611 research outputs found
Accuracy and range of validity of the Wigner surmise for mixed symmetry classes in random matrix theory
Schierenberg et al. [Phys. Rev. E 85, 061130 (2012)] recently applied the
Wigner surmise, i.e., substitution of \infty \times \infty matrices by their 2
\times 2 counterparts for the computation of level spacing distributions, to
random matrix ensembles in transition between two universality classes. I
examine the accuracy and the range of validity of the surmise for the crossover
between the Gaussian orthogonal and unitary ensembles by contrasting them with
the large-N results that I evaluated using the Nystrom-type method for the
Fredholm determinant. The surmised expression at the best-fitting parameter
provides a good approximation for 0 \lesssim s \lesssim 2, i.e., the validity
range of the original surmise.Comment: 3 pages in REVTeX, 10 figures. (v2) Title changed, version to appear
in Phys. Rev.
Reply to Comment on Dirac spectral sum rules for QCD in three dimensions
I reply to the comment by Dr S. Nishigaki (hep-th/0007042) to my papers Phys.
Rev. D61 (2000) 056005 and Phys. Rev. D62 (2000) 016005.Comment: 2 pages, LaTeX, no figure
Universality of random matrices in the microscopic limit and the Dirac operator spectrum
We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant orthogonal polynomials into a Bessel equation governing the local asymptotics around the origin. The possible physical interpretation as the universality of the soft spectrum of the Dirac operator is briefly discussed
Comments on Supersymmetric Vector and Matrix Models
Some results in random matrices are generalized to supermatrices, in
particular supermatrix integration is reduced to an integration over the
eigenvalues and the resulting volume element is shown to be equivalent to a one
dimensional Coulomb gas of both positive and negative charges.It is shown
that,for polynomial potentials, after removing the instability due to the
annihilation of opposite charges, supermatrix models are indistinguishable from
ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and
Manes. It is pointed out however that this may not be true for more general
potentials such as for instance the supersymmetric generalization of the Penner
model.Comment: 6 page
Variational approach to the scattering of charged particles by a many-electron system
We report a variational approach to the nonlinearly screened interaction of
charged particles with a many-electron system. This approach has been developed
by introducing a modification of the Schwinger variational principle of
scattering theory, which allows to obtain nonperturbative scattering
cross-sections of moving projectiles from the knowledge of the linear and
quadratic density-response functions of the target. Our theory is illustrated
with a calculation of the energy loss per unit path length of slow antiprotons
moving in a uniform electron gas, which shows good agreement with a fully
nonlinear self-consistent Hartree calculation. Since available self-consistent
calculations are restricted to low heavy-projectile velocities, we expect our
theory to have novel applications to a variety of processes where nonlinear
screening plays an important role.Comment: 10 pages, 2 figures; Accepted to Physical Review
Scaling Behaviors of Branched Polymers
We study the thermodynamic behavior of branched polymers. We first study
random walks in order to clarify the thermodynamic relation between the
canonical ensemble and the grand canonical ensemble. We then show that
correlation functions for branched polymers are given by those for
theory with a single mass insertion, not those for the theory
themselves. In particular, the two-point function behaves as , not as
, in the scaling region. This behavior is consistent with the fact that
the Hausdorff dimension of the branched polymer is four.Comment: 17 pages, 3 figure
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