2,779 research outputs found
Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach
We determine the asymptotic level spacing distribution for the Laguerre
Ensemble in a single scaled interval, , containing no levels,
E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the
Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by
both Edelman and Forrester, while for , the leading terms of
, found by Tracy and Widom, are reproduced without the use of the
Bessel kernel and the associated Painlev\'e transcendent. In the same
approximation, the next leading term, due to a ``finite temperature''
perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe
A random matrix decimation procedure relating to
Classical random matrix ensembles with orthogonal symmetry have the property
that the joint distribution of every second eigenvalue is equal to that of a
classical random matrix ensemble with symplectic symmetry. These results are
shown to be the case of a family of inter-relations between eigenvalue
probability density functions for generalizations of the classical random
matrix ensembles referred to as -ensembles. The inter-relations give
that the joint distribution of every -st eigenvalue in certain
-ensembles with is equal to that of another
-ensemble with . The proof requires generalizing a
conditional probability density function due to Dixon and Anderson.Comment: 19 pages, 1 figur
Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets
The manifestation of the spin-wave interaction in the low-temperature series
of the partition function has been investigated extensively over more than
seven decades in the case of the three-dimensional ferromagnet. Surprisingly,
the same problem regarding ferromagnets in two spatial dimensions, to the best
of our knowledge, has never been addressed in a systematic way so far. In the
present paper the low-temperature properties of two-dimensional ideal
ferromagnets are analyzed within the model-independent method of effective
Lagrangians. The low-temperature expansion of the partition function is
evaluated up to two-loop order and the general structure of this series is
discussed, including the effect of a weak external magnetic field. Our results
apply to two-dimensional ideal ferromagnets which exhibit a spontaneously
broken spin rotation symmetry O(3) O(2) and are defined on a square,
honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave
interaction only sets in at three-loop order. In particular, there is no
interaction term of order in the low-temperature series for the free
energy density. This is the analog of the statement that, in the case of
three-dimensional ferromagnets, there is no interaction term of order in
the free energy density. We also provide a careful discussion of the
implications of the Mermin-Wagner theorem in the present context and thereby
put our low-temperature expansions on safe grounds.Comment: 24 pages, 3 figure
The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum
We calculate the probability to find exactly eigenvalues in a spectral
interval of a large random matrix when this interval contains eigenvalues on average. The calculations exploit an analogy to the
problem of finding a two-dimensional charge distribution on the interface of a
semiconductor heterostructure under the influence of a split gate.Comment: 4 pages, postscrip
On frequencies of small oscillations of some dynamical systems associated with root systems
In the paper by F. Calogero and author [Commun. Math. Phys. 59 (1978)
109-116] the formula for frequencies of small oscillations of the Sutherland
system ( case) was found. In present note the generalization of this
formula for the case of arbitrary root system is given.Comment: arxiv version is already officia
Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux
The Anderson transition in three dimensions in a randomly varying magnetic
flux is investigated in detail by means of the transfer matrix method with high
accuracy. Both, systems with and without an additional random scalar potential
are considered. We find a critical exponent of with random
scalar potential. Without it, is smaller but increases with the system
size and extrapolates within the error bars to a value close to the above. The
present results support the conventional classification of universality classes
due to symmetry.Comment: 4 pages, 2 figures, to appear in Phys. Rev.
Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
The distribution of energy level separations for lattices of sizes up to
282828 sites is numerically calculated for the Anderson model.
The results show one-parameter scaling. The size-independent universality of
the critical level spacing distribution allows to detect with high precision
the critical disorder . The scaling properties yield the critical
exponent, , and the disorder dependence of the correlation
length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded
using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.
The evolution of mass loaded supernova remnants: II. Temperature dependent mass injection rates
We investigate the evolution of spherically symmetric supernova remnants in which mass loading takes place due to conductively driven evaporation of embedded clouds. Numerical simulations reveal significant differences between the evolution of conductively mass loaded and the ablatively mass loaded remnants studied in Paper I. A main difference is the way in which conductive mass loading is extinguished at fairly early times, once the interior temperature of the remnant falls below ~ 107 K. Thus, at late times remnants that ablatively mass load are dominated by loaded mass and thermal energy, while those that conductively mass load are dominated by swept-up mass and kinetic energy. Simple approximations to the remnant evolution, complementary to those in Paper I, are given
Wigner-Dyson Statistics from the Replica Method
We compute the correlation functions of the eigenvalues in the Gaussian
unitary ensemble using the fermionic replica method. We show that non--trivial
saddle points, which break replica symmetry, must be included in the
calculation in order to reproduce correctly the exact results for the
correlation functions at large distance.Comment: 13 pages, added reference
T-duality in supersymmetric theory of disordered quantum systems
A new super-symmetric representation for quantum disordered systems is
derived. This representation is exact and is dual to that of the nonlinear
sigma-model. The new formalism is tested by calculating the distribution of
wave function amplitudes in the 1d Anderson model. The deviation from the
distribution found for a thick wire is detected near the band center E=0.Comment: 4 page
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