The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation of the spectrum of a Schrödinger operator with a disordered potential. Unlike plane waves or Bloch waves that arise as Schrödinger eigenfunctions for period...

We analyze the localization properties for eigenvectors of the Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition. Studying the characteristic differences between the Z3 sectors above the critical temperature T(c), we find indications for the presence of calorons.

We analyze the eigenvalues and eigenvectors of the staggered Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition using the Lüscher-Weisz gauge action. The spectral and localization properties of the low-lying eigenmodes show characteristic differences between the Z3 sectors above the critical temperature Tc. These findings can be interpreted in terms of ...

In the present article, we define Mexican hat wavelet Stieltjes transform (MHWST) by applying concept of [9]. The proposed serves as a centralized method to analyze both discrete and continuous time-frequency localization. Besides formulation all fundamental results, reconstruction formula is also obtained for MHWST. Further, unified approach applied obtain necessary sufficient conditions same....

We calculate exactly the Lyapunov exponent and the integrated density of states for the random string operator whose density and elastic compliance are functions of a binary Markov chain. For all values of interest short and long wave asymptotic expansions are obtained. Finally we discuss conditions of propagation and localization of waves in a binary random medium.

This paper has two immediate goals: Developing a simplified lumped parameters model that approximates the distributed parameters structure of steam superheaters; and developing a structure for fault detection and localization using actuators fault detection that can inform the operator about the faults following actuators blocking or changes in the burning process and heat transfer conditions. ...

The Virasoro operations in Witten’s theory of two-dimensional topological gravity have a homotopy-theoretic interpretation as endomorphisms of an ordinary cohomology theory with coefficients in a localization of I. Schur’s ring ∆ of Q-functions. The resulting theory has many of the features of a vertex operator algebra.

We study the correspondence between phase-space localization of quantum (quasi-)energy eigenstates and classical correlation decay, given by Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown that scarred (quasi-)energy eigenstates are correlated: Pairs of eigenstates strongly overlap in phase space (scar in same phase-space regions) if the difference of their eigene...

We introduce a new approach for the localization of 3D anatomical point landmarks based on 3D parametric intensity models which are directly fit to the image. We propose an analytic intensity model based on the Gaussian error function in conjunction with 3D rigid transformations as well as deformations to efficiently model tip-like structures of ellipsoidal shape. The approach has been successf...

Local integrals of motion play a central role in the understanding many-body localization quantum systems one dimension subject to random external potential, but question how these local change deterministic quasiperiodic potential is that has received significantly less attention. Here we develop powerful new implementation continuous unitary transform formalism and use this method directly co...