Related papers: A criterion for the existence of non-real eigenval…
We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…
We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These bounds are applied to obtain new results on the distribution of…
We consider wave functions in the Hilbert space $\mathcal{H}=L^2(\mathbb{R}^3,\mathbb{C}^4)$ of a single Dirac particle, specifically from the positive-energy subspace $\mathcal{H}_+$ of the free Dirac Hamiltonian. Over the decades, various…
We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using…
There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random non-Hermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a…
In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(\Omega; \mathbb{C}^4)$, where $\Omega \subset \mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a particular discrete symmetry. Applications to the PT-symmetric…
We consider the operator $ L = - (d/dx)^2 + x^2 y + w(x) y , y \in L^2(\mathbb{R}) $, where $ w(x) = s [ \delta(x - b) - \delta(x + b)], b \neq 0,$ real, $s \in \mathbb{C}$. This operator has a discrete spectrum: eventually the eigenvalues…
Magnetic monopoles --- particles that behave as isolated north or south magnetic poles --- have been the subject of speculation since the first detailed observations of magnetism several hundred years ago. Numerous theoretical…
In this paper the spectral properties of Dirac operators $A_\eta$ with electrostatic $\delta$-shell interactions of constant strength $\eta$ supported on compact smooth surfaces in $\mathbb{R}^3$ are studied. Making use of boundary triple…
We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet…
For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
The Reissner-Weyl-Nordstr\"om (RWN) spacetime of a point nucleus features a naked singularity for the empirically known nuclear charges $Ze$ and masses $M = A(Z,N)m_{\mathrm{p}}$, where $m_{\mathrm{p}}$ is the proton mass and $A(Z,N)\approx…
In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$. We impose the Neumann boundary condition on a disc window of radius $a$ and Dirichlet…
We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov-Shabat) operator on the real line with general analytic potential. We provide Bohr-Sommerfeld quantization conditions near energy levels where the potential exhibits…
In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random…
The purpose of this paper is to prove that the spectrum of the non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433--6443) has interior points. We do this by first recalling that the…
In this article, we prove that on any compact spin manifold of dimension m congruent 0,6,7 mod 8, there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by…