LOWER BOUNDS ON THE LOWEST SPECTRAL GAP OF SINGULAR POTENTIAL HAMILTONIANS (2008)
We analyze Schrodinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two...
We consider Schr\"odinger operators in $L^2(\mathbb{R}^3)$ with a singular interaction supported by a finite curve $\Gamma$. We present a proper definition of the operators and study their...
Spectral gap of segments of periodic waveguides (2006)
Kondej, Sylwia, Veselic', Ivan
We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of $L$ periodicity cells,...
Lower bounds on the lowest spectral gap of singular potential Hamiltonians (2006)
Kondej, Sylwia, Veselic', Ivan
We analyze Schr\"odinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two...
On relations between stable and Zeno dynamics in a leaky graph decay model (2005)
Exner, Pavel, Ichinose, Takashi, Kondej, Sylwia
We use a caricature model of a system consisting of a quantum wire and a finite number of quantum dots, to discuss relation between the Zeno dynamics and the stable one which governs time evolution...
Scattering by local deformations of a straight leaky wire (2004)
We consider a model of a leaky quantum wire with the Hamiltonian $-\Delta -\alpha \delta(x-\Gamma)$ in $L^2(\R^2)$, where $\Gamma$ is a compact deformation of a straight line. The existence of wave...
Schroedinger operators with singular interactions: a model of tunneling resonances (2003)
We discuss a generalized Schr\"odinger operator in $L^2(\mathbb{R}^d), d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It...
Leaky quantum wire and dots: a resonance model (2003)
We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in $L^2(\mathbb{R}^2)$ with an attractive singular perturbation supported by a line and a finite number...
Bound states due to a strong $\delta$ interaction supported by a curved surface (2002)
We study the Schr\"odinger operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\R^3)$ with a $\delta$ interaction supported by an infinite non-planar surface $\Gamma$ which is smooth, admits a...
We study the Laplacian in $L^2(\mathbb{R}^3)$ perturbed on an infinite curve $\Gamma$ by a $\delta$ interaction defined through boundary conditions which relate the corresponding generalized boundary...
On Eigenvalues Problem for Self-adjoint Operators with Singular Perturbations (2001)
We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singular cases. We...