Lindblad master equation for the damped harmonic oscillator with deformed dissipation

Abstract

In the framework of the Lindblad theory for open quantum systems, a master equation for the quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived for the case when the interaction is based on deformed algebra. The equations of motion for observables strongly depend on the deformation function. The expectation values of the number operator and squared number operator are calculated in the limit of a small deformation parameter for the case of zero temperature of the thermal bath. The steady state solution of the equation for the density matrix in the number representation is obtained and its independence of the deformation is shown.

15 pages, 2 figures

References in corpus (7)

• f-Oscillators and Nonlinear Coherent States
• Open quantum systems
• Quantum Groups and Their Applications in Nuclear Physics
• Physical nonlinear aspects of classical and quantum q-oscillators
• Correlation functions of quantum q-oscillators
• Quantum dynamics of a damped deformed oscillator
• Deformed quantum harmonic oscillator with diffusion and dissipation

Cited by in corpus (7)

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• Robustness of the quantum Mpemba effect against state-preparation errors
• Limitations of the Markovian approximation in the harmonic oscillator
• Diffusion coefficients preserving long-time correlations: Consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system