2018/12/31 by Abhishek Dhar, Aritra Kundu, Joel L. Lebowitz +1 · 20 citations
Physics and Astronomy · #Energy (signal processing) #Energy transport #Harmonic #Harmonic oscillator #Integrable system #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Quartic function #Scaling #Toda lattice #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1007/s10955-019-02284-6
published in Journal of Statistical Physics 175(6), 1298-1310 (Springer Science+Business Media) · 9 Pages,12 figures
arxiv created 2018/12/31 · openalex created_date 2019/01/11 · openalex publication_date 2019/04/11 · arxiv updated 2019/05/01 · openalex updated_date 2026/08/06
We consider energy transport in the classical Toda chain in the presence of an additional pinning potential. The pinning potential is expected to destroy the integrability of the system and an interesting question is to see the signatures of this breaking of integrability on energy transport. We investigate this by a study of the non-equilibrium steady state of the system connected to heat baths as well as the study of equilibrium correlations. Typical signatures of integrable systems are a size-independent energy current, a flat bulk temperature profile and ballistic scaling of equilibrium dynamical correlations, these results being valid in the thermodynamic limit. We find that, as expected, these properties change drastically on introducing the pinning potential in the Toda model. In particular, we find that the effect of a harmonic pinning potential is drastically smaller at low temperatures, compared to a quartic pinning potential. We explain this by noting that at low temperatures the Toda potential can be approximated by a harmonic inter-particle potential for which the addition of harmonic pinning does not destroy integrability.