Abstract:
We study the spectrum of the operator
generating an infinite-dimensional diffusion process Ξ (t), in space . Here ν is a “natural”Ξ (t)-invariant measure on which is a Gibbs distribution corresponding to a (formal) Hamiltonian H of an anharmonic crystal, with a value of the inverse temperature β > 0. For β small enough, we establish the existence of an L-invariant subspace such that has a distinctive character related to a “quasi-particle” picture. In particular, has a Lebesgue spectrum separated from the rest of the spectrum of L and concentrated near a point κ1>0 giving the smallest non-zero eigenvalue of a limiting problem associated with β= 0.
An immediate corollary of our result is an exponentially fast L 2-convergence to equilibrium for the process Ξ(t) for small values of β.
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Received: 6 October 1998 / Accepted: 9 April 1999
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Minlos, R., Suhov, Y. On the Spectrum of the Generator of an Infinite System of Interacting Diffusions. Comm Math Phys 206, 463–489 (1999). https://doi.org/10.1007/s002200050714
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DOI: https://doi.org/10.1007/s002200050714