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

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...

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Bibliographic Details
Published inElectronic communications in probability Vol. 22; no. none
Main Authors Cuneo, Noé, Poquet, Christophe
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics (IMS) 01.01.2017
Subjects
Mathematical Physics
Mathematics
Physics
Probability
subgeometric ergodicity
chains of rotors
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Summary: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.
ISSN:1083-589X
1083-589X
DOI:10.1214/17-ECP62