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View article: On Schrödinger operators with oblique transmission conditions on non-smooth curves
On Schrödinger operators with oblique transmission conditions on non-smooth curves Open
In a recent paper Behrndt, Holzmann, and Stenzel introduced a new class of two-dimensional Schrödinger operators with oblique transmissions along smooth curves. We extend most components of this analysis to the case of Lipschitz curves.
View article: On Neumann-Poincaré operators and self-adjoint transmission problems
On Neumann-Poincaré operators and self-adjoint transmission problems Open
We discuss the self-adjointness in $L^2$-setting of the operators acting as $-\nabla\cdot h\nabla$, with piecewise constant functions $h$ having a jump along a Lipschitz hypersurface $Σ$, without explicit assumptions on the sign of $h$. We…
View article: Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions
Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions Open
We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the inter…
View article: A Poincaré-Steklov map for the MIT bag model
A Poincaré-Steklov map for the MIT bag model Open
The purpose of this paper is to introduce and study Poincaré-Steklov (PS) operators associated to the Dirac operator $D_m$ with the so-called MIT bag boundary condition. In a domain $Ω\subset\mathbb{R}^3$, for a complex number $z$ and for …
View article: Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains
Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains Open
Given an open set Ω⊂R3, we deal with the spectral study of Dirac operators of the form Ha,τ = H + Aa,τδ∂Ω, where H is the free Dirac operator in R3 and Aa,τ is a bounded, invertible, and self-adjoint operator in L2(∂Ω)4, depending on param…
View article: Spectral Properties of the Dirac Operator coupled with $δ$-Shell Interactions
Spectral Properties of the Dirac Operator coupled with $δ$-Shell Interactions Open
Let $Ω\subset\mathbb{R}^3$ be an open set, we study the spectral properties of the free Dirac operator $\mathcal{H}$ coupled with the singular potential $V_κ=(εI_4 +μβ+η(α\cdot N))δ_{\partialΩ}$. The open set $Ω$ can be either a $\mathcal{…
View article: Spectral Asymptotic for the Infinite Mass Dirac Operator in bounded domain
Spectral Asymptotic for the Infinite Mass Dirac Operator in bounded domain Open
In this paper, we study a singular perturbation of a problem used in dimension two to model graphene or in dimension three to describe the quark confinement phenomenon in hadrons. The operators we consider are of the form $H + MβV (x)$, wh…