Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review Letters Année : 2015

Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time

Résumé

We consider the system of $N$ one-dimensional free fermions confined by a harmonic well $V(x) = m\omega^2 {x^2}/{2}$ at finite inverse temperature $\beta = 1/T$. The average density of fermions $\rho_N(x,T)$ at position $x$ is derived. For $N \gg 1$ and $\beta \sim {\cal O}(1/N)$, $\rho_N(x,T)$ is described by a scaling function interpolating between a Gaussian at high temperature, for $\beta \ll 1/N$, and the Wigner semi-circle law at low temperature, for $\beta \gg N^{-1}$. In the latter regime, we unveil a scaling limit, for $\beta {\hbar \omega}= b N^{-1/3}$, where the fluctuations close to the edge of the support, at $x \sim \pm \sqrt{2\hbar N/(m\omega)}$, are described by a limiting kernel $K^{\rm ff}_b(s,s')$ that depends continuously on $b$ and is a generalization of the Airy kernel, found in the Gaussian Unitary Ensemble of random matrices. Remarkably, exactly the same kernel $K^{\rm ff}_b(s,s')$ arises in the exact solution of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions at finite time $t$, with the correspondence $t= b^3$.
Fichier principal
Vignette du fichier
DeanPRL2015_PostPrint.pdf (393.7 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01135370 , version 1 (26-03-2015)

Identifiants

Citer

David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time. Physical Review Letters, 2015, 114 (11), pp.110402 (1-5). ⟨10.1103/PhysRevLett.114.110402⟩. ⟨hal-01135370⟩
341 Consultations
148 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More