Eigenstate randomization hypothesis: Why does the long-time average equal the microcanonical average?
Year: 2011
Type: article
Abstract: We derive an upper bound on the difference between the long-time average and the microcanonical ensemble average of observables in isolated quantum systems. We propose, numerically verify, and analytically support a new hypothesis, the eigenstate randomization hypothesis (ERH), which implies that in the energy eigenbasis the diagonal elements of observables fluctuate randomly. We show that ERH includes the eigenstate thermalization hypothesis (ETH) and makes the aforementioned bound vanishingly small. Moreover, ERH is applicable to integrable systems for which ETH breaks down. We argue that the range of the validity of ERH determines that of the microcanonical description.
Source: Physical Review E
Authors: Tatsuhiko N. Ikeda, Yu Watanabe, Masahito Ueda
Institutions: The University of Tokyo, Japan Science and Technology Agency
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2010364663