[La loi de Fourier et les systèmes quantiques à n corps]
Cet article porte sur les propriétés de transport de chaînes quantiques à n corps en s'accompagnant de simulations de type « groupe de renormalisation de matrice de densité » du modèle de Bose–Hubbard. Pour dresser une vue d'ensemble, nous présentons d'abord une très brève introduction à la théorie quantique à n corps et aux approximations des réseaux de tenseurs. Les propriétés de transport sont étudiées à l'aide de fonctions dynamiques de corrélation de densité, en suivant la théorie de la réponse linéaire. Nous observons un comportement diffusif à « température infinie » . Enfin, nous mentionnons d'autres approches permettant d'étudier le transport, par exemple en imposant explicitement un gradient de température via des réservoirs thermiques aux bords.
The topic of this article are transport properties of many-body quantum chains accompanying DMRG-type simulations of the Bose–Hubbard model. To set the stage, we first provide a very brief introduction to many-body quantum theory and tensor network approximations. Transport properties are studied via dynamical density correlation functions, in line with linear response theory. We observe diffusive behavior at “infinite temperature” . Finally, we mention other approaches to study transport, e.g., explicitly imposing a temperature gradient via thermal reservoirs at the boundary.
Mot clés : Chaînes quantiques à n corps, Transport diffusif, Fonctions de corrélation dynamiques, GRMD / réseaux de tenseurs
Christian B. Mendl 1
@article{CRPHYS_2019__20_5_442_0,
author = {Christian B. Mendl},
title = {Fourier's law and many-body quantum systems},
journal = {Comptes Rendus. Physique},
pages = {442--448},
publisher = {Elsevier},
volume = {20},
number = {5},
year = {2019},
doi = {10.1016/j.crhy.2019.08.006},
language = {en},
}
Christian B. Mendl. Fourier's law and many-body quantum systems. Comptes Rendus. Physique, Volume 20 (2019) no. 5, pp. 442-448. doi : 10.1016/j.crhy.2019.08.006. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.08.006/
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