Quantum harmonic oscillators and thermalization
Abstract
We study a quantum harmonic oscillator undergoing thermalization. To describe the thermalization process, we generalize the ErmakovLewisRiesenfeld (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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05737
 Bibcode:
 2021arXiv211005737K
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2103.08132