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Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

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Related Experiment Video

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Thermalization in a Quantum Harmonic Oscillator with Random Disorder.

Ya-Wei Hsueh¹, Che-Hsiu Hsueh², Wen-Chin Wu²

¹Department of Physics, National Central University, Jhong-li 32001, Taiwan.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

Random disorder induces thermalization in quantum harmonic oscillators, conserving total energy. Unlike classical systems, energy transforms from mechanical to thermodynamic, evenly distributing kinetic and potential forms.

Keywords:

quantum harmonic oscillator random disorder thermalization

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Area of Science:

Quantum mechanics
Statistical physics
Condensed matter physics

Background:

Quantum harmonic oscillators are fundamental systems in physics.
Understanding thermalization is crucial for bridging quantum and classical mechanics.
The role of disorder in quantum system dynamics is an active research area.

Purpose of the Study:

To investigate the phenomenon of thermalization in a quantum harmonic oscillator subjected to random disorder.
To explore the energy dynamics and conservation laws in such a disordered quantum system.
To analyze the distribution of energy at equilibrium and the consistency of entropy measures.

Main Methods:

Development of a theoretical scheme to model the disordered quantum harmonic oscillator.
Implementation of numerical simulations to observe the system's evolution.
Analysis of energy conservation and distribution (kinetic, potential, thermodynamic).
Calculation and comparison of Shannon entropy in different bases.

Main Results:

Numerical simulations demonstrate a transition from a non-equilibrium to an equilibrium state driven by random disorder.
Total energy is conserved throughout the thermalization process, contrasting with classical damped oscillators.
At equilibrium, initial mechanical energy is converted into thermodynamic energy with even distribution of kinetic and potential energies.
Shannon entropy calculations in various bases confirm consistent results during thermalization.

Conclusions:

Random disorder can drive thermalization in quantum harmonic oscillators while conserving total energy.
The system achieves an equilibrium state where energy is redistributed thermodynamically.
Shannon entropy serves as a reliable indicator of thermalization in this disordered quantum system.