On the relaxation rate of short chains of rotors interacting with Langevin thermostats

Abstract

In this short note, we consider a system of two rotors, one of which interacts with a Langevin heat bath. We show that the system relaxes to its invariant measure (steady state) no faster than a stretched exponential $\exp (-c{t}^{1/2})$. This indicates that the exponent $1/2$ obtained earlier by the present authors and J.-P. Eckmann for short chains of rotors is optimal.

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• Role of conserved quantities in Fourier's law for diffusive mechanical systems
• Glassy dynamics in strongly anharmonic chains of oscillators
• Thermo-mechanical transport in rotor chains
• Asymptotic behaviour of a network of oscillators coupled to thermostats of finite energy