# Eigenstate Thermalization Hypothesis

**Authors:** Joshua M. Deutsch  
**arXiv:** [1805.01616](https://arxiv.org/abs/1805.01616)  
**Date:** 2018-05-04  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1805.01616v1/

## Key points

- The Eigenstate Thermalization Hypothesis (ETH) is a fundamental concept in the study of quantum systems
- It bridges classical statistical mechanics and quantum dynamics, drawing inspiration from chaotic dynamics and ergodicity in classical systems
- According to the ETH, individual energy eigenstates in quantum systems behave similarly to a statistical ensemble
- The hypothesis has roots in Wigner's work on random matrix theory and evolving understanding of quantum chaos
- Extensively studied through analytical and numerical methods with applications in diverse physical scenarios such as black hole physics and condensed matter systems
- Recent experiments in isolated systems highlight the relevance of ETH in real-world settings
- Current theoretical investigations focus on identifying limitations of ETH and exploring novel phenomena when it breaks down
- Researchers aim to deepen comprehension of complex many-body quantum states by elucidating why ETH is effective

## Summary

The Eigenstate Thermalization Hypothesis (ETH) is a fundamental concept in the study of quantum systems. It serves as a bridge between classical statistical mechanics and quantum dynamics, drawing inspiration from chaotic dynamics and ergodicity in classical systems. According to the ETH, individual energy eigenstates in quantum systems behave similarly to a statistical ensemble. This hypothesis has its roots in Wigner's pioneering work on random matrix theory and our evolving understanding of quantum chaos. Extensively studied through both analytical and numerical methods, the ETH has found applications across diverse physical scenarios. These range from black hole physics to condensed matter systems. Furthermore, recent experiments in highly isolated systems have highlighted the relevance of the ETH in real-world settings. Current theoretical investigations are focused on identifying the limitations of the ETH and exploring novel phenomena that arise when this hypothesis breaks down. Researchers take an intuitive approach to elucidate why the ETH is effective, aiming to deepen our comprehension of complex many-body quantum states. Authored by Joshua M. Deutsch, this review provides a comprehensive overview of the Eigenstate Thermalization Hypothesis. It sheds light on its significance in advancing our understanding of quantum phenomena.