Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Helffer, Bernard, and Ramond, Thierry. "Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator." Journées équations aux dérivées partielles (2000): 1-17. <http://eudml.org/doc/93390>.

@article{Helffer2000,
abstract = {We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit $\Lambda (h)$ of the ground state energy of this operator. For Kac’s spin model, $\Lambda (h)$ is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied by the physical examples we have in mind, we construct a formal asymptotic expansion for $\Lambda (h)$ in powers of $h$, from which we derive precise estimates on $\Lambda (h)$. We work in the settings of Standard Functions introduced by J. Sjöstrand for the study of similar questions in the case of Schrödinger operators.},
author = {Helffer, Bernard, Ramond, Thierry},
journal = {Journées équations aux dérivées partielles},
keywords = {transfer operator; Kac operator; thermodynamical limit; standard functions},
language = {eng},
pages = {1-17},
publisher = {Université de Nantes},
title = {Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator},
url = {http://eudml.org/doc/93390},
year = {2000},
}

TY - JOUR
AU - Helffer, Bernard
AU - Ramond, Thierry
TI - Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
SP - 1
EP - 17
AB - We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit $\Lambda (h)$ of the ground state energy of this operator. For Kac’s spin model, $\Lambda (h)$ is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied by the physical examples we have in mind, we construct a formal asymptotic expansion for $\Lambda (h)$ in powers of $h$, from which we derive precise estimates on $\Lambda (h)$. We work in the settings of Standard Functions introduced by J. Sjöstrand for the study of similar questions in the case of Schrödinger operators.
LA - eng
KW - transfer operator; Kac operator; thermodynamical limit; standard functions
UR - http://eudml.org/doc/93390
ER -