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arXiv · 1506.07265

Necessity of Eigenstate Thermalization

Giacomo De Palma·Alessio Serafini·Vittorio Giovannetti·Marcus Cramer
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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 behaviour, reducing it to checking whether its Hamiltonian satisfies the ETH.

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Giacomo De Palma, Alessio Serafini, Vittorio Giovannetti, Marcus Cramer. 2015-06-24. Necessity of Eigenstate Thermalization. https://doi.org/10.1103/physrevlett.115.220401

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