Geodesic
Expansion of the Many-body quantum Gibbs state of the Bose–Hubbard model on a finite graph
Documenta mathematica, Tome 30 (2025) no. 2, pp. 475-496

Voir la notice de l'article provenant de la source EMS Press

We consider the many-body quantum Gibbs state for the Bose–Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of the average particle number. For this model it is known that the many-body Gibbs state converges, as temperature goes to infinity, to the Gibbs measure of a discrete nonlinear Schrödinger equation, i.e., a Gibbs measure defined in terms of a one-body theory. In this article we extend these results by proving an expansion to any order of the many-body Gibbs state with inverse temperature as a small parameter. The coefficients in the expansion can be calculated as vacuum expectation values using a recursive formula, and we compute the first two coefficients explicitly.
DOI : 10.4171/dm/1001
Classification : 81V70, 81V73, 82B20
Mots-clés : Bose–Hubbard model, Many-body quantum Gibbs state, Gibbs measure, discrete nonlinear Schrödinger equation 
@article{10_4171_dm_1001,
     author = {Zied Ammari and Shahnaz Farhat and S\"oren Petrat},
     title = {Expansion of the {Many-body} quantum {Gibbs} state {of~the~Bose{\textendash}Hubbard} model on a finite graph},
     journal = {Documenta mathematica},
     pages = {475--496},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2025},
     doi = {10.4171/dm/1001},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/1001/}
}
TY  - JOUR
AU  - Zied Ammari
AU  - Shahnaz Farhat
AU  - Sören Petrat
TI  - Expansion of the Many-body quantum Gibbs state of the Bose–Hubbard model on a finite graph
JO  - Documenta mathematica
PY  - 2025
SP  - 475
EP  - 496
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/1001/
DO  - 10.4171/dm/1001
ID  - 10_4171_dm_1001
ER  - 
%0 Journal Article
%A Zied Ammari
%A Shahnaz Farhat
%A Sören Petrat
%T Expansion of the Many-body quantum Gibbs state of the Bose–Hubbard model on a finite graph
%J Documenta mathematica
%D 2025
%P 475-496
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/1001/
%R 10.4171/dm/1001
%F 10_4171_dm_1001
Zied Ammari; Shahnaz Farhat; Sören Petrat. Expansion of the Many-body quantum Gibbs state of the Bose–Hubbard model on a finite graph. Documenta mathematica, Tome 30 (2025) no. 2, pp. 475-496. doi: 10.4171/dm/1001

Cité par Sources :