Semi-Classical Analysis of Non-Self-Adjoint Transfer Matrices in Statistical Mechanics I

Margherita Disertori*, Sasha Sodin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer operator is a perturbation of a normal one. Then the transfer operator is studied using methods of semi-classical analysis. In this paper, we concentrate on the second step, the main technical result being a semi-classical estimate for powers of an integral operator which is approximately normal.

Original languageEnglish
Pages (from-to)437-458
Number of pages22
JournalAnnales Henri Poincare
Volume17
Issue number2
DOIs
StatePublished - 1 Feb 2016

Funding

FundersFunder number
ERC Starting
National Sleep FoundationPHY-1305472
Institute for Advanced Study
Seventh Framework Programme239694, 1305472

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