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42.
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.
Received: 6 October 1998 / Accepted: 9 April 1999 相似文献
43.
A model of radiative decay with a fixed atom and not more than three photons is studied. A spectral analysis of the Hamiltonian is made. This is done by means of scattering theory in a pair of spaces with a specially chosen embedding. The existence of wave operators and their asymptotic completeness are proved. The constructions are based on a detailed analysis of the resolvent of the Hamiltonian.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 1, pp. 63–81, April, 1995. 相似文献
44.
The quantum anharmonic crystal is made up of a large number of multidimensional anharmonic oscillators arranged in a periodic spatial lattice with a nearest neighbor coupling. If the coupling coefficient is sufficiently small, then there is a convergent expansion for the ground state of the crystal. The estimates on the convergence are independent of the size of the crystal. The proof uses the path integral representation of the ground state in terms of diffusion processes. The convergence of the cluster expansion depends on the ergodicity properties of these processes. 相似文献
45.
This paper is a continuation of the authors paper published in no. 3 of this journal in the previous year, where a detailed statement of the problem on the two-particle bound state spectrum of transfer matrices was given for a wide class of Gibbs fields on the lattice +1 in the high-temperature region (T 1). In the present paper, it is shown that for = 1 the so-called adjacent bound state levels (i.e., those lying at distances of the order of T
–, > 2, from the continuous spectrum) can appear only for values of the total quasimomentum of the system that satisfy the condition | –
j
mult
|<c/T
2 (here c is a constant), where
j/mult are the quasimomentum values for which the symbol {(k), k
1} has two coincident extrema. Conditions under which such levels actually appear are also presented.__________Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 39–55, 2005Original Russian Text Copyright © by E. L. Lakshtanov and R. A. MinlosIn memory of A. N. ZemlyakovThe work of the second author was supported by the Russian Foundation for Basic Research (grant 02-01-00444) and also by the Presidential Foundation for Support to Scientific Schools (grant NSh-90.934.2003.1).Translated by V. M. Volosov 相似文献