Power-law decay exponents: A dynamical criterion for predicting thermalization
Open accessAbstract
From the analysis of the relaxation process of isolated lattice many-body quantum systems quenched far from equilibrium, we deduce a criterion for predicting when they are certain to thermalize. It is based on the algebraic behavior $\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\gamma}}$ of the survival probability at long times. We show that the value of the power-law exponent $\ensuremath{\gamma}$ depends on the shape and filling of the weighted energy distribution of the initial state. Two scenarios are explored in detail: $\ensuremath{\gamma}\ensuremath{\ge}2$ and $\ensuremath{\gamma}<1$. Exponents $\ensuremath{\gamma}\ensuremath{\ge}2$ imply that the energy distribution of the initial state is ergodically filled and the eigenstates are uncorrelated, so thermalization is guaranteed to happen. In this case, the power-law behavior is caused by bounds in the energy spectrum. Decays with $\ensuremath{\gamma}<1$ emerge when the energy eigenstates are correlated and signal lack of ergodicity. They are typical of systems undergoing localization due to strong onsite disorder and are found also in clean integrable systems.
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Under quite general conditions, a power-law decay holds.
“Under quite general conditions, a power-law decay holds, as has been demonstrated in single-particle [23], few-body [30] and many-body systems [25, 31-33].”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [23]
Following Khalfin, the survival amplitude A(β,t) is the Fourier transform of a function with support on the half energy axis.
“Following Khalfin [23, 29], we note that A ( β, t ) is then the Fourier transform of a function with support on the half energy axis, ˜ ρ ( E ) ≡ ρ ( E )Θ( E -E 0 ).”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [23]
Under unitary evolution, the short-time decay of the survival probability is nonexponential.
“Under unitary evolution, the short-time decay of the survival probability is nonexponential [23].”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [23]
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Scrambling the spectral form factor: Unitarity constraints and exact results
del Campo, A., Molina-Vilaplana, J., & Sonner, J. (2017) · Physical Review D · doi:10.1103/physrevd.95.126008 · Cited by 133 · see citing works
- Authors
- Távora, M., Torres-Herrera, E. J., & Santos, L. F.
- Affiliations
- Yeshiva University (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2017-01-05
- Volume
- 95
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2538409170
- Cited by
- 53
- References
- 96
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 3 · 2023: 1 · 2022: 3 · 2021: 5 · 2020: 7 · 2019: 10 · 2018: 12 · 2017: 6
- FWCI
- 4.70
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (DMR-1147430)
- Consejo Nacional de Ciencia y Tecnología
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- thermalization, power-law decay, survival probability, isolated quantum systems, quantum many-body systems, quench dynamics, ergodicity, energy distribution, localization, integrable systems
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