Quenched asymptotics of the ground state energy of random Schrödinger operators with scaled Gibbsian potentials |
| |
Authors: | Franz Merkl |
| |
Institution: | (1) Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands. e-mail: merkl@math.leidenuniv.nl, NL |
| |
Abstract: | This article describes the almost sure infinite volume asymptotics of the ground state energy of random Schr?dinger operators
with scaled Gibbsian potentials. The random potential is obtained by distributing soft obstacles according to an infinite
volume grand canonical tempered Gibbs measure with a superstable pair interaction. There is no restriction on the strength
of the pair interaction: it may be taken, e.g., at a critical point. The potential is scaled with the box size in a critical
way, i.e. the scale is determined by the typical size of large deviations in the Gibbsian cloud. The almost sure infinite
volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles
involving only thermodynamic quantities. The qualitative behaviour of the ground state energy asymptotics is analysed: Depending
on the dimension and on the H?lder exponents of the free energy density, it is identified which cases lead to a phase transition
of the asymptotic behaviour of the ground state energy.
Received: 24 June 2002 / Revised version: 17 February 2003
Published online: 12 May 2003
Mathematics Subject Classification (2000): Primary 82B44; Secondary 60K35
Key words or phrases: Gibbs measure – H?lder exponents – Random Schr?dinger operator – Ground state – Large deviations |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|