 01264 G. Gallavotti, J.L. Lebowitz, V. Mastropietro
 Large deviations in rarefied quantum gases
(94K, TeX)
Jul 12, 01

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The probability of observing a large deviation (LD) in the number
of particles in a region $\Lambda$ in a dilute quantum gas contained
in a much larger region $V$ is shown to decay as
$\exp[\Lambda\Delta F\,]$, where $\L$ is the volume of $\Lambda$
and $\Delta F$ is the change in the appropriate free energy density,
the same as in classical systems. However, in contrast with the
classical case, where this formula holds at all
temperatures and chemical potentials our proof is restricted to
rarefied gases, both for the typical and observed density, at least
for Bose or Fermi
systems. The case of Boltzmann statistics with a bounded repulsive
potential can be treated at all temperatures and densities. Fermions
on a lattice in any dimension, or in the continuum in one dimension,
can be treated at all densities and temperatures if the interaction
is small enough (depending on density and temperature), provided one
assumes periodic boundary conditions.
 Files:
01264.src(
01264.comments ,
01264.keywords ,
larged.tex ,
gr2.ps ,
grafici.ps )