289 research outputs found
Norm-dependent Random Matrix Ensembles in External Field and Supersymmetry
The class of norm-dependent Random Matrix Ensembles is studied in the
presence of an external field. The probability density in those ensembles
depends on the trace of the squared random matrices, but is otherwise
arbitrary. An exact mapping to superspace is performed. A transformation
formula is derived which gives the probability density in superspace as a
single integral over the probability density in ordinary space. This is done
for orthogonal, unitary and symplectic symmetry. In the case of unitary
symmetry, some explicit results for the correlation functions are derived.Comment: 19 page
Arbitrary Rotation Invariant Random Matrix Ensembles and Supersymmetry
We generalize the supersymmetry method in Random Matrix Theory to arbitrary
rotation invariant ensembles. Our exact approach further extends a previous
contribution in which we constructed a supersymmetric representation for the
class of norm-dependent Random Matrix Ensembles. Here, we derive a
supersymmetric formulation under very general circumstances. A projector is
identified that provides the mapping of the probability density from ordinary
to superspace. Furthermore, it is demonstrated that setting up the theory in
Fourier superspace has considerable advantages. General and exact expressions
for the correlation functions are given. We also show how the use of hyperbolic
symmetry can be circumvented in the present context in which the non-linear
sigma model is not used. We construct exact supersymmetric integral
representations of the correlation functions for arbitrary positions of the
imaginary increments in the Green functions.Comment: 36 page
The k-Point Random Matrix Kernels Obtained from One-Point Supermatrix Models
The k-point correlation functions of the Gaussian Random Matrix Ensembles are
certain determinants of functions which depend on only two arguments. They are
referred to as kernels, since they are the building blocks of all correlations.
We show that the kernels are obtained, for arbitrary level number, directly
from supermatrix models for one-point functions. More precisely, the generating
functions of the one-point functions are equivalent to the kernels. This is
surprising, because it implies that already the one-point generating function
holds essential information about the k-point correlations. This also
establishes a link to the averaged ratios of spectral determinants, i.e. of
characteristic polynomials
Transition from Poisson to gaussian unitary statistics: The two-point correlation function
We consider the Rosenzweig-Porter model of random matrix which interpolates
between Poisson and gaussian unitary statistics and compute exactly the
two-point correlation function. Asymptotic formulas for this function are given
near the Poisson and gaussian limit.Comment: 19 pages, no figure
Spectral correlations in the crossover between GUE and Poisson regularity: on the identification of scales
Motivated by questions of present interest in nuclear and condensed matter
physics we consider the superposition of a diagonal matrix with independent
random entries and a GUE. The relative strength of the two contributions is
determined by a parameter suitably defined on the unfolded scale.
Using results for the spectral two-point correlator of this model obtained in
the framework of the supersymmetry method we focus attention on two different
regimes. For << 1 the correlations are given by Dawson's integral
while for >> 1 we derive a novel analytical formula for the two-point
function. In both cases the energy scales, in units of the mean level spacing,
at which deviations from pure GUE behavior become noticable can be identified.
We also derive an exact expansion of the local level density for finite level
number.Comment: 15 pages, Revtex, no figures, to be published in special issue of J.
Math. Phys. (1997
Surprising relations between parametric level correlations and fidelity decay
Unexpected relations between fidelity decay and cross form--factor, i.e.,
parametric level correlations in the time domain are found both by a heuristic
argument and by comparing exact results, using supersymmetry techniques, in the
framework of random matrix theory. A power law decay near Heisenberg time, as a
function of the relevant parameter, is shown to be at the root of revivals
recently discovered for fidelity decay. For cross form--factors the revivals
are illustrated by a numerical study of a multiply kicked Ising spin chain.Comment: 4 pages 3 figure
Supersymmetric Extensions of Calogero--Moser--Sutherland like Models: Construction and Some Solutions
We introduce a new class of models for interacting particles. Our
construction is based on Jacobians for the radial coordinates on certain
superspaces. The resulting models contain two parameters determining the
strengths of the interactions. This extends and generalizes the models of the
Calogero--Moser--Sutherland type for interacting particles in ordinary spaces.
The latter ones are included in our models as special cases. Using results
which we obtained previously for spherical functions in superspaces, we obtain
various properties and some explicit forms for the solutions. We present
physical interpretations. Our models involve two kinds of interacting
particles. One of the models can be viewed as describing interacting electrons
in a lower and upper band of a one--dimensional semiconductor. Another model is
quasi--two--dimensional. Two kinds of particles are confined to two different
spatial directions, the interaction contains dipole--dipole or tensor forces.Comment: 21 pages, 4 figure
Weak localization of the open kicked rotator
We present a numerical calculation of the weak localization peak in the
magnetoconductance for a stroboscopic model of a chaotic quantum dot. The
magnitude of the peak is close to the universal prediction of random-matrix
theory. The width depends on the classical dynamics, but this dependence can be
accounted for by a single parameter: the level curvature around zero magnetic
field of the closed system.Comment: 8 pages, 8 eps figure
From perfect to fractal transmission in spin chains
Perfect state transfer is possible in modulated spin chains, imperfections
however are likely to corrupt the state transfer. We study the robustness of
this quantum communication protocol in the presence of disorder both in the
exchange couplings between the spins and in the local magnetic field. The
degradation of the fidelity can be suitably expressed, as a function of the
level of imperfection and the length of the chain, in a scaling form. In
addition the time signal of fidelity becomes fractal. We further characterize
the state transfer by analyzing the spectral properties of the Hamiltonian of
the spin chain.Comment: 8 pages, 10 figures, published versio
Adaptive control of an electromagnetically actuated presser-foot for industrial sewing machines
This study describes some possibilities of setting up an adaptive control method for an electromagnetically actuated presser-foot in an industrial high-speed sewing machine. The control of fabrics feeding in sewing machines is difficult not only because of the complexity of relations between the intervening variables (material properties, sewing speed), but also because in many operations a varying number of material plies are crossed. This implies that the reference for the controller has to be adapted dynamically. Several methods, using PID and/or fuzzy logic control, have been tried and are described in this paper. A preliminary sewing test is able to provide data to tune the controller variables. With these adaptation techniques, the machine would be able to automatically adapt its feeding system according to the material being sewn.Fundação para a CiĂȘncia e a Tecnologia (FCT
- âŠ