arXiv subjects

Shinsuke M. Nishigaki

Publications and source records attributed to Shinsuke M. Nishigaki.

24 records · Page 2Linked to original sources

arXiv2001

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.

cond-mat.dis-nn↗

arXiv2000

Chiral Lagrangians from lattice gauge theories in the strong coupling limit

We derive nonlinear sigma models (chiral Lagrangians) over symmetric spaces U(n), U(2n)/Sp(2n), and U(2n)/O(2n) from U(N), O(N), and Sp(2N) lattice gauge theories coupled to n flavors of staggered fermions, in the large-N and g^2 N limit. To this end, we employ Zirnbauer's color-flavor transformation. We prove the spatial homogeneity of the vacuum configurations of mesons by explicitly solving the large-N saddle point equations, and thus establish the above patterns of spontaneous chiral symmetry breaking without any assumptions.

hep-lat↗

arXiv1999

Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x)^2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient $a$ is small, spectral correlations in the bulk are universally governed by a translationally invariant, one-parameter generalization of the sine kernel. We provide analytic expressions for the level spacing distribution functions of this kernel, which are hybrids of the Wigner-Dyson and Poisson distributions. By tuning the single parameter, our results can be excellently fitted to the numerical data for three symmetry classes of the three-dimensional Anderson Hamiltonians at the metal-insulator transition, previously measured by several groups using exact diagonalization.

cond-mat.dis-nn↗

arXiv1998

Level Spacing Distribution of Critical Random Matrix Ensembles

We consider unitary invariant random matrix ensembles which obey spectral statistics different from the Wigner-Dyson, including unitary ensembles with slowly (~(log x)^2) growing potentials and the finite-temperature fermi gas model. If the deformation parameters in these matrix ensembles are small, the asymptotically translational-invariant region in the spectral bulk is universally governed by a one-parameter generalization of the sine kernel. We provide an analytic expression for the distribution of the eigenvalue spacings of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and the Poisson distributions, by determining the Fredholm determinant of the universal kernel in terms of a Painleve VI transcendental function.

cond-mat.dis-nn↗

arXiv1998

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).

hep-th↗

arXiv1997

Microscopic universality in random matrix models of QCD

I shall present a proof of universality of the microscopic spectral correlations in Verbaarschot's random matrix models of QCD, to corroborate the beautiful agreement between the predictions from the gaussian model and the numerical data. Rather than following closely the original proof, I shall disguise it with the conventional approach of Q, P operators and with the method employed in an alternative proof by Kanzieper-Freilikher, in a hope that borrowing notions from quantum mechanics may add the proof some pedagogical flavor. I shall also discuss a problem associated with the multi-criticality.

hep-th↗