From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics

This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine…

• NS
  National Science Foundation

  Award: PHY-1318303
• US
  United States - Israel Binational Science Foundation

  Award: 2010318
• IS
  Israel Science Foundation

  Award: 1156/13
• OO
  Office of Naval Research

  Award: N000141410540
• AF
  Air Force Office of Scientific Research

  Award: FA9550-13-1-0039
• AR
  Army Research Office

  Award: W911NF1410540