Comptes Rendus
no. 5
Fourier and the science of today / Fourier et la science d'aujourd'hui
Fourier's law and many-body quantum systems
[La loi de Fourier et les systèmes quantiques à n corps]
Christian B. Mendl1
1 Technische Universität Dresden, Institute of Scientific Computing, Zellescher Weg 12-14, 01069 Dresden, Germany
Comptes Rendus. Physique, Fourier and the science of today / Fourier et la science d’aujourd’hui, Volume 20 (2019) no. 5, pp. 442-448.

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 » T→∞. 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” T→∞. Finally, we mention other approaches to study transport, e.g., explicitly imposing a temperature gradient via thermal reservoirs at the boundary.

Publié le :
DOI : 10.1016/j.crhy.2019.08.006
Keywords: Many-body quantum chains, Diffusive transport, Dynamical correlation functions, DMRG/tensor networks
Mots-clés : Chaînes quantiques à n corps, Transport diffusif, Fonctions de corrélation dynamiques, GRMD / réseaux de tenseurs

Christian B. Mendl 1

1 Technische Universität Dresden, Institute of Scientific Computing, Zellescher Weg 12-14, 01069 Dresden, Germany 
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Christian B. Mendl. Fourier's law and many-body quantum systems. Comptes Rendus. Physique, Fourier and the science of today / Fourier et la science d’aujourd’hui, 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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