Quantum harmonic oscillators and thermalization

• URL: http://arxiv.org/abs/2110.05737v2
• Date: Tue, 27 Sep 2022 06:07:05 GMT
• Title: Quantum harmonic oscillators and thermalization
• Authors: Hyeong-Chan Kim and Youngone Lee
• Abstract summary: We write down the first law for thermalization in the same form as that for ordinary thermodynamics. We obtain the oscillator's energy undergoing thermalization as a function of entropy and its time derivative.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a quantum harmonic oscillator undergoing thermalization. To describe the thermalization process, we generalize the Ermakov-Lewis-Riesenfeld (ELR) invariant method for the oscillator. After imposing appropriate conditions on the thermalization process, we introduce an ansatz equation that describes the time evolution effectively. We write down the first law for thermalization in the same form as that for ordinary thermodynamics. Here, the thermalization effect appears through a change of the ELR frequency. Finally, we obtain the oscillator's energy undergoing thermalization as a function of entropy and its time derivative.

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