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

Journal of Sichuan Normal University

An Analytical Solution to the Master Equation for the Dissipative Harmonic Oscillator Driven by an External Field

Hou Bang-pin

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

By using the algebraic structure of the dual space of the density operator in the master equation for the driven dissipative harmonic oscillator, we first rewrite the master equation as a Schrdinger-like equation. Then we use three gauge transformations to obtaine an exact solution to the master equation in the particle number representation. Finally, we discuss the steady-state solution when the evolving time tends to infinity.

Related papers

An Exact Solution to the Master Equation for the Dissipative Harmonic Oscillator Driven by an External Field

Hou Bang-pin, Shun-Jin Wang, Yu Wan‐Lun

By using the algebraic structure in the operator dual space in the master equation for the driven dissipative harmonic oscillator, we have rewritten the master equation as a Schrödinger-like equation. Then we have used three gauge transformations and obtained an exact solution to the master equation in the particle number representation.

Chinese Physics Letters•Jun 17, 2003•6 citations

An Exact solution to the Master Equation for the Dissipative Harmonic Oscillator Driven by an External Field

侯邦品, Shun-Jin Wang, 余万伦

By using the algebraic structure in the operator dual space in the master equation for the driven dissipative harmonic oscillator,we have rewritten the master equation as a Schroedinger-like equation.Then we have used three gauge transformations and obtained an exact solution to the master equation in the particle number representation.

Chinese Physics Letters•Jan 1, 2003•0 citations

Evolution of the Density Operator in a Dissipative System—A Non-master-Equation Approach

Duan Lu-ming, Guo Guang-Can

For a typical dissipative system, a driven harmonic oscillator put in a heat bath, we obtain a simple and exact solution for the reduced density operator of the system, which gives the result obtained by the master equation approach under the small damping approximation. This method gives a simple way to get exact solutions of many problems about dissipative systems in quantum optics.

Chinese Physics Letters•Oct 1, 1995•3 citations

Density operator for describing driven damped harmonic oscillator in the diffusion-limited channel

Hong-Yi Fan, Qian-Fan Chen

In the present work, the Kraus-operator sum representation of the exact solution to the master equation describing a harmonic oscillator (driven by an external source) damping in the diffusion-limited channel is obtained by virtue of the thermo-entangled state representation and the technique of integration within an ordered product of operators. According to this solution, the initial coherent state will evolve into a displaced chaotic state that manifestly exhibits quantum decoherence.

Canadian Journal of Physics•Jan 23, 2014•2 citations

An Exact Solution to Master Equation of the Generalized Dissipative Two-mode Quantum Optical System

Hou Bang-pin

The algebraic structure for the master equation of the generalized dissipative two-mode optical system has been set up in this paper. Based on the structure, the master equation is rewritten as a Schrdinger-like equation, then the exact solution to the master equation in the particle number representation has been obtained by using algebraic dynamical method.

Journal of Sichuan Normal University•Jan 1, 2005•0 citations

Analytic solutions to various dissipation models of the simple and driven quantum harmonic oscillator

Pablo Carlos López Vázquez, Roberto Santos Silva

We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open quantum harmonic oscillator. The environmental models we use are based on optical master equations for the zero and finite temperature bath and whose open dynamics are described by a Lindblad master equation, and also we use the Caldeira-Leggett model for the high temperature limit, in the the under damped an the over damped case. Under the Wigner Fourier transform or chord function as it has been called, it becomes particularly simple to solve the dynamics of the open oscillator in the sense that the dynamics of the system are reduced to the application of an evolution matrix related to the damped motion of the oscillator.

arXiv:1801.05943•Jan 18, 2018•2 citations
By using the algebraic structure of the dual space of the density operator in the master equation for the driven dissipative harmonic oscillator, we first rewrite the master equation as a Schrdinger-like equation. Then we use three gauge transformations to obtaine an exact solution to the master equation in the particle number representation. Finally, we discuss the steady-state solution when the evolving time tends to infinity.
We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open quantum harmonic oscillator. The environmental models we use are based on optical master equations for the zero and finite temperature bath and whose open dynamics are described by a Lindblad master equation, and also we use the Caldeira-Leggett model for the high temperature limit, in the the under damped an the over damped case. Under the Wigner Fourier transform or chord function as it has been called, it becomes particularly simple to solve the dynamics of the open oscillator in the sense that the dynamics of the system are reduced to the application of an evolution matrix related to the damped motion of the oscillator.