FM 97-3


Title: Electric fields on a surface of constant negative
       curvature

Authors: F. Bonetto, G. Gentile, V. Mastropietro

Abstract: A one parameter family of time reversible Anosov
flows is studied and shown to be dissipative, in the sense that
the average volume contraction rate is positive and the
Sinai-Ruelle-Bowen measure is singular with respect to the
volume. Therefore the systems, physically describing a particle
moving on a surface of constant negative curvature under the
action of an electric field (corresponding to an automorphic
form) and of a "thermostatting" force (given by Gauss' least
constraint principle), verify the assumptions for the validity
of the continuous time version of Gallavotti-Cohen's
fluctuation theorem for the large fluctuations of the average
volume contraction rate. If the surface genus is g>2 several
independent electric fields can be considered and it makes
sense to ask for the validity of Onsager's reciprocity: we
show, by explicitly computing the relevant transport
coefficients, that it is indeed obeyed.


Dipartimento di Matematica, 
Universita' di Roma "La Sapienza",
I-10085 Roma
e-mail: bonetto@physics-sun.rockefeller.edu

IHES, F-91440 Bures sur Yvette
e-mail: gentileg@ipparco.roma1.infn.it

Dipartimento di Matematica, 
Universita' di Roma "Tor Vergata",
I-00133 Roma
e-mail: vieri@ipparco.roma1.infn.it