We prove analytically and show numerically that the dynamics of the Fermi-Pasta-Ulam-Tsingou chain is characterized by a transient Burgers turbulence regime on a wide range of time and energy scales. This regime is present at long wavelengths and energy per particle small enough that equipartition is not reached on a fast timescale. In this range, we prove that the driving mechanism to thermalization is the formation of a shock that can be predicted using a pair of generalized Burgers equations. We perform a perturbative calculation at small energy per particle, proving that the energy spectrum of the chain Ek decays as a power law, Ek & SIM; k-zeta ot thorn , on an extensive range of wave numbers k. We predict that zeta ot thorn takes first the value 8=3 at the Burgers shock time, and then reaches a value close to 2 within two shock times. The value of the exponent zeta 1/4 2 persists for several shock times before the system eventually relaxes to equipartition. During this wide time window, an exponential cutoff in the spectrum is observed at large k, in agreement with previous results. Such a scenario turns out to be universal, i.e., independent of the parameters characterizing the system and of the initial condition, once time is measured in units of the shock time.

Burgers Turbulence in the Fermi-Pasta-Ulam-Tsingou Chain / Gallone, Matteo; Marian, Matteo; Ponno, Antonio; Ruffo, Stefano. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 129:11(2022), pp. 1-6. [10.1103/PhysRevLett.129.114101]

Burgers Turbulence in the Fermi-Pasta-Ulam-Tsingou Chain

Gallone, Matteo;Ponno, Antonio;Ruffo, Stefano
2022-01-01

Abstract

We prove analytically and show numerically that the dynamics of the Fermi-Pasta-Ulam-Tsingou chain is characterized by a transient Burgers turbulence regime on a wide range of time and energy scales. This regime is present at long wavelengths and energy per particle small enough that equipartition is not reached on a fast timescale. In this range, we prove that the driving mechanism to thermalization is the formation of a shock that can be predicted using a pair of generalized Burgers equations. We perform a perturbative calculation at small energy per particle, proving that the energy spectrum of the chain Ek decays as a power law, Ek & SIM; k-zeta ot thorn , on an extensive range of wave numbers k. We predict that zeta ot thorn takes first the value 8=3 at the Burgers shock time, and then reaches a value close to 2 within two shock times. The value of the exponent zeta 1/4 2 persists for several shock times before the system eventually relaxes to equipartition. During this wide time window, an exponential cutoff in the spectrum is observed at large k, in agreement with previous results. Such a scenario turns out to be universal, i.e., independent of the parameters characterizing the system and of the initial condition, once time is measured in units of the shock time.
2022
129
11
1
6
114101
10.1103/PhysRevLett.129.114101
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.114101
https://arxiv.org/abs/2208.08818
Gallone, Matteo; Marian, Matteo; Ponno, Antonio; Ruffo, Stefano
File in questo prodotto:
File Dimensione Formato  
PhysRevLett.129.114101.pdf

accesso aperto

Descrizione: pdf editoriale
Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 651.61 kB
Formato Adobe PDF
651.61 kB Adobe PDF Visualizza/Apri

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/20.500.11767/132070
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact