Necessity of Eigenstate Thermalization

Giacomo De Palma, Alessio Serafini, Vittorio Giovannetti, and Marcus Cramer
Phys. Rev. Lett. 115, 220401 – Published 24 November 2015
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Abstract

Under the eigenstate thermalization hypothesis (ETH), quantum-quenched systems equilibrate towards canonical, thermal ensembles. While at first glance the ETH might seem a very strong hypothesis, we show that it is indeed not only sufficient but also necessary for thermalization. More specifically, we consider systems coupled to baths with well-defined macroscopic temperature and show that whenever all product states thermalize then the ETH must hold. Our result definitively settles the question of determining whether a quantum system has a thermal behavior, reducing it to checking whether its Hamiltonian satisfies the ETH.

  • Received 30 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.220401

© 2015 American Physical Society

Authors & Affiliations

Giacomo De Palma1,2, Alessio Serafini3,1, Vittorio Giovannetti1, and Marcus Cramer4

  • 1NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy
  • 2INFN, Pisa, Italy
  • 3Department of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
  • 4Institut für Theoretische Physik, Universität Ulm, Ulm, Germany

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Issue

Vol. 115, Iss. 22 — 27 November 2015

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