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UID:0-568@lptms.universite-paris-saclay.fr
DTSTART:20180220T110000Z
DTEND:20180220T113000Z
DTSTAMP:20180215T095633Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-chikashi-arita/
SUMMARY:Séminaire du LPTMS: Chikashi Arita - LPTMS\, salle 201\, 2ème ét
 age\, Bât 100\, Campus d'Orsay - 20 Fév 18 11:00
DESCRIPTION:Variational calculation of diffusion coefficients in stochastic
  lattice gases\nChikashi Arita (Universität des Saarlandes\, Saarbrücken
 )\nDeriving macroscopic behaviors from microscopic dynamics of particles 
   is a fundamental problem. In stochastic lattice gases one tries to  de
 monstrate this hydrodynamic limit. The evolution of a stochastic   latti
 ce gas with symmetric hopping rules is described by a diffusion   equati
 on with density-dependent diffusion coefficient. In practice\,  even when
  the equilibrium properties of a lattice gas are analytically  known\, th
 e diffusion coefficient cannot be explicitly computed\, except  when a la
 ttice gas additionally satisfies the "gradient condition"\,  e.g. the dif
 fusion coefficients of the simple exclusion process and   non-interactin
 g random walks are exactly identical to their hopping  rates. We develop 
 a procedure to obtain systematic analytical approximations for the diffusi
 on coefficient in non-gradient lattice  gases with known equilibrium. The
  method relies on a variational  formula found by Varadhan and Spohn. Res
 triction on test functions to  finite-dimensional sub-spaces allows one t
 o perform the minimization  and gives upper bounds for the diffusion coef
 ficient. We apply the   procedure to the following two models\; one-dime
 nsional generalized  exclusion processes\, where each site can accommodat
 e at most two   particles (2-GEPs) [1]\, and the Kob-Andersen (KA) model
  on the square  lattice\, which is classified into kinetically-constraine
 d gas [2]. The   prediction of the diffusion coefficient depends on the 
 domain  ("shape") of test functions. The smallest shapes give approximati
 ons  which coincide with the mean-field theory\, but the larger shapes\, 
 the   more precise upper bounds we obtain. For the 2-GEPs\, our analytic
 al  predictions provide upper bounds which are very close to simulation 
   results throughout the entire density range. For the KA model\, we also
   find improved upper bounds when the density is small. By combining the
    variational method with a perturbation approach\, we discuss the  as
 ymptotic behavior of the diffusion coefficient in the high density   lim
 it.\n\n	[1] C. Arita\, P. L. Krapivsky and K. Mallick\, Variational calcul
 ation of transport coefficients in diffusive lattice gases\, Phys. Rev. E 
 95\, 032121 (2017)\n	[2] C. Arita\, P. L. Krapivsky and K. Mallick\, Bulk 
 diffusion in a kinetically constrained lattice gas\, preprint cond-mat arX
 iv:1711.10616\n\n&nbsp\;
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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