60 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.
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
Level Spacing Distribution of Critical Random Matrix Ensembles
We consider unitary invariant random matrix ensembles which obey spectral
statistics different from the Wigner-Dyson, including unitary ensembles with
slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas
model. If the deformation parameters in these matrix ensembles are small, the
asymptotically translational-invariant region in the spectral bulk is
universally governed by a one-parameter generalization of the sine kernel. We
provide an analytic expression for the distribution of the eigenvalue spacings
of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and
the Poisson distributions, by determining the Fredholm determinant of the
universal kernel in terms of a Painleve VI transcendental function.Comment: 5 pages, 1 figure, REVTeX; restriction on the parameter stressed,
figure replaced, refs added (v2); typos (factors of pi) in (35), (36)
corrected (v3); minor changes incl. title, version to appear in Phys.Rev.E
(v4
Critical statistics in a power-law random banded matrix ensemble
We investigate the statistical properties of the eigenvalues and eigenvectors
in a random matrix ensemble with . It is known that
this model shows a localization-delocalization transition (LDT) as a function
of the parameter . The model is critical at and the eigenstates
are multifractals. Based on numerical simulations we demonstrate that the
spectral statistics at criticality differs from semi-Poisson statistics which
is expected to be a general feature of systems exhibiting a LDT or `weak
chaos'.Comment: 4 pages in PS including 5 figure
La variation des indicateurs bactériens et des flux de MES dans les systèmes séparatifs d'eaux pluviales à Östersund, en Suède - Résultats préliminaires
Faecal bacteria are a major pollution threat of water bodies designated for multipurpose use including drinking water sources or recreational purposes. Even though stormwater discharges may contribute significantly to microbiological pollution, they have not been fully investigated in the European context. We have studied the presence of indicator bacteria and total suspended solids (TSS) in stormwater discharged from four urban catchments, with areas between 5 and 40 ha, in Östersund, Sweden. The aim was to determine local variation of standard bacteria strains and TSS in Swedish urban catchments with specific land uses. Further, intra event variations were investigated. During dry weather, indicator bacteria concentrations in sewers conveying baseflow did not exceed 100 CFU/100 mL. During storm runoff, total coliform and int. enterococci concentrations increased 102 to 103 times, compared to those in baseflow. Compared to these two parameters, considerably lower concentrations were observed for E. coli and C. perfringens. Bacteria concentrations differed significantly among the sampling sites and partly, a first flush phenomenon was observed. Partly, significant correlations between TSS and indicator bacteria were observed. These were catchment specific and need a more detailed assessment. Further research will focus on seasonal variations and influential factors.Godkänd; 2013; 20130821 (helgal)</p
Energy level statistics of a critical random matrix ensemble
We study level statistics of a critical random matrix ensemble of a power-law
banded complex Hermitean matrices. We compute numerically the level
compressibility via the level number variance and compare it with the
analytical formula for the exactly solvable model of Moshe, Neuberger and
Shapiro.Comment: 8 pages, 3 figure
Spectral properties of a generalized chGUE
We consider a generalized chiral Gaussian Unitary Ensemble (chGUE) based on a
weak confining potential. We study the spectral correlations close to the
origin in the thermodynamic limit. We show that for eigenvalues separated up to
the mean level spacing the spectral correlations coincide with those of chGUE.
Beyond this point, the spectrum is described by an oscillating number variance
centered around a constant value. We argue that the origin of such a rigid
spectrum is due to the breakdown of the translational invariance of the
spectral kernel in the bulk of the spectrum. Finally, we compare our results
with the ones obtained from a critical chGUE recently reported in the
literature. We conclude that our generalized chGUE does not belong to the same
class of universality as the above mentioned model.Comment: 12 pages, 3 figure
Spectral Correlations from the Metal to the Mobility Edge
We have studied numerically the spectral correlations in a metallic phase and
at the metal-insulator transition. We have calculated directly the two-point
correlation function of the density of states . In the metallic phase,
it is well described by the Random Matrix Theory (RMT). For the first time, we
also find numerically the diffusive corrections for the number variance
predicted by Al'tshuler and Shklovski\u{\i}. At the
transition, at small energy scales, starts linearly, with a slope
larger than in a metal. At large separations , it is found to
decrease as a power law with and , in good agreement with recent microscopic
predictions. At the transition, we have also calculated the form factor , Fourier transform of . At large , the number variance
contains two terms \tilde{K}(0)t \to 0$.Comment: 7 RevTex-pages, 10 figures. Submitted to PR
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