Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds

TY - JOUR

T1 - Slow dissipation and spreading in disordered classical systems

T2 - A direct comparison between numerics and mathematical bounds

AU - De Roeck, Wojciech

AU - Huveneers, Francois

AU - Prośniak, Oskar A.

N1 - Publisher Copyright: © 2024 American Physical Society.

PY - 2024/4

Y1 - 2024/4

N2 - We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter λ, and on the other hand our numerics show that it follows a power law for a broad range of values of λ. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

AB - We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter λ, and on the other hand our numerics show that it follows a power law for a broad range of values of λ. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

UR - http://www.scopus.com/inward/record.url?scp=85190348193&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.109.044207

DO - 10.1103/PhysRevE.109.044207

M3 - Article

C2 - 38755865

AN - SCOPUS:85190348193

SN - 2470-0045

VL - 109

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 044207

ER -