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Entropy 2019, 21(1), 51; https://doi.org/10.3390/e21010051

Chaotic Dynamics in a Quantum Fermi–Pasta–Ulam Problem

1
Department of Chemistry, Tulane University, New Orleans, LA 70118, USA
2
National Research Center “Kurchatov Institute”, 123182 Moscow, Russia
3
Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia
*
Author to whom correspondence should be addressed.
Received: 14 December 2018 / Revised: 28 December 2018 / Accepted: 8 January 2019 / Published: 10 January 2019
(This article belongs to the Special Issue Thermalization in Isolated Quantum Systems)
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Abstract

We investigate the emergence of chaotic dynamics in a quantum Fermi—Pasta—Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed. View Full-Text
Keywords: quantum chaos; Fermi—Pasta—Ulam problem; anharmonic vibrations; molecular vibrations; vibrational energy relaxation and transport quantum chaos; Fermi—Pasta—Ulam problem; anharmonic vibrations; molecular vibrations; vibrational energy relaxation and transport
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Burin, A.L.; Maksymov, A.O.; Schmidt, M.; Polishchuk, I.Y. Chaotic Dynamics in a Quantum Fermi–Pasta–Ulam Problem. Entropy 2019, 21, 51.

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