73 research outputs found
Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model
We consider a quantum moany-body problem in one-dimension described by a
Jastrow type, characterized by an exponent and a parameter .
We show that with increasing , the Fermi Liquid state (
crosses over to non-Fermi liquid states, characterized by effective
"temperature".Comment: 8pp. late
Rotationally invariant family of L\'evy like random matrix ensembles
We introduce a family of rotationally invariant random matrix ensembles
characterized by a parameter . While corresponds to
well-known critical ensembles, we show that describes "L\'evy
like" ensembles, characterized by power law eigenvalue densities. For the density is bounded, as in Gaussian ensembles, but
describes ensembles characterized by densities with long tails. In particular,
the model allows us to evaluate, in terms of a novel family of orthogonal
polynomials, the eigenvalue correlations for L\'evy like ensembles. These
correlations differ qualitatively from those in either the Gaussian or the
critical ensembles.Comment: 9 pages, 5 figure
Impact of localization on Dyson's circular ensemble
A wide variety of complex physical systems described by unitary matrices have
been shown numerically to satisfy level statistics predicted by Dyson's
circular ensemble. We argue that the impact of localization in such systems is
to provide certain restrictions on the eigenvalues. We consider a solvable
model which takes into account such restrictions qualitatively and find that
within the model a gap is created in the spectrum, and there is a transition
from the universal Wigner distribution towards a Poisson distribution with
increasing localization.Comment: To be published in J. Phys.
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Colloque avec actes et comité de lecture. Internationale.International audienc
Transitions In Spectral Statistics
We present long range statistical properties of a recently introduced unitary
random matrix ensemble, whose short range correlations were found to describe a
transition from Wigner to Poisson type as a function of a single parameter.Comment: 12 pp. late
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