Related papers: Eigenvalues and Eigenfunctions of q-Dirac System
Recent results on the spectral properties of the Hermitian Wilson-Dirac operator are presented.
This paper deals with q-analogue of sampling theory associated with q-Dirac system. We derive sampling representation for transform whose kernel is a solution of this q-Dirac system. As a special case, three examples are given.
We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement…
We perform a comprehensive study of the properties of Dirac eigenvalue spectrum in QCD as a function of temperature on the lattice. In addition to effects due to interplay between interactions and disorder inherently present in a many-body…
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization. Also, for the study of open quantum systems, non-Hermitian systems have attracted much attention. As mathematical models for such systems,…
It has been observed that a quantum mechanical theory need not to be Hermitian to have a real spectrum. In this paper we obtain the eigenvalues of a Dirac charged particle in a complex static and spherically symmetric potential.…
The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good…
In this note, we prove some combinatorial identities and obtain a simple form of the eigenvalues of $q$-Kneser graphs.
This is an informal and mostly expository note describing some asymptotic behavior and qualitative properties of the q-binomial coefficients. The results are mostly not new, but the overall story we present does not seem to be well known --…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…
In this paper we study in detail some spectral properties of the magnetic discrete Laplacian. We identify its form-domain, characterize the absence of essential spectrum and provide the asymptotic eigenvalue distribution.
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
We discuss some properties of zero and near-zero modes of the Dirac operator, as observed in a recent simulation of 2-flavor QCD. The quarks have been implemented with the so-called Chirally Improved Dirac operator, which obeys the…
In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…
This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…
In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues…
In this paper we consider the problem of the occurrence of spurious modes when computing the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an atom or a molecule. We present recent mathematical…
In this paper, we investigate the spectral properties of Andr\'asfai graphs, focusing on key parameters: the second-largest and smallest eigenvalues, the number of distinct eigenvalues, and the multiplicities of the eigenvalues 1 and -1.…
It is popular to discuss low energy physics in lattice gauge theory in terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra.