Related papers: Isospectral Dirac operators
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to…
We consider discrete Schr\"odinger operators with real periodic potentials on periodic graphs. The spectra of the operators consist of a finite number of bands. By "rolling up" a periodic graph along some appropriate directions we obtain…
In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the…
The purpose of this note is to describe a unified approach to the fundamental results in the spectral theory of boundary value problems, restricted to the case of Dirac type operators. Even though many facts are known and well presented in…
Self-adjoint rank two commuting ordinary differential operators are studied in this paper. Such operators with trigonometric, elliptic and rapid decay coefficients corresponding to hyperelliptic spectral curves are constructed. Some…
We compute the Dirac spectrum of SU(3) for a one parameter family of Dirac operators, including the Levi-Civita, cubic, and trivial Dirac operators. We then proceed to compute the spectral action for the entire family.
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…
We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.
We study families of Dirac-type operators, with compatible perturbations, associated to wedge metrics on stratified spaces. We define a closed domain and, under an assumption of invertible boundary families, prove that the operators are…
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped…
For a class of zero order pseudodifferential operators we find the asymptotics of eigenvalues converging to a non-isolated tip of the essential spectrum.
In this work we study traces of spectral decompositions corresponding to self adjoint elliptic pseudo-differential operators of distributions in the classes of Soboloev-Liouville and Nikolskii-Besov
We discuss abstract Birman-Schwinger principles to study spectra of self-adjoint operators subject to small non-self-adjoint perturbations in a factorised form. In particular, we extend and in part improve a classical result by Kato which…
This text is a slightly expanded version of my 6 hour mini-course at the PDE-meeting in \'Evian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted…
We give more details about an integrable system in which the Dirac operator D=d+d^* on a finite simple graph G or Riemannian manifold M is deformed using a Hamiltonian system D'=[B,h(D)] with B=d-d^* + i b. The deformed operator D(t) = d(t)…
We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x) -i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-time dimensions, is underlined by a certain generalization of supersymmetric quantum…
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of all operators from that family coincides. As shown recently…
This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl…
Using the graded eigenvalue method and a recently computed extension of the Itzykson-Zuber integral to complex matrices, we compute the $k$-point spectral correlation functions of the Dirac operator in a chiral random matrix model with a…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…