Microscopic quantum generalization of classical Li\'{e}nard oscillators
Abstract
Based on a system-reservoir model and an appropriate choice of nonlinear coupling, we have explored the microscopic quantum generalization of classical Li\'{e}nard systems. Making use of oscillator coherent states and canonical thermal distributions of the associated c-numbers, we have derived the quantum Langevin equation of the reduced system which admits of single or multiple limit cycles. It has been shown that detailed balance in the form of fluctuation-dissipation relation preserves the dynamical stability of the attractors even in case of vacuum excitation. The quantum versions of Rayleigh, Van der Pol and several other variants of Li\'{e}nard oscillators are derived as special cases in our theoretical scheme within a mean-field description.
Cite
@article{arxiv.2009.07142,
title = {Microscopic quantum generalization of classical Li\'{e}nard oscillators},
author = {Srijan Bhattacharyya and Arnab Ghosh and Deb Shankar Ray},
journal= {arXiv preprint arXiv:2009.07142},
year = {2021}
}
Comments
Submitted to Physical review E