We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size sqrt{N} (where N is the chain length) that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.

Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis

S. Lepri;R. Livi;A. Politi
2010

Abstract

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size sqrt{N} (where N is the chain length) that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.
2010
Istituto dei Sistemi Complessi - ISC
Stochastic processes
Nonlinear dynamics
Matrix theory
Heat conduction
File in questo prodotto:
File Dimensione Formato  
prod_57624-doc_12113.pdf

solo utenti autorizzati

Descrizione: Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
Tipologia: Versione Editoriale (PDF)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 801.77 kB
Formato Adobe PDF
801.77 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/35715
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 23
social impact