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Updated: Apr 29, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Finite-size scaling of eigenstate thermalization
W Beugeling1, R Moessner1, Masudul Haque1
1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Summary
Isolated quantum systems can thermalize, according to the eigenstate thermalization hypothesis (ETH). This study shows fluctuations in generic nonintegrable systems scale universally with Hilbert space dimension, providing numerical evidence and heuristic explanations for this quantum thermalization phenomenon.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- The eigenstate thermalization hypothesis (ETH) posits that isolated quantum systems can thermalize.
- Thermalization in quantum systems is understood through vanishing eigenstate-to-eigenstate fluctuations of observables in large systems.
- Numerical studies of finite-size systems are crucial for understanding the finite-size scaling of these fluctuations.
Purpose of the Study:
- To investigate the finite-size scaling of eigenstate expectation value fluctuations in isolated quantum systems.
- To provide numerical evidence for universal scaling laws governing these fluctuations.
- To explore the influence of integrability on the emergence of universal scaling.
Main Methods:
- Numerical evaluation of eigenstate expectation value fluctuations for several observables across three model families.
- Analysis of finite-size scaling behavior of these fluctuations.
- Comparison between nonintegrable and integrable systems within the studied models.
Main Results:
- Demonstrated a universal power-law scaling of fluctuations with the Hilbert space dimension (D-1/2) for generic nonintegrable systems.
- Provided heuristic arguments supporting the observed universal scaling, consistent with the ETH.
- Observed that proximity to integrability affects the system size at which universal scaling becomes apparent.
Conclusions:
- The study provides strong numerical support for universal finite-size scaling of fluctuations in quantum systems.
- The findings contribute to a deeper understanding of thermalization in isolated quantum systems.
- The research highlights the impact of integrability on the manifestation of universal quantum phenomena.
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