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 Russian Laser Research

Classical representation of a quantum damped oscillator—Comparison between the caldirola-kanai model, the kinetic equation, and the kostin equation

Vladimir I. Man’ko, Sergey S. Safonov

Published Mar 1, 1999• 5 citations
Publisher
DOI
10.1007/bf02508688

Related papers

The Caldirola-Kanai Model and Its Equivalent Theories for a Damped Oscillator

Ming-Chang Huang, Ming‐Chya Wu

Chinese Journal of Physics•Aug 1, 1998•10 citations

Damping in the Interaction of a Field and Two Three-Level Atoms Through Quantized Caldirola–Kanai Hamiltonian

Tarek M. El-Shahat, Mohamad Kh. Ismail, Abdullah Faisal Al Naim

Journal of Russian Laser Research•May 1, 2018•6 citations

Quantum mechanics of the inverted Caldirola-Kanai oscillator

Sotirios Baskoutas, A. D. Jannussis

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B•Mar 1, 1992•19 citations

Damping in the Interaction of a Two-Photon Field and a Two-Level Atom Through Quantized Caldirola-Kanai Hamiltonian

Alireza Dehghani, B. Mojaveri, R. Jafarzadeh Bahrbeig

International Journal of Theoretical Physics•Dec 19, 2018•3 citations

Fluid-dynamical interpretation of quantum damped oscillators

Mohammed A. Z. Habeeb

The model of a quantum damped oscillator based on the Caldirola-Kanai equation is investigated by exploiting its coherent state basis. It is shown how these coherent states facilitate the derivation of fluid-dynamical equations corresponding to this model in the classical limit. From the conservative form of these equations it is concluded that the system represented by the Caldirola-Kanai equation cannot be considered as the quantum analogue of the classical damped oscillator. This is contrasted with the case of a harmonic oscillator interacting with a heat bath.

Journal of Physics A Mathematical and General•Dec 1, 1987•1 citation

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

Francisco F. López-Ruiz, Julio Guerrero, V. Aldaya +1 more

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

Journal of Physics Conference Series•Aug 24, 2012•1 citation
The model of a quantum damped oscillator based on the Caldirola-Kanai equation is investigated by exploiting its coherent state basis. It is shown how these coherent states facilitate the derivation of fluid-dynamical equations corresponding to this model in the classical limit. From the conservative form of these equations it is concluded that the system represented by the Caldirola-Kanai equation cannot be considered as the quantum analogue of the classical damped oscillator. This is contrasted with the case of a harmonic oscillator interacting with a heat bath.
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.