Related papers: Density of states for Random Band Matrix
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
We compute the volume of the convex N^2-1 dimensional set M_N of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area of the boundary of this set is also found and its ratio to the volume provides an…
The large N limit of mean spectral density for the ensemble of NxN sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41 (2008) 50201) is calculated by a modification of the saddle point method. It is shown that the…
We study the spectrum of adjacency matrices of random graphs. We develop two techniques to lower bound the mass of the continuous part of the spectral measure or the density of states. As an application, we prove that the spectral measure…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h.…
In the class of nonlinear one-parameter real maps we study those with bifurcation that exhibits period doubling cascade. The fixed points of such a map form a finite discrete real set with dimension (2^n)m, where m is the (odd) number of…
The present work represents a review for the numerical calculation of the density of states (DoS) for two-dimensional tight-binding models with first neighbors in its normal state and for two superconducting order parameters. One is a…
We numerically investigate the vibrational spectra of single-component clusters in two-dimensions. Stable configurations of clusters at local energy minima are obtained, and for each the hessian matrix is evaluated and diagonalized to…
Let {\rho} the density matrix of a mixed Gaussian state. Assuming that one of the Robertson--Schr\"odinger uncertainty inequalities is saturated by {\rho}, e.g.…
We explicitly describe the possible pairs of triangle and square densities for r-regular finite simple graphs. We also prove that every r-regular unimodular random graph can be approximated by r-regular finite graphs with respect to these…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
It has been established that the low frequency quasi-localized modes of amorphous solids at zero temperature exhibit universal density of states, depending on the frequencies as $D(\omega) \sim \omega^4$. It remains an open question whether…
Recently the problem of Unambiguous State Discrimination (USD) of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [1]. For two mixed states they are given in terms of…
We present a correction method for the density of states (DOS) obtained from the generalized ensemble simulations. The DOS is proportionally corrected to match the exact values and/or good approximations known for the system. We demonstrate…
It is shown that in a large class of disordered systems with non-degenerate disorder, in presence of non-local interactions, the Integrated Density of States (IDS) is at least H\"older continuous in one dimension and universally infinitely…
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for…
We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…
We investigate the addition of applied stress to a random block matrix model introduced by Parisi to study the Hessian matrix of soft spheres near the jamming point. In the infinite dimensional limit the applied stress translates the…
We are interested in the phase transition of the correlation function of local densities of states at mesoscopic scales of random band matrices of width $W$ in dimension $2$. As a result, we show that the local densities of states are…