title: Necessity of Eigenstate Thermalization.
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.
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy.|INFN, Pisa, Italy.
authors.forename: Giacomo
authors.initials: G
authors.lastname: De Palma
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy.|Department of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
authors.forename: Alessio
authors.initials: A
authors.lastname: Serafini
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy.
authors.forename: Vittorio
authors.initials: V
authors.lastname: Giovannetti
authors.affiliation: Institut für Theoretische Physik, Universität Ulm, Ulm, Germany.
authors.forename: Marcus
authors.initials: M
authors.lastname: Cramer