Related papers: Non-local relativistic $\delta$-shell interactions

We show that the one-dimensional Dirac operator with quite general point interaction may be approximated in the norm resolvent sense by the Dirac operator with a scaled regular potential of the form $1/\varepsilon~h(x/\varepsilon)\otimes…

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials $V$ decaying like $\langle x \rangle ^{-\d}$ at infinity for some $\d >0$. By…

We investigate the spectrum of the Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a smooth compact hypersurface in $\mathbb{R}^n$ without boundary. We prove that when the tubular neighborhood…

A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…

We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy…

We derive a lower bound on the location of global extrema of eigenfunctions for a large class of non-local Schr\"odinger operators in convex domains under Dirichlet exterior conditions, featuring the symbol of the kinetic term, the strength…

Let -\Delta denote the Dirichlet Laplace operator on a bounded open set in \mathbb{R}^d. We study the sum of the negative eigenvalues of the operator -h^2 \Delta - 1 in the semiclassical limit h \to 0+. We give a new proof that yields not…

Let $(M^{n}, g)$ denote a Riemannian spin manifold of dimension $n$ with Dirac operator $D$ induced from the Levi-Cevita connection acing on the spinor bundle, $S$ ($D$ is also called the Atiyah-Singer Operator). Let $c: Cl(TM^{n})…

This paper concerns Hodge-Dirac operators D = d + $\delta$ acting in L p ($\Omega$, {\lambda}) where $\Omega$ is a bounded open subset of R n satisfying some kind of Lipschitz condition, {\lambda} is the exterior algebra of R n , d is the…

We consider the linear Dirac operator with a (-1)-homogeneous locally periodic potential that varies with respect to a small parameter. Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove…

The transmission poles of $N$ number of identical Dirac delta potentials placed periodically in one-dimension are examined in the complex-energy plane. The numerical results show that the imaginary part of the poles scales with 1/N. An…

We extend and clarify the large-charge expansion of the conformal dimension $\Delta_Q$ of the lowest operator of charge $Q$ in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an…

We investigate spectral properties of Gesztesy-\v{S}eba realizations D_{X,\alpha} and D_{X,\beta} of the 1-D Dirac differential expression D with point interactions on a discrete set $X=\{x_n\}_{n=1}^\infty\subset \mathbb{R}.$ Here $\alpha…

In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…

We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We use a random matrix model approach to calculate analytically all correlation functions at weak and strong non-Hermiticity for…

Eigenvalue behaviors of Schr\"odinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$, and lower…

The spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background built from two Dirac delta potentials is studied. A distinction will be made between mass-spike and…

We report on some recent work of the authors showing the relations between singular (point) perturbation of the Laplacian and the dynamical system describing a charged point particle interacting with the self-generated radiation field (the…

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive…