相关论文: Bound states in point-interaction star-graphs

We prove an approximation result showing how operators of the type $-\Delta -\gamma \delta (x-\Gamma)$ in $L^2(\mathbb{R}^2)$, where $\Gamma$ is a graph, can be modeled in the strong resolvent sense by point-interaction Hamiltonians with an…

Weak-strong coupling duality relations are shown to be present in the quantum-mechanical many-body system with the interacting potential proportional to the pair-wise inverse-squared distance in addition to the harmonic potential. Using…

We discuss the problem of constructing self-adjoint and lower bounded Hamiltonians for a system of $n>2$ non-relativistic quantum particles in dimension three with contact (or zero-range or $\delta$) interactions. Such interactions are…

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…

A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…

We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has…

We consider two particles interacting via a contact interaction that are constrained to a sphere, or $S^2$. We determine their spectrum to arbitrary precision and for arbitrary angular momentum. We show how the non-inertial frame leads to…

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…

We show that in d>1 dimensions the N-particle kinetic energy operator with periodic boundary conditions has symmetric eigenfunctions which vanish at particle encounters, and give a full description of these functions. In two and three…

We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we…

At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…

We consider a Hamiltonian describing the weak decay of the massive vector boson Z0 into electrons and positrons. We show that the spectrum of the Hamiltonian is composed of a unique isolated ground state and a semi-axis of essential…

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…

In the paper we study the discrete spectrum of a pair of quantum two-dimensional waveguides having common boundary in which a window of finite length is cut out. We study the phenomenon of new eigenvalues emerging from the threshold of the…

Quantum graphs without interaction which contain equilateral cycles possess "topological" bound states which do not correspond to zeroes of one of the two variants of the secular equation for quantum graphs. Instead, their eigenvalues lie…

We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…

We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…

We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex…

We consider the Hamiltonian for a charged particle in a harmonic potential in the presence of a magnetic field. The most symmetric case depends on one parameter, the variation of which leads from a spectrum bounded from below to an…

We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…