相关论文: Spherically symmetric Dirac operators with variabl…
We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems (including characterization): in terms of zeros of reflection coefficient and in terms of poles of reflection…
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
We study the multi-dimensional operator $(H_x u)_n=\sum_{|m-n|=1}u_{m}+f(T^n(x))u_n$, where $T$ is the shift of the torus $\T^d$. When $d=2$, we show the spectrum of $H_x$ is almost surely purely continuous for a.e. $\alpha$ and generic…
We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.
Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how to extract information about these geometries from the…
We consider the wave equation with a distributional Dirac damping and Dirichlet boundary conditions on a compact interval. It is shown that the spectrum of the corresponding wave operator is fully determined by zeroes of an entire function.…
We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum,…
The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the…
The microscopic spectrum of the QCD Dirac operator is shown to obey random matrix model statistics in the bulk region of the spectrum close to the origin using finite-volume partition functions.
The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral…
In this paper, we investigate the Schr\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all…
In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar…
We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schr\"odinger operators with attractive $\delta$-interactions supported by infinite cones. Under the assumption that…
This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is…
This paper blends two techniques recently developed in [2] and [3] to prove the presence of absolutely continuous spectrum for the multidimensional Schrodinger operator provided that the potential is summable over trajectory with positive…
We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term…
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the the Dirac Hamiltonian and the other is…
We consider Sch\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\Delta +…