Nonequilibrium quantum many-body physics from perspectives of operator dynamics and the Lanczos picture
Merlin Füllgraf
This cumulative doctoral thesis, based on the works [P1–P5], addresses various topical concepts as well as foundational questions in the nonequilibrium physics of quantum many-body systems. Publication [P1] concerns itself with the question of time’s arrow in quantum mechanics. Based on the recursion method, we attribute autocorrelation functions of few-body observables at infinite temperature (almost) monotonously decreasing functions, constructed from temporal derivatives of the correlation function that indicate a directed approach to equilibrium. We numerically find that in chaotic models, these constructions comprise a notion of simplicity of the underlying dynamics. Addressing the ubiquity of simple relaxation dynamics in otherwise complex chaotic systems, in Ref. [P3] we introduce a scheme based on Lanczos coefficients to approximate correlation functions in the thermodynamic limit. Examining several pertinent condensed-matter type models and benchmarking with state-of-the-art numerics, we find the method to yield good results already for a low number of included Lanczos coefficients, provided that the latter exhibit a smooth and increasing structure. We underpin these findings with analytical arguments on the method’s applicability. Ref. [P2] provides an estimate on the equilibration time of such infinite-temperature correlation functions in the thermodynamic limit. Similarly to Ref. [P3], we find the estimate to capture the equilibration times very reasonably, given that the corresponding Lanczos coefficients exhibit a smooth growth. Substantiated by analytical considerations, the convergence of the estimate implies that equilibration timescales of the relaxation processes are finite and conceivably short. In Ref. [P5] we scrutinize the interpretative power of the Lanczos coefficients concerning the system’s integrability or chaoticity, operator growth and the indicativeness of physical behavior. To this end, we analytically deter- mine the Lanczos coefficients for a Majorana observable in a strictly quadratic model and illustrate that within this model any structure of the Lanczos coefficients may be realised. Different to the other works, Ref. [P4] is not cast in the language of the recursion method. Focusing on the full eigenstate thermalization hypothesis, it explores the connection between thermalization dynamics of multi-point correlation functions and the scaling of thermal free cumulants in setups mimicking a system-bath situation.
•Jul 6, 2026•0 citations