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

Comment on Dirac spectral sum rules for QCD_3

Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000); Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point out that these computations are incorrect, and that they contradict with the exact results for the spectral densities unambiguously derived from random matrix theory by Nagao and myself.Comment: REVTeX 3.1, 2 pages, no figure. (v2) redundant part removed, conclusion unchange

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

Use of Satisfaction-Satisfaction Matrix (SSM) to evaluate e-government services from the perspective of Japanese citizens and government service providers

This paper addresses the issue of Japanese e-government benefits evaluation and stresses the need to develop a new measurement tool to evaluate e-government services from the perspective of Japanese citizens and government service providers. While research has used SERVQUAL, SERVPERF and Importance-Performance Analysis (IPA) as evaluation tools to measure quality of services, most of these tools are developed to evaluate quality of services from the perspective of citizens or service providers. In this paper, we propose a new evaluation tool, namely Satisfaction-Satisfaction Matrix (SSM), to gauge both the perceptions of citizens and service providers concerning the performance of e-government services. The matrix not only serves as a useful tool to identify satisfaction responses, but also serves as a strategic decision making tool in the allocation of resources for improving e-government services

Eigenvalue correlations in non-Hermitean symplectic random matrices

Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are studied in detail in the regimes of weak and strong non-Hermiticity.Comment: 14 page

Smallest Dirac Eigenvalue Distribution from Random Matrix Theory

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function in the mesoscopic regime. Their universality is explicitly related to that of the microscopic massive Bessel kernel.Comment: 4 pages, 1 figure, REVTeX. Minor typos in subscripts corrected. Version to appear in Phys. Rev.

On gonihedric loops and quantum gravity

We present an analysis of the gonihedric loop model, a reformulation of the two dimensional gonihedric spin model, using two different techniques. First, the usual regular lattice statistical physics problem is mapped onto a height model and studied analytically. Second, the gravitational version of this loop model is studied via matrix models techniques. Both methods lead to the conclusion that the model has $c_{matter}=0$ for all values of the parameters of the model. In this way it is possible to understand the absence of a continuous transition

Replica treatment of non-Hermitian disordered Hamiltonians

We employ the fermionic and bosonic replicated nonlinear sigma models to treat Ginibre unitary, symplectic, and orthogonal ensembles of non-Hermitian random matrix Hamiltonians. Using saddle point approach combined with Borel resummation procedure we derive the exact large-N results for microscopic density of states in all three ensembles. We also obtain tails of the density of states as well the two-point function for the unitary ensemble.Comment: REVTeX 3.1, 13 pages, 1 figure; typos fixed (v2

Universal Massive Spectral Correlators and QCD_3

Based on random matrix theory in the unitary ensemble, we derive the double-microscopic massive spectral correlators corresponding to the Dirac operator of QCD_3 with an even number of fermions N_f. We prove that these spectral correlators are universal, and demonstrate that they satisfy exact massive spectral sum rules of QCD_3 in a phase where flavor symmetries are spontaneously broken according to U(N_f) -> U(N_f/2) x U(N_f/2).Comment: 5 pages, REVTeX. Misprint correcte