We consider the time evolution of a disk under the action of a constant force and interacting with a free gas in the mean-field approximation. Letting V-0 > 0 be the initial velocity of the disk and V-infinity > 0 its equilibrium velocity, namely the one for which the external field is balanced by the friction force exerted by the background, we show that, if V-infinity - V-0 is positive and sufficiently small, then the disk reaches V-infinity with the power law t(-(d+2)), d = 1, 2, 3 being the dimension of the physical space. The reason for this behavior is the long tail memory due to recollisions. Any Markovian approximation (or simply neglecting the recollisions) yields an exponential approach to equilibrium.

Caprino, S., Marchioro, C., Pulvirenti, M. (2006). Approach to equilibrium in a microscopic model of friction. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 264(1), 167-189 [10.1007/s00220-006-1542-7].

### Approach to equilibrium in a microscopic model of friction

#### Abstract

We consider the time evolution of a disk under the action of a constant force and interacting with a free gas in the mean-field approximation. Letting V-0 > 0 be the initial velocity of the disk and V-infinity > 0 its equilibrium velocity, namely the one for which the external field is balanced by the friction force exerted by the background, we show that, if V-infinity - V-0 is positive and sufficiently small, then the disk reaches V-infinity with the power law t(-(d+2)), d = 1, 2, 3 being the dimension of the physical space. The reason for this behavior is the long tail memory due to recollisions. Any Markovian approximation (or simply neglecting the recollisions) yields an exponential approach to equilibrium.
##### Scheda breve Scheda completa Scheda completa (DC)
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - Fisica Matematica
English
HAMILTONIAN MODEL; PARTICLES; DYNAMICS; SYSTEM; MOTION; PISTON
Caprino, S., Marchioro, C., Pulvirenti, M. (2006). Approach to equilibrium in a microscopic model of friction. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 264(1), 167-189 [10.1007/s00220-006-1542-7].
Caprino, S; Marchioro, C; Pulvirenti, M
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2108/38027`
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