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Quantum relaxation in a system of harmonic oscillators with time-dependent coupling
Francisco Bento Lustosa1, Samuel Colin2,3, Santiago E Perez Bergliaffa4
1Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, CEP: 22290-180 Rio de Janeiro-RJ, Brazil.
Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
Summary
States initially violating quantum equilibrium rules typically return to normal distributions over time. This study shows that for coupled harmonic oscillators, relaxation can be slowed by specific parameter choices, especially interaction strength.
Area of Science:
- Quantum mechanics
- Pilot-wave theory
- Statistical mechanics
Background:
- The de Broglie-Bohm pilot-wave theory offers an alternative interpretation of quantum mechanics.
- Previous simulations indicated that non-equilibrium quantum states usually relax to Born rule distributions (|ψ|²).
- Understanding relaxation dynamics is crucial for testing foundational quantum principles.
Purpose of the Study:
- To analyze the relaxation of non-equilibrium quantum states in a system of coupled harmonic oscillators.
- To investigate the influence of time-dependent coupling on relaxation dynamics.
- To determine how parameters like mode number, coarse-graining length, and coupling strength affect relaxation.
Main Methods:
- Numerical simulations of a system of coupled one-dimensional harmonic oscillators.
- Introduction of time-dependent coupling to study its effect on relaxation.
- Systematic variation of parameters including number of modes, coarse-graining length, and coupling constant.
Main Results:
- The studied system generally tends towards equilibrium, supporting the relaxation hypothesis.
- Relaxation times can be significantly retarded by specific parameter choices.
- The strength of the interaction (coupling constant) is a particularly influential parameter in retarding relaxation.
Conclusions:
- The relaxation of non-equilibrium quantum states in coupled harmonic oscillators is confirmed, but can be modulated.
- The findings highlight the importance of parameter selection in quantum relaxation studies.
- This research has potential implications for detecting relic non-equilibrium quantum systems.
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