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Canonical Density Matrices from Eigenstates of Mixed Systems.
Mahdi Kourehpaz1, Stefan Donsa1, Fabian Lackner1
1Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
Entropy (Basel, Switzerland)
|December 23, 2022
Summary
Statistical mechanics explains how quantum systems reach equilibrium. This study shows that quantum chaos controls how thermal states emerge in many-body systems, offering a tunable mechanism.
Area of Science:
- Quantum statistical mechanics
- Condensed matter physics
- Quantum chaos
Background:
- A fundamental challenge in statistical mechanics is understanding how isolated quantum systems reach equilibrium.
- Canonical typicality suggests that large quantum systems exhibit thermal properties for subsystems due to entanglement and quantum complexity.
- Eigenstate thermalization hypothesis links thermalization to quantum chaos in individual eigenstates.
Purpose of the Study:
- To investigate the emergence of thermal states in a quantum system with a mixed phase space.
- To study how the canonical density matrix of an impurity arises from energy eigenstates of a larger system.
- To explore the role of quantum chaos in controlling this emergence.
Main Methods:
- Analysis of an impurity embedded in a tunable quantum many-body system, transitioning from integrability to chaos.
- Examination of the reduction of isolated energy eigenstates to determine the probability of forming a canonical density matrix.
- Quantification of chaoticity using the Brody parameter and Shannon entropy.
Main Results:
- The probability of obtaining a canonical density matrix is quantitatively tunable by the degree of quantum chaos.
- A continuous and universal relationship exists between the fraction of canonical eigenstates and chaoticity during the transition.
- The system exhibits a mixed quantum phase space, bridging integrability and chaos.
Conclusions:
- Quantum chaos plays a crucial role in the emergence of thermal states in quantum many-body systems.
- The degree of chaoticity directly influences the system's ability to form canonical ensembles.
- Findings provide a new perspective on the foundation of statistical mechanics and thermalization in quantum systems.
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