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

The European Physical Journal Plus

Quantum dynamics of a driven damped harmonic oscillator in Heisenberg picture: exact results and possible generalizations

Fardin Kheirandish

Published Feb 1, 2020• 5 citations
Publisher
DOI
10.1140/epjp/s13360-020-00264-4

Related papers

Quantum theory of the damped harmonic oscillator

Hermann Grabert, Ulrich Weiß, Peter Talkner A

The European Physical Journal B•Mar 1, 1984•272 citations

Non-Markovian master equation for a damped oscillator with time-varying parameters

K. W. Chang, C. K. Law

We derive an exact non-Markovian master equation that generalizes the previous work [Hu, Paz and Zhang, Phys. Rev. D 45, 2843 (1992)] to damped harmonic oscillators with time-varying parameters. This is achieved by exploiting the linearity of the system and operator solution in Heisenberg picture. Our equation governs the non-Markovian quantum dynamics when the system is modulated by external devices. As an application, we apply our equation to parity kick decoupling problems. The time-dependent dissipative coefficients in the master equation are shown to be modified drastically when the system is driven by $\ensuremath{\pi}$ pulses. For coherence protection to be effective, our numerical results indicate that kicking period should be shorter than memory time of the bath. The effects of using soft pulses in an ohmic bath are also discussed.

arXiv:1003.5975•Physical Review A•May 10, 2010•29 citations

Open quantum systems in Heisenberg picture

Fardin Kheirandish

In the framework of the Heisenberg picture, an alternative derivation of the reduced density matrix of a driven dissipative quantum harmonic oscillator as the prototype of an open quantum system is investigated. The reduced density matrix for different initial states of the combined system is obtained from a general formula, and different limiting cases are studied. Exact expressions for the corresponding characteristic function in quantum thermodynamics and Wigner quasi distribution function are found. A possible generalization based on the Magnus expansion of the evolution operator is presented.

arXiv:1903.08551•Mar 20, 2019•0 citations

Classical and quantum mechanics of the damped harmonic oscillator

H. Dekker

Physics Reports•Dec 1, 1981•645 citations

Dynamics of a Quantum Damped Oscillator with Relaxation

Oleg Yu. Dinariev

Russian Physics Journal•May 1, 2003•0 citations

Heisenberg-picture approach to the exact quantum motion of a time-dependent harmonic oscillator

Jeong‐Young Ji, Jae Kwan Kim, Sang Pyo Kim

The generalized invariant and the exact quantum motions are found in the Heisenberg picture for a harmonic oscillator with time-dependent mass and frequency in terms of classical solutions. It is shown that the Heisenberg pictures gives a relatively simpler picture that the Schr\"odinger picture and also manifestly exhibits the time independency of the invariant. We apply this method to the system with a linear sweep of frequency and Paul trap and study the squeezing properties.

Physical Review A•May 1, 1995•114 citations
We derive an exact non-Markovian master equation that generalizes the previous work [Hu, Paz and Zhang, Phys. Rev. D 45, 2843 (1992)] to damped harmonic oscillators with time-varying parameters. This is achieved by exploiting the linearity of the system and operator solution in Heisenberg picture. Our equation governs the non-Markovian quantum dynamics when the system is modulated by external devices. As an application, we apply our equation to parity kick decoupling problems. The time-dependent dissipative coefficients in the master equation are shown to be modified drastically when the system is driven by $\ensuremath{\pi}$ pulses. For coherence protection to be effective, our numerical results indicate that kicking period should be shorter than memory time of the bath. The effects of using soft pulses in an ohmic bath are also discussed.
In the framework of the Heisenberg picture, an alternative derivation of the reduced density matrix of a driven dissipative quantum harmonic oscillator as the prototype of an open quantum system is investigated. The reduced density matrix for different initial states of the combined system is obtained from a general formula, and different limiting cases are studied. Exact expressions for the corresponding characteristic function in quantum thermodynamics and Wigner quasi distribution function are found. A possible generalization based on the Magnus expansion of the evolution operator is presented.