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

Canadian Journal of Physics

Statistical mechanics of quantum one-dimensional damped harmonic oscillator

E. N. M. Borges, O. N. Borges, L. A. Amarante Ribeiro

Published May 1, 1985• 6 citations
Publisher

Abstract

We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola–Kanai Hamiltonian.
DOI
10.1139/p85-093

Related papers

Statistical mechanics of quantum one-dimensional damped harmonic oscillators: II

O. N. Borges, L. A. Amarante Ribeiro

We show that the Caldirola–Kanai Hamiltonian of the one-dimensional damped oscillator describes in a specified basis a Gaussian, Markoffian process, in the weak coupling limit. We also discuss which assumption makes the process stationary and clarify the relationship with the master-equation approach.

Canadian Journal of Physics•Jul 1, 1987•1 citation

The quantum damped driven harmonic oscillator

Chung‐In Um, Kyu Hwang Yeon, W. H. Kahng

Using the Caldirola-Kanai Hamiltonian with an external driving force for the damped driven harmonic oscillator as the quantum dissipative system, the authors have exactly evaluated the propagator, wavefunction, uncertainty relation and the transition amplitudes by the Feynman path integral method.

Journal of Physics A Mathematical and General•Feb 21, 1987•48 citations

Comment on ``The one-dimensional harmonic oscillator damped with Caldirola--Kanai Hamiltonian''

G. F. Torres del Castillo

Several conceptual errors in a recently published paper ({\it Rev.\ Mex.\ F\'{\i}s.\ E} {\bf 64} (2018) 47) dealing with the damped one-dimensional harmonic oscillator are pointed out.

Revista Mexicana de Física E•Jul 1, 2019•2 citations

Exact results for a damped quantum-mechanical harmonic oscillator

Peter S. Riseborough, Peter Hänggi A, Ulrich Weiß

Exact calculations for a quantum oscillator linearly coupled to a thermal reservoir are presented. Explicit results (variances and correlations) for the response and the spontaneous fluctuations are evaluated for two different models of the heat bath; a reservoir with a spectrum which is similar to that of acoustic phonons and another which is analogous to optic phonons. The low-temperature behavior is shown to depend sensitively on the spectral density of the thermal reservoir. The mass and the frequency of the oscillator become renormalized through the coupling to the bath. These renormalizations are intrinsically frequency dependent. Moreover, the commonly used form of Ehrenfest's equation for the dynamics of the linearly damped oscillator is shown to only be a reasonable approximation within certain frequency regimes.

Physical Review A•Jan 1, 1985•131 citations

Quantum Theory of Damped Harmonic Oscillator

Akaninyene Daniel Antia, Eno E. Ituen, A. N. Ikot +2 more

The exact solutions of the Schrodinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle.

Global Journal of Pure and Applied Sciences•Jan 1, 2010•3 citations

Quantum Damped Mechanical Oscillator

A. N. Ikot, Louis E. Akpabio, Ita O. Akpan +2 more

The exact solutions of the Schrödinger equation for quantum damped oscillator with modified Caldirola-Kanai Hamiltonian are evaluated. We also investigate the cases of under-, over-, and critical damping.

International Journal of Optics•Jan 1, 2010•6 citations
Exact calculations for a quantum oscillator linearly coupled to a thermal reservoir are presented. Explicit results (variances and correlations) for the response and the spontaneous fluctuations are evaluated for two different models of the heat bath; a reservoir with a spectrum which is similar to that of acoustic phonons and another which is analogous to optic phonons. The low-temperature behavior is shown to depend sensitively on the spectral density of the thermal reservoir. The mass and the frequency of the oscillator become renormalized through the coupling to the bath. These renormalizations are intrinsically frequency dependent. Moreover, the commonly used form of Ehrenfest's equation for the dynamics of the linearly damped oscillator is shown to only be a reasonable approximation within certain frequency regimes.