TY - JOUR
T1 - Too Close to Integrable
T2 - Crossover from Normal to Anomalous Heat Diffusion
AU - Lepri, Stefano
AU - Livi, Roberto
AU - Politi, Antonio
PY - 2020/7/21
Y1 - 2020/7/21
N2 - Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path â.,". Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.
AB - Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path â.,". Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.
KW - cond-mat.stat-mech
KW - Statistical Mechanics
KW - ENERGY-TRANSPORT
KW - LAW
KW - CONDUCTION
KW - TODA LATTICE
UR - http://www.scopus.com/inward/record.url?scp=85089376139&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.125.040604
DO - 10.1103/PhysRevLett.125.040604
M3 - Article
SN - 0031-9007
VL - 125
JO - Physical Review Letters
JF - Physical Review Letters
IS - 4
M1 - 040604
ER -