Microscopic quantum generalization of classical Li\'{e}nard oscillators

• URL: http://arxiv.org/abs/2009.07142v1
• Date: Tue, 15 Sep 2020 14:53:47 GMT
• Title: Microscopic quantum generalization of classical Li\'{e}nard oscillators
• Authors: Srijan Bhattacharyya, Arnab Ghosh and Deb Shankar Ray
• Abstract summary: We have explored the microscopic quantum generalization of classical Li'enard systems. 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.
• Score: 3.2768228723567527
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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