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Statistical complexity and the road to equilibrium in many-body chaotic quantum systems
1Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Physical Review. E
|November 18, 2022
Summary
This study explores the path to equilibrium in quantum chaotic systems. We prove that this process follows a thermodynamic second law and forms a hierarchy of diagonal ensembles over time.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Thermodynamics
Background:
- Understanding equilibration in isolated many-body quantum systems is crucial.
- The Eigenstate Thermalization Hypothesis (ETH) describes equilibrium properties but not the process.
- Quantum chaotic Hamiltonians are key to studying thermalization.
Purpose of the Study:
- To investigate the equilibration process (the road to equilibrium) in quantum chaotic systems.
- To provide an information-theoretic proof for the emergent second law of thermodynamics during equilibration.
- To analyze the uniqueness and stability of equilibration trajectories using statistical complexity.
Main Methods:
- Focusing on the dynamics of the equilibration process rather than asymptotic states.
- Developing an information-theoretic proof for the emergent second law of thermodynamics.
- Introducing and utilizing statistical complexity and the entropy-complexity plane.
- Comparing equilibration trajectories of chaotic systems with those of random Hamiltonians.
- Analyzing the stability of equilibration trajectories under perturbation.
Main Results:
- The road to equilibrium in quantum chaotic systems obeys an emergent second law of thermodynamics.
- Equilibration is demonstrated to be a hierarchy in time of diagonal ensembles.
- The study provides insights into the uniqueness of equilibration trajectories by mapping them onto the entropy-complexity plane.
- The stability of these trajectories was analyzed for chaotic Hamiltonians and various initial states.
Conclusions:
- The equilibration process in isolated many-body quantum systems is characterized by an emergent second law of thermodynamics.
- The road to equilibrium can be understood as a temporal hierarchy of diagonal ensembles.
- Statistical complexity offers a novel perspective for analyzing the uniqueness and stability of quantum system dynamics.
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