Steady state current fluctuations for one-dimensional driven lattice gases

• Applicant: Professor Dr. Herbert Spohn
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2007 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 41857742

• Final Report Year: 2012

Final Report Abstract

In dem Projekt werden die Stromfluktuationen von eindimensionalen getriebenen Gittergasen untersucht. Diese stochastischen Teilchensysteme modellieren, unter anderem, ionische Leiter, Oberflächenwachstum und Domängrenzen in energieungeordneten Ferromagneten. Ziel ist es, in speziellen Modellen die genaue Statistik der Fluktuationen für den zeitintegrierten Strom zu bestimmen und mit den zugehörigen grossen Abweichungen zu verknüpfen. Die grossen Abweichungen sollten dem Gallavotti-Cohen Fluktuationstheorem genügen. Dessen Gültigkeitsbereich wird ausgelotet.

Publications

• Current moments of ID ASEP by duality
  T. Imamura and T. Sasamoto
  
• A combinatorial solution for the current fluctuations in the exclusion process. (2009)
  S. Prolhac
  
• Superdiffusivity of the ID lattice Kardar-Parisi-Zhang equation. J. Stat. Phys. 137, 917-935 (2009)
  T. Sasamoto and H. Spohn
  
• Bethe ansatz derivation of the Tracy-Widom distribution for onedimensional directed polymers. EPL 90, 20003 (2010)
  V. Dotsenko
  
• Exact height distributions for the KPZ equation with narrow wedge initial condition. Nuclear Phys. B 834, 523-542 (2010)
  T. Sasamoto and H. Spohn
  
• Free-energy distribution of the directed polymer at high temperature. EPL 90, 20002 (2010)
  P. Calabrese, P. Le Doussai, and A. Rosso
  
• One-dimensional Kadar-Parisi-Zhang equation: an exact solution and its universality. Phys. Rev. Lett. 104, 230602 (2010)
  T. Sasamoto and H. Spohn
  
• The crossover regime for the weakly asymmetric simple exclusion process. J. Stat. Phys. 128, 799-846 (2010)
  T. Sasamoto and H. Spohn
  
• Growing interfaces uncover universal fluctuations behind scale invariance. Scientific Reports 1, 34 (2011)
  K. Takeuchi, M. Sano, T. Sasamoto, H. Spohn
  
• KPZ, ASEP and delta-Bose gas. Journal of Physics; Conference Series 297 (2011) 012016
  T. Imamura, T. Sasamoto, H. Spohn
  
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions. Comm. Pure Appl. Math. 64, 466537 (2011)
  G. Amir, I. Corwin, and J. Quastel
  
• Random Growth Models. The Oxford Handbook of Random Matrix Theory, Oxford University Press, 2011
  P.L. Ferrari and H. Spohn
  
• Recursive structures in the multispecies TASEP. J. Phys. A: Math. Theor. 44, 335004 (2011)
  C. Arita, A. Ayyer, K. Mallick, S. Prolhac
  
• The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class. Proceedings StatPhys 24, J. Stat. Mech. (2011) P01031 (18 pages)
  T. Sasamoto and H. Spohn
  
• The one-dimensional KPZ equation and the Airy process. J. Stat. Mech. (2011) P03020
  S. Prolhac and H. Spohn
  
• The propagator of the attractive delta-Bose gas in one dimension. J. Math. Phys. 52, 122106 (2011)
  S. Prolhac and H. Spohn
  
• Two-point generating function of the free energy for a directed polymer in a random medium. J. Stat. Mech. (2011) P01031
  S. Prolhac and H. Spohn