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

Physical Review A

Comment on “Induced transitions and energy of a damped oscillator”

George J. Papadopoulos, Ioannis A. Hadjiagapiou

Published Apr 1, 1999• 4 citations
Publisher

Abstract

In a recent paper Croxson [Phys. Rev. A $49,$ 588 (1994)] reported dissipation-induced transition probabilities from the ground state to higher states for a quantum harmonic oscillator. A partial approximate result was given for the oscillator to remain in its ground state, while for higher transitions the situation became complicated. Our approach provides an exact simple form closed expression for any order of transition. In addition, we supply the evolution of the work done by the system on its environment.

DOI
10.1103/physreva.59.3127

Related papers

Dissipation-induced transition of a simple harmonic oscillator

Zong-Qian Shao, Yuqi Li, Xiao‐Yin Pan

We investigate the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. Using the method developed by Yu and Sun [Phys. Rev. A 49, 592 (1994)], the general analytical expressions for the transition probabilities are obtained. The special cases: transition probabilities from the ground state to the first few excited states are then discussed in detail. Different from the previous studies in the literature where only the effect of damping was considered, it is found that the Brownian motion makes the transitions between states of different parity possible. The limitations of the applicability of our results are also discussed.

The Journal of Chemical Physics•Dec 9, 2014•5 citations

Induced transitions and energy of a damped oscillator

P. Croxson

Damped harmonic-oscillator pseudostationary-state wave functions are used to calculate transitions probabilities for a simple harmonic oscillator (SHO) subjected to damping from time t=0. The mean and variance of the energy operator are obtained in the state which was initially an SHO stationary state. This state is an instantaneous eigenstate of the energy at times when sin(\ensuremath{\omega}t)=0, \ensuremath{\omega} being the reduced frequency.

Physical Review A•Jan 1, 1994•16 citations

Response to “Comment on ‘Quantization of the damped harmonic oscillator’” [J. Math. Phys. 60, 094101 (2019)]

M. Serhan, M. Abusini, Ahmed Al-Jamel +2 more

This is a response to a recently reported comment [F. M. Fernández, J. Math. Phys. 60, 094101 (2019)] on paper [M. Serhan et al., J. Math. Phys. 59, 082105 (2018)] regarding the quantization of the damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)] is incorrect, and thus the subsequent steps via the Nikiforov-Uvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be first achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. The canonical quantization on the resulted Hermitian Hamiltonian yields the real energy eigenvalues as exactly given by Eq. (35) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)].

arXiv:1903.00352•Journal of Mathematical Physics•Sep 1, 2019•4 citations

Minimal coupling method for a quantum damped harmonic oscillator

Fardin Kheirandish, Majid Amooshahi

Quantum mechanics of a damped harmonic oscillator investigated by its coupling with a Klein-Gordon field as an environment. A new minimal coupling method introduced. Correct Heisenberg equation including a dissipative term proportional to velocity obtained. Energy flow between oscillator and environment investigated by some transition probabilities.

•Feb 13, 2005•0 citations

Dissipation and decoherence in a quantum oscillator

Ambegaokar, V

The time development of the reduced density matrix for a quantum oscillator damped by coupling it to an ohmic environment is calculated via an identity of the Debye-Waller form. Results obtained some years ago by Hakim and the author in the free particle limit [1] are thus recovered. The evolution of a free particle in a prepared initial state is examined, and a previously published exchange [2,3] is illuminated with figures showing no decoherence without dissipation. [1] V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985). [2] G.W. Ford and R.F. O'Connell, Phys. Rev. A 70, 026102 (2004). [3] D. Gobert, J. von Delft, and V. Ambegaokar, Phys. Rev. A 70, 0261001 (2004).

•Jun 10, 2005•11 citations

Initial-Slip Term Effects on the Dissipation-Induced Transition of a Simple Harmonic Oscillator

Kang-Kang Ju, Cui-Xian Guo, Xiao‐Yin Pan

We investigate the effects of the initial-slip term by studying the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. The general analytical expressions for the transition probabilities are obtained, then the special cases of transition probabilities ignoring the Brownian motion from the ground state to the first few excited states are discussed. It is found that the initial-slip term not only makes the forbidden transitions between states of different parity possible but also lifts the initial value of the transition probabilities.

Chinese Physics Letters•Jan 1, 2017•1 citation
In a recent paper Croxson [Phys. Rev. A 49,49,49, 588 (1994)] reported dissipation-induced transition probabilities from the ground state to higher states for a quantum harmonic oscillator. A partial approximate result was given for the oscillator to remain in its ground state, while for higher transitions the situation became complicated. Our approach provides an exact simple form closed expression for any order of transition. In addition, we supply the evolution of the work done by the system on its environment.
We investigate the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. Using the method developed by Yu and Sun [Phys. Rev. A 49, 592 (1994)], the general analytical expressions for the transition probabilities are obtained. The special cases: transition probabilities from the ground state to the first few excited states are then discussed in detail. Different from the previous studies in the literature where only the effect of damping was considered, it is found that the Brownian motion makes the transitions between states of different parity possible. The limitations of the applicability of our results are also discussed.
This is a response to a recently reported comment [F. M. Fernández, J. Math. Phys. 60, 094101 (2019)] on paper [M. Serhan et al., J. Math. Phys. 59, 082105 (2018)] regarding the quantization of the damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)] is incorrect, and thus the subsequent steps via the Nikiforov-Uvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be first achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. The canonical quantization on the resulted Hermitian Hamiltonian yields the real energy eigenvalues as exactly given by Eq. (35) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)].
The time development of the reduced density matrix for a quantum oscillator damped by coupling it to an ohmic environment is calculated via an identity of the Debye-Waller form. Results obtained some years ago by Hakim and the author in the free particle limit [1] are thus recovered. The evolution of a free particle in a prepared initial state is examined, and a previously published exchange [2,3] is illuminated with figures showing no decoherence without dissipation. [1] V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985). [2] G.W. Ford and R.F. O'Connell, Phys. Rev. A 70, 026102 (2004). [3] D. Gobert, J. von Delft, and V. Ambegaokar, Phys. Rev. A 70, 0261001 (2004).
We investigate the effects of the initial-slip term by studying the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. The general analytical expressions for the transition probabilities are obtained, then the special cases of transition probabilities ignoring the Brownian motion from the ground state to the first few excited states are discussed. It is found that the initial-slip term not only makes the forbidden transitions between states of different parity possible but also lifts the initial value of the transition probabilities.