相关论文: Wigner-Dyson Statistics from the Replica Method
A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…
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…
We provide a measurement protocol to estimate 2- and 4-point fermionic correlations in ultra-cold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for…
The calculation of correlation functions for $\beta=1$ random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N. This same…
Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a…
We derive simple linear, inhomogeneous recurrences for the variance of the index by utilising the fact that the generating function for the distribution of the number of positive eigenvalues of a Gaussian unitary ensemble is a…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
We compute the large scale (macroscopic) correlations in ensembles of normal random matrices with an arbitrary measure and in ensembles of general non-Hermition matrices with a class of non-Gaussian measures. In both cases the eigenvalues…
We give a short, operator-theoretic proof of the asymptotic independence (including a first correction term) of the minimal and maximal eigenvalue of the n \times n Gaussian Unitary Ensemble in the large matrix limit n \to \infty. This is…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…
We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric…
We calculate, through Monte Carlo numerical simulations, the partial total and direct correlation functions of the three dimensional symmetric Widom-Rowlinson mixture. We find that the differences between the partial direct correlation…
We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…
We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the Functional Renormalization Group approach. Our method is based on the same analytic continuation from…
We study spontaneous symmetry breaking in quantum field theories with fermionic order parameters and construct, for the first time in the literature, the constraint effective potential for it. The Grassmann-valued constraint we encounter is…
We investigate the replica trick for the microscopic spectral density, $\rho_s(x)$, of the Euclidean QCD Dirac operator. Our starting point is the low-energy limit of the QCD partition function for $n$ fermionic flavors (or replicas) in the…