Thermalization without chaos in harmonic systems

Abstract

Recent numerical results showed that thermalization of Fourier modes is achieved in short time-scales in the Toda model, despite its integrability and the absence of chaos. Here we provide numerical evidence that the scenario according to which chaos is irrelevant for thermalization is realized even in the simplest of all classical integrable system: the harmonic chain. We study relaxation from an atypical condition given with respect to "random" modes, showing that a thermal state with equilibrium properties is attained in short times. Such a result is independent from the orthonormal base used to represent the chain state, provided it is random.

8 pages, 5 figures

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• Effective thermal dynamics following a quantum quench in a spin chain
• Quantum bounds and fluctuation-dissipation relations
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Cited by in corpus (7)

• Ergodic observables in non-ergodic systems: the example of the harmonic chain
• Long-time relaxation of a finite spin bath linearly coupled to a qubit
• On the foundations of statistical mechanics
• Open-system eigenstate thermalization in a noninteracting integrable model
• Symplectic Quantization: numerical results for the Feynman propagator on a 1+1 lattice and the theoretical relation with Quantum Field Theory
• Thermalization is typical in large classical and quantum harmonic systems
• Generalised Gibbs Ensemble for spherically constrained harmonic models