Electronic Resource
On laplace integrals and transfer operators in large dimension: Examples in the nonconvex case
(1996)
Springer
ISSN:
15730530
Keywords:
81Q20
;
82B21
;
Laplace integrals
;
semiclassical
analysis
;
WKB constructions
Source:
Springer Online Journal Archives 18602000
Topics:
Mathematics
,
Physics
Notes:
Abstract This Letter gives detailed proofs concerning the analysis of the pair correlations for a nonconvex model. Using the transfer matrix approach, the problem is reduced to the analysis of the spectral properties of this transfer operator. Although the problem is similar to the semiclassical study of the Kac operator presented in a paper with M. Brunaud, which was devoted⋆⋆ to the study of exp(v/2) exp h 2 Δ exp(v/2) for h small, new features appear for the model exp(v/2h) exp hΔ exp(v/2h). Our principal results concern the splitting of this operator between the two largest eigenvalues. We give an upper and a lower bound for this splitting in the semiclassical regime. As a corollary, we get good control of the decay of the pair correlation. Some of the results were announced in a previous paper. Related WKB constructions will be developed in a later paper.
Type of Medium:
Electronic Resource
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