We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential V and is subjected to a restoring force of potential U . We assume that U and V are even nonnegative polynomials of degree 2σ1 and 2σ2. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a perturbation. This is an extension to the case σ1 < 2σ2 − 1 of some already known results obtained for σ1 ≥ 2σ2 − 1.

Dynamics of Infinite Classical Anharmonic Crystals / Butta', Paolo; Marchioro, Carlo. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 164:3(2016), pp. 680-692. [10.1007/s10955-016-1540-x]

Dynamics of Infinite Classical Anharmonic Crystals

BUTTA', Paolo;MARCHIORO, Carlo
2016

Abstract

We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential V and is subjected to a restoring force of potential U . We assume that U and V are even nonnegative polynomials of degree 2σ1 and 2σ2. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a perturbation. This is an extension to the case σ1 < 2σ2 − 1 of some already known results obtained for σ1 ≥ 2σ2 − 1.
2016
Anharmonic crystals; infinite dynamics; local energy; propagation velocity; statistical and nonlinear physics; mathematical physics
01 Pubblicazione su rivista::01a Articolo in rivista
Dynamics of Infinite Classical Anharmonic Crystals / Butta', Paolo; Marchioro, Carlo. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 164:3(2016), pp. 680-692. [10.1007/s10955-016-1540-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/878013
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