50 research outputs found
Exact Thermodynamics of Disordered Impurities in Quantum Spin Chains
Exact results for the thermodynamic properties of ensembles of magnetic
impurities with randomly distributed host-impurity couplings in the quantum
antiferromagnetic Heisenberg model are presented. Exact calculations are done
for arbitrary values of temperature and external magnetic field. We have shown
that for strong disorder the quenching of the impurity moments is absent. For
weak disorder the screening persists, but with the critical non-Fermi-liquid
behaviors of the magnetic susceptibility and specific heat. A comparison with
the disordered Kondo effect experiments in dirty metallic alloys is performed.Comment: 4 pages Late
Emergence of Quantum Ergodicity in Rough Billiards
By analytical mapping of the eigenvalue problem in rough billiards on to a
band random matrix model a new regime of Wigner ergodicity is found. There the
eigenstates are extended over the whole energy surface but have a strongly
peaked structure. The results of numerical simulations and implications for
level statistics are also discussed.Comment: revtex, 4 pages, 4 figure
Equivalence of Fokker-Planck approach and non-linear -model for disordered wires in the unitary symmetry class
The exact solution of the Dorokhov-Mello-Pereyra-Kumar-equation for quasi
one-dimensional disordered conductors in the unitary symmetry class is employed
to calculate all -point correlation functions by a generalization of the
method of orthogonal polynomials. We obtain closed expressions for the first
two conductance moments which are valid for the whole range of length scales
from the metallic regime () to the insulating regime () and
for arbitrary channel number. In the limit (with )
our expressions agree exactly with those of the non-linear -model
derived from microscopic Hamiltonians.Comment: 9 pages, Revtex, one postscript figur
A Uniform Approximation for the Fidelity in Chaotic Systems
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve
in highly complex, yet deterministic ways. A slight perturbation of the system,
though, will cause the evolution to diverge from its original behavior
increasingly with time. This divergence can be measured by the fidelity, which
is defined as the squared overlap of the two time evolved states. For chaotic
systems, two main decay regimes of either Gaussian or exponential behavior have
been identified depending on the strength of the perturbation. For perturbation
strengths intermediate between the two regimes, the fidelity displays both
forms of decay. By applying a complementary combination of random matrix and
semiclassical theory, a uniform approximation can be derived that covers the
full range of perturbation strengths. The time dependence is entirely fixed by
the density of states and the so-called transition parameter, which can be
related to the phase space volume of the system and the classical action
diffusion constant, respectively. The accuracy of the approximations are
illustrated with the standard map.Comment: 16 pages, 4 figures, accepted in J. Phys. A, special edition on
Random Matrix Theor
Energy level statistics of the two-dimensional Hubbard model at low filling
The energy level statistics of the Hubbard model for square
lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for
a wide range of the coupling strength. All known symmetries of the model
(space, spin and pseudospin symmetry) have been taken into account explicitly
from the beginning of the calculation by projecting into symmetry invariant
subspaces. The details of this group theoretical treatment are presented with
special attention to the nongeneric case of L=4, where a particular complicated
space group appears. For all the lattices studied, a significant amount of
levels within each symmetry invariant subspaces remains degenerated, but except
for L=4 the ground state is nondegenerate. We explain the remaining
degeneracies, which occur only for very specific interaction independent
states, and we disregard these states in the statistical spectral analysis. The
intricate structure of the Hubbard spectra necessitates a careful unfolding
procedure, which is thoroughly discussed. Finally, we present our results for
the level spacing distribution, the number variance , and the
spectral rigidity , which essentially all are close to the
corresponding statistics for random matrices of the Gaussian ensemble
independent of the lattice size and the coupling strength. Even very small
coupling strengths approaching the integrable zero coupling limit lead to the
Gaussian ensemble statistics stressing the nonperturbative nature of the
Hubbard model.Comment: 31 pages (1 Revtex file and 10 postscript figures
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory
An exact solution is presented of the Fokker-Planck equation which governs
the evolution of an ensemble of disordered metal wires of increasing length, in
a magnetic field. By a mapping onto a free-fermion problem, the complete
probability distribution function of the transmission eigenvalues is obtained.
The logarithmic eigenvalue repulsion of random-matrix theory is shown to break
down for transmission eigenvalues which are not close to unity. ***Submitted to
Physical Review B.****Comment: 20 pages, REVTeX-3.0, INLO-PUB-931028
Universal Conductance Distributions in the Crossover between Diffusive and Localization Regimes
The full distribution of the conductance in quasi-one-dimensional
wires with rough surfaces is analyzed from the diffusive to the localization
regime. In the crossover region, where the statistics is dominated by only one
or two eigenchannels, the numerically obtained P(G) is found to be independent
of the details of the system with the average conductance as the only
scaling parameter. For < e^2/h, P(G) is given by an essentially
``one-sided'' log-normal distribution. In contrast, for e^2/h <= 2e^2/h,
the shape of P(G) remarkable agrees with those predicted by random matrix
theory for two fluctuating transmission eigenchannels.Comment: Accepted for publication in Phys. Rev. Let
Non-perturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide
A non-perturbative random-matrix theory is applied to the transmission of a
monochromatic scalar wave through a disordered waveguide. The probability
distributions of the transmittances T_{mn} and T_n=\sum_m T_{mn} of an incident
mode n are calculated in the thick-waveguide limit, for broken time-reversal
symmetry. A crossover occurs from Rayleigh or Gaussian statistics in the
diffusive regime to lognormal statistics in the localized regime. A
qualitatively different crossover occurs if the disordered region is replaced
by a chaotic cavity. ***Submitted to Physical Review E.***Comment: 7 pages, REVTeX-3.0, 5 postscript figures appended as self-extracting
archive. A complete postscript file with figures and text (4 pages) is
available from http://rulgm4.LeidenUniv.nl/preprints.htm
Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport
The scattering approach to quantum transport through a disordered
quasi-one-dimensional conductor in the insulating regime is discussed in terms
of its transfer matrix \bbox{T}. A model of one-dimensional wires which
are coupled by random hopping matrix elements is compared with the transfer
matrix model of Mello and Tomsovic. We derive and discuss the complete
Fokker-Planck equation which describes the evolution of the probability
distribution of \bbox{TT}^{\dagger} with system length in the insulating
regime. It is demonstrated that the eigenvalues of \ln\bbox{TT}^{\dagger}
have a multivariate Gaussian limiting probability distribution. The parameters
of the distribution are expressed in terms of averages over the stationary
distribution of the eigenvectors of \bbox{TT}^{\dagger}. We compare the
general form of the limiting distribution with results of random matrix theory
and the Dorokhov-Mello-Pereyra-Kumar equation.Comment: 25 pages, revtex, no figure