Year: 2024
Type: article
Abstract: In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and nonintegrable quantum-mechanical systems, respectively. We show that the saturation value and timescale of spectral complexity may be used to probe the nonintegrability of the system since we find that when computed for the circle billiard, it saturates at a later timescale compared to the stadium billiards. This observation is verified for different temperatures. Furthermore, we study the Krylov complexity of the position operator and its associated Lanczos coefficients at finite temperature using the Wightman inner product. We find that the growth rate of the Lanczos coefficients saturates the conjectured universal bound at low temperatures. Additionally, we also find that even a subset of the Lanczos coefficients can potentially serve as an indicator of integrability, as they demonstrate erratic behavior specifically in the circle billiard case, in contrast to the stadium billiard. Finally, we also study Krylov entropy and verify its early-time logarithmic relation with Krylov complexity in both types of billiard systems. Published by the American Physical Society 2024
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Funders: National Research Foundation, Gwangju Institute of Science and Technology, Ministry of Education, Ministerio de Economía y Competitividad, Ministry of Science, ICT and Future Planning, National Research Foundation of Korea, Ministerio de Ciencia e Innovación, Ministry of Science and ICT, South Korea, Karl Landsteiner Privatuniversität für Gesundheitswissenschaften, European Regional Development Fund, Agencia Estatal de Investigación
Awards: G1175115578, G1622782223, G1790280558, G2233160401, G2262748287, G254583402, G2554159582, G2804322916, G282847690, G2994561218, G300979063, G3259866395, G34346518, G3480869486, G3754688009, G410571670, G425668148, G451917667, G4810088317, G5080475149, G5346390160, G5539308778, G5967599077, G6221293036, G650978199, G6786806714, G7042188131, G7084143925, G929308097
OpenAlex ID: W4392182964