oscillator is studied and the propagator and wave function are obtained by using a generalized canonical transformation and path integral method. We then proceed to construct the squeezed states for the system by making use of the wave function. The damped driven harmonic oscillator and the harmonic oscillator with strongly pulsating mass under the action of an arbitrary driving force are discussed as illustrative examples.

Physica Scripta•Sep 1, 1997•3 citations
In the present paper we derive in an exact closed form the sign solved propagator of a general time dependent system of two coupled and forced harmonic oscillators with coupling of the form The method is based on the use of the central limit theorem in the phase of the path expression. The result is applied on the time evolution of the Wigner distribution of the present system.
We consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x 1 x α 2 and we derive the relevant sign solved propagator.
The problem of a quantal harmonic oscillator with damping and a time-dependent frequency acted on by a time-dependent perturbative force is exactly solved. The wavefunctions are found in Schrödinger representation using the theory of explicitly time-dependent invariants and also by an expansion of the Feynman propagator. The propagator is obtained in exactly closed form by an explicit path integration of the classical Lagrangian. It is found that the wavefunctions and the propagator depend only on the solution of classical damped oscillator through a single function ρ (t). The function ρ (t) itself may be obtained as a solution of a second order nonlinear differential equation under the appropriate set of initial conditions.
The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.