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Fast Thermalization from the Eigenstate Thermalization Hypothesis
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Fast Thermalization from the Eigenstate Thermalization Hypothesis
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The Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. However, its connection to the timescale of thermalization for open system dynamics has remained elusive. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Specifically, we demonstrate fast thermalization for a system coupled weakly to a bath of quasi-free Fermions that we refresh periodically. To describe the joint evolution, we derive a finite-time version of Davies' generator with explicit error bounds and resource estimates. Our approach exploits a critical feature of ETH: operators in the energy basis can be modeled by independent random matrices in a near-diagonal band. This gives quantum expanders at nearby eigenstates of the Hamiltonian and reduces the problem to a one-dimensional classical random walk on the energy eigenstates. Our results explain finite-time thermalization in chaotic open quantum systems.
Forward citations
Cited by 4 Pith papers
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Efficient thermalization and universal quantum computing with quantum Gibbs samplers
Quantum Gibbs samplers thermalize to Gibbs states in polynomial time at high temperatures for Lieb-Robinson bounded Hamiltonians and are BQP-complete at low temperatures via circuit-to-Hamiltonian reductions.
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Overcoming the Lamb Shift in System-Bath Interaction Models via KMS Detailed Balance: High-Accuracy Thermalization with Time-Bounded Interactions
Proves KMS detailed balance on the transition part of an approximate Lindbladian suffices for the fixed point to approach the Gibbs state arbitrarily closely regardless of Lamb shift structure, giving O(ε^{-1}) therma...
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