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Bounds on Chaos from the Eigenstate Thermalization Hypothesis
Chaitanya Murthy1, Mark Srednicki1
1Department of Physics, University of California, Santa Barbara, California 93106, USA.
Physical Review Letters
|December 24, 2019
Summary
The study demonstrates how the bound on quantum chaos growth rates directly arises from the structure of operator matrix elements in systems obeying the eigenstate thermalization hypothesis. This links two fundamental concepts of thermal behavior in quantum systems.
Area of Science:
- Quantum Many-Body Physics
- Statistical Mechanics
Background:
- Chaotic many-body quantum systems exhibit complex dynamics.
- Out-of-time-order correlators (OTOCs) are crucial for quantifying quantum chaos.
- The eigenstate thermalization hypothesis (ETH) explains thermalization in isolated quantum systems.
Purpose of the Study:
- To demonstrate that the established bound on OTOC growth rates in chaotic quantum systems is a direct consequence of ETH.
- To establish a theoretical link between OTOC dynamics and the fundamental principles of ETH.
Main Methods:
- Analysis of the general structure of operator matrix elements within the framework of ETH.
- Derivation of the OTOC growth rate bound from these matrix element properties.
Main Results:
- The known bound on the growth rate of the out-of-time-order four-point correlator is shown to follow directly from the structure of operator matrix elements.
- A direct theoretical connection is established between OTOC growth rates and the eigenstate thermalization hypothesis.
Conclusions:
- The findings unify two key theoretical paradigms for understanding thermal behavior in isolated many-body quantum systems.
- This work provides a deeper insight into the relationship between quantum chaos and thermalization in quantum statistical mechanics.
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