Semi-Classical Analysis of Non-Self-Adjoint Transfer Matrices in Statistical Mechanics I
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...
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| Veröffentlicht in: | Annales Henri Poincaré 2016-02, Vol.17 (2), p.437-458 |
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| container_title | Annales Henri Poincaré |
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| creator | Disertori, Margherita Sodin, Sasha |
| description | 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. |
| doi_str_mv | 10.1007/s00023-015-0397-x |
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Henri Poincaré</addtitle><description>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. 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| language | eng |
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| subjects | Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Mathematical and Computational Physics Mathematical Methods in Physics Operators (mathematics) Perturbation Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Statistical mechanics Theoretical Transfer matrices |
| title | Semi-Classical Analysis of Non-Self-Adjoint Transfer Matrices in Statistical Mechanics I |
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