Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?

Details Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average? Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?

2010-12-15

arxiv.org/abs/1012.3237v4

Phys. Rev. E 84, 021130 (2011)

Physics

Condensed Matter

Statistical Mechanics

manuscript including 4 pages and 3 figures

Scientific paper

10.1103/PhysRevE.84.021130

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, eigenstate randomization hypothesis (ERH), which implies that in the energy eigenbasis the diagonal elements of observables fluctuate randomly. We show that ERH includes 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.

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