Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time
| hal.structure.identifier | Laboratoire Ondes et Matière d'Aquitaine [LOMA] | |
| dc.contributor.author | DEAN, David S. | |
| hal.structure.identifier | Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] [LPTENS] | |
| dc.contributor.author | LE DOUSSAL, Pierre | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | MAJUMDAR, Satya N. | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | SCHEHR, Grégory | |
| dc.date.created | 2014-12-04 | |
| dc.date.issued | 2015-03-18 | |
| dc.identifier.issn | 0031-9007 | |
| dc.description.abstractEn | 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 $t= b^3$. | |
| dc.description.sponsorship | Marcheurs Browniens répulsifs et matrices aléatoires - ANR-11-BS04-0013 | |
| dc.description.sponsorship | Paris Sciences et Lettres - ANR-10-IDEX-0001 | |
| dc.language.iso | en | |
| dc.publisher | American Physical Society | |
| dc.subject.en | Fermion systems and Electron gas | |
| dc.subject.en | Matrix theory | |
| dc.subject.en | Probability theory Stochastic processes and Statistics | |
| dc.title.en | Finite-Temperature Free Fermions and the Kardar-Parisi-Zhang Equation at Finite Time | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1103/PhysRevLett.114.110402 | |
| dc.subject.hal | Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech] | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 1412.1590 | |
| bordeaux.journal | Physical Review Letters | |
| bordeaux.page | 110402 (1-5) | |
| bordeaux.volume | 114 | |
| bordeaux.issue | 11 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01135370 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01135370v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Physical%20Review%20Letters&rft.date=2015-03-18&rft.volume=114&rft.issue=11&rft.spage=110402%20(1-5)&rft.epage=110402%20(1-5)&rft.eissn=0031-9007&rft.issn=0031-9007&rft.au=DEAN,%20David%20S.&LE%20DOUSSAL,%20Pierre&MAJUMDAR,%20Satya%20N.&SCHEHR,%20Gr%C3%A9gory&rft.genre=article |
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