Related papers: Dirac bag model on thin domains: a microlocal view…

The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay,…

The operator associated to the angular part of the Dirac equation in the Kerr-Newman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational…

We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.

We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a connected compact n-dimensional manifold without boundary. The eigenvalues of the principal symbol are…

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…

We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of eigenfunctions…

We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - and therefore on the volume of the domain - must fail. Here we…

In this work we prove that the eigenvalues of the $n$-dimensional massive Dirac operator $\mathscr{D}_0 + V$, $n\ge2$, perturbed by a possibly non-Hermitian potential $V$, are localized in the union of two disjoint disks of the complex…

We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected…

In this paper we consider Dirac operators in $\mathbb R^n$, $n\geq2$, with a potential $V$. Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the operator, we prove a limiting absorption principle for the…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…

We prove that the massless Dirac operator in $\mathbb{R^3}$ with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued potentials are considered as well.

We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's…

We consider the Laplace operator in a planar waveguide, i.e., an infinite two-dimensional straight strip of constant width, with particular types of Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian…

This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary condition. The thin set is taken to be a tubular neighborhood of a planar smooth domain. We show that, as the…

We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The…

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a…

We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e. a true crossing of two Bloch bands. The…