3,069 research outputs found
Lattice Dirac fermions in a non-Abelian random gauge potential: Many flavors, chiral symmetry restoration and localization
In the previous paper we studied Dirac fermions in a non-Abelian random
vector potential by using lattice supersymmetry. By the lattice regularization,
the system of disordered Dirac fermions is defined without any ambiguities. We
showed there that at strong-disorder limit correlation function of the fermion
local density of states decays algebraically at the band center. In this paper,
we shall reexamine the multi-flavor or multi-species case rather in detail and
argue that the correlator at the band center decays {\em exponentially} for the
case of a {\em large} number of flavors. This means that a
delocalization-localization phase transition occurs as the number of flavors is
increased. This discussion is supported by the recent numerical studies on
multi-flavor QCD at the strong-coupling limit, which shows that the phase
structure of QCD drastically changes depending on the number of flavors. The
above behaviour of the correlator of the random Dirac fermions is closely
related with how the chiral symmetry is realized in QCD.Comment: Version appears in Mod.Phys.Lett.A17(2002)135
A theory of the electric quadrupole contribution to resonant x-ray scattering: Application to multipole ordering phases in Ce_{1-x}La_{x}B_{6}
We study the electric quadrupole (E2) contribution to resonant x-ray
scattering (RXS). Under the assumption that the rotational invariance is
preserved in the Hamiltonian describing the intermediate state of scattering,
we derive a useful expression for the RXS amplitude. One of the advantages the
derived expression possesses is the full information of the energy dependence,
lacking in all the previous studies using the fast collision approximation. The
expression is also helpful to classify the spectra into multipole order
parameters which are brought about. The expression is suitable to investigate
the RXS spectra in the localized f electron systems. We demonstrate the
usefulness of the formula by calculating the RXS spectra at the Ce L_{2,3}
edges in Ce_{1-x}La_{x}B_{6} on the basis of the formula. We obtain the spectra
as a function of energy in agreement with the experiment of
Ce_{0.7}La_{0.3}B_{6}. Analyzing the azimuthal angle dependence, we find the
sixfold symmetry in the \sigma-\sigma' channel and the threefold onein the
\sigma-\pi' channel not only in the antiferrooctupole (AFO) ordering phase but
also in the antiferroquadrupole (AFQ) ordering phase, which behavior depends
strongly on the domain distribution. The sixfold symmetry in the AFQ phase
arises from the simultaneously induced hexadecapole order. Although the AFO
order is plausible for phase IV in Ce_{1-x}La_{x}B_{6}, the possibility of the
AFQ order may not be ruled out on the basis of azimuthal angle dependence
alone.Comment: 12 pages, 6 figure
Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
The spectral correlation of a chaotic system with spin 1/2 is universally
described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the
semiclassical limit. In semiclassical theory, the spectral form factor is
expressed in terms of the periodic orbits and the spin state is simulated by
the uniform distribution on a sphere. In this paper, instead of the uniform
distribution, we introduce Brownian motion on a sphere to yield the parametric
motion of the energy levels. As a result, the small time expansion of the form
factor is obtained and found to be in agreement with the prediction of
parametric random matrices in the transition within the GSE universality class.
Moreover, by starting the Brownian motion from a point distribution on the
sphere, we gradually increase the effect of the spin and calculate the form
factor describing the transition from the GOE (Gaussian Orthogonal Ensemble)
class to the GSE class.Comment: 25 pages, 2 figure
Universality for orthogonal and symplectic Laguerre-type ensembles
We give a proof of the Universality Conjecture for orthogonal (beta=1) and
symplectic (beta=4) random matrix ensembles of Laguerre-type in the bulk of the
spectrum as well as at the hard and soft spectral edges. Our results are stated
precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and Corollaries 1.2, 1.5,
1.7). They concern the appropriately rescaled kernels K_{n,beta}, correlation
and cluster functions, gap probabilities and the distributions of the largest
and smallest eigenvalues. Corresponding results for unitary (beta=2)
Laguerre-type ensembles have been proved by the fourth author in [23]. The
varying weight case at the hard spectral edge was analyzed in [13] for beta=2:
In this paper we do not consider varying weights.
Our proof follows closely the work of the first two authors who showed in
[7], [8] analogous results for Hermite-type ensembles. As in [7], [8] we use
the version of the orthogonal polynomial method presented in [25], [22] to
analyze the local eigenvalue statistics. The necessary asymptotic information
on the Laguerre-type orthogonal polynomials is taken from [23].Comment: 75 page
Determinantal process starting from an orthogonal symmetry is a Pfaffian process
When the number of particles is finite, the noncolliding Brownian motion
(BM) and the noncolliding squared Bessel process with index
(BESQ) are determinantal processes for arbitrary fixed initial
configurations. In the present paper we prove that, if initial configurations
are distributed with orthogonal symmetry, they are Pfaffian processes in the
sense that any multitime correlation functions are expressed by Pfaffians. The
skew-symmetric matrix-valued correlation kernels of the Pfaffians
processes are explicitly obtained by the equivalence between the noncolliding
BM and an appropriate dilatation of a time reversal of the temporally
inhomogeneous version of noncolliding BM with finite duration in which all
particles start from the origin, , and by the equivalence between
the noncolliding BESQ and that of the noncolliding squared
generalized meander starting from .Comment: v2: AMS-LaTeX, 17 pages, no figure, corrections made for publication
in J.Stat.Phy
Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
Spatially and temporally inhomogeneous evolution of one-dimensional vicious
walkers with wall restriction is studied. We show that its continuum version is
equivalent with a noncolliding system of stochastic processes called Brownian
meanders. Here the Brownian meander is a temporally inhomogeneous process
introduced by Yor as a transform of the Bessel process that is a motion of
radial coordinate of the three-dimensional Brownian motion represented in the
spherical coordinates. It is proved that the spatial distribution of vicious
walkers with a wall at the origin can be described by the eigenvalue-statistics
of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field
theory of superconductivity, which have the particle-hole symmetry. We report
that the time evolution of the present stochastic process is fully
characterized by the change of symmetry classes from the type to the type
I in the nonstandard classes of random matrix theory of Altland and
Zirnbauer. The relation between the non-colliding systems of the generalized
meanders of Yor, which are associated with the even-dimensional Bessel
processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction
Effects of Rattling Phonons on the Quasiparticle Excitation and Dynamics in the Superconducting -Pyrochlore KOsO
Microwave penetration depth and surface resistance at 27 GHz are
measured in high quality crystals of KOsO. Firm evidence for
fully-gapped superconductivity is provided from . Below the second
transition at K, the superfluid density shows a step-like
change with a suppression of effective critical temperature .
Concurrently, the extracted quasiparticle scattering time shows a steep
enhancement, indicating a strong coupling between the anomalous rattling motion
of K ions and quasiparticles. The results imply that the rattling phonons help
to enhance superconductivity, and that K sites freeze to an ordered state with
long quasiparticle mean free path below .Comment: 5 pages, 5 figures, to be published in Phys. Rev. Let
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