‎‎‎This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = begin{pmatrix}‎ ‎A & B \‎ ‎C & D_0‎ ‎end{pmatrix} $ to set of block normal matrix $G_{D}$ (as same as $G_{D_0}$ except block $D$ which is replaced by block $D_0$)‎, ‎in which $A in mathbb{C}^{ntimes n}$ is invertible‎, ‎$ B in mathbb{C}^{ntimes m}‎, ‎C in mathbb{C}^{mti...

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic many-body quantum chaos. In addition, partial factors (PSFFs) can be defined which refer to subsystems the system. They provide unique insights into eigenstate systems, as we show in an analysis on basis random matrix theory and thermalization hypothesis. We propose protocol that allows measurem...

a b s t r a c t introduction:we investigated differential role of cortical and subcortical regions in verbal and non-verbal sound processing in ten patients who were native speakers of persian with unilateral cortical and/or unilateral and bilateral subcortical lesions and 40 normal speakers as control subjects. methods: the verbal tasks included monosyllabic, disyllabic dichotic and diotic tas...

We establish Fredholm properties for a class of nonlocal differential operators. Using mild convergence and localization conditions on the nonlocal terms, we also show how to compute Fredholm indices via a generalized spectral flow, using crossing numbers of generalized spatial eigenvalues. We illustrate possible applications of the results in a nonlinear and a linear setting. We first prove th...

We study the properties of low-lying Dirac modes in quenched compact QED at β = 1.01, employing 12 ×Nt (Nt = 4, 6, 8, 10, 12) lattices and the overlap formalism for the fermion action. We pay attention to the spatial distributions of low-lying Dirac modes below/above the “phase transition temperature” Tc. Near-zero modes are found to have universal anticorrelations with monopole currents, and a...

We use Brownian motion ideas to study Schriidinger operators H = +A + V on Lp(R”). In particular: (a) We prove that limt+m t-l In /I e&H j111.9 is p-independent for a very large class of V’s where 11 A ll,,,n = norm of A as an operator from L’ to L”. (b) For Y > 3 and V E LY/~--E n L”Ip+c, we show that sup jl eetH Ilm,m -: (D if and only if H has no negative eigenvalues or zero energy resonance...

We prove a localization theorem for continuous ergodic Schrödinger operators Hω := H0+Vω, where the random potential Vω is a nonnegative Anderson-type perturbation of the periodic operator H0. We consider a lower spectral band edge of σ(H0), say E = 0, at a gap which is preserved by the perturbation Vω . Assuming that all Floquet eigenvalues of H0, which reach the spectral edge 0 as a minimum, ...

We define a set of operators which localize in both time and frequency. Tltese operators are similar to but different from the low-pass time-liting operators, the singular functions of which are the prolate spheroidal wave functions. Our construction differs from the usual ap proach in that we treat the time-frequency plane as one geometric whole (phase space) rather than as two separate spaces...