Year: 2024
Type: article
Abstract: We consider an autocorrelation function of a quantum mechanical system through the lens of the so-called recursive method, by iteratively evaluating Lanczos coefficients or solving a system of coupled differential equations in the Mori formalism. We first show that both methods are mathematically equivalent, each offering certain practical advantages. We then propose an approximation scheme to evaluate the autocorrelation function and use it to estimate the equilibration time τ for the observable in question. With only a handful of Lanczos coefficients as the input, this scheme yields an accurate order of magnitude estimate of τ, matching state-of-the-art numerical approaches. We develop a simple numerical scheme to estimate the precision of our method. We test our approach using several numerical examples exhibiting different relaxation dynamics. Our findings provide a practical way to quantify the equilibration time of isolated quantum systems, a question which is both crucial and notoriously difficult.
Source: Physical review. E
Authors: Christian Bartsch, Anatoly Dymarsky, Mats H. Lamann, Jiaozi Wang, Robin Steinigeweg, Jochen Gemmer
Institutions: Osnabrück University, University of Kentucky
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
Awards: Nichtgleichgewichtsdynamik in 2D Clustern aus der
Perspektive von Quantentypikalität und Eigenzustandsthermalisierung, Klassische und quantenmechanische Arbeitsverteilungen in getriebenen Billards, NSF-BSF: New Approaches to Conformal Field Theory - Codes, Ensembles, and Complexity, FOR 2692: Fundamental Aspects of Statistical Mechanics and the Emergence of Thermodynamics in NonEquilibrium Systems, G62979356, G6741907483, Kombinationen gedämpfter harmonischen Oszillationen als stabile Bausteine von Autokorrelationsfunktionen in Quantenvielteilchensystemen, G8157016452
OpenAlex ID: W4402026976