Related papers: Compact submanifolds supporting singular interacti…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model.…
We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient…
Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently…
This work proposes a reconstruction of the quantum field theory (QFT) scattering framework: the path integral governs an interaction kernel region, while the Hilbert space encodes asymptotic free boundary conditions. We critically reexamine…
Bound states arise in many interactions among elementary field states, and are represented by poles in the scattering matrix. The emergent nature of bound states suggests that they play a perhaps under-appreciated role in specifying the…
Salpeter equations with potential functions rising to infinity in configuration space do not automatically predict stable bound states. For this to happen, also the Lorentz behaviour of the involved Bethe-Salpeter kernels is crucial. At…
A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the…
We propose two new strategies to construct a family of non-integrable spin chains with exactly solvable subspace based on the idea of quasiparticle excitations from the matrix product vacuum state. The first one allows the boundary…
We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $ \ell $ in the common boundary. We show that such a system has at least one bound state for any $ \ell>0 $. We find the corresponding…
The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue. In this work, we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of…
In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy…
Using an approach that allows us to probe the electronic structure of strongly pinched-off quantum point contacts (QPCs), we provide evidence for the formation of self-consistently realized bound states (BSs) in these structures. Our…
We present a theoretical formulation of the one-electron problem constrained on the surface of a cylindrical tubule with varying diameter. Because of the cylindrical symmetry, we may reduce the problem to a one-dimensional equation for each…
Quantum correlations between distant particles remain enigmatic since the birth of quantum mechanics. Here we predict a novel kind of bound quantum state in the simplest one-dimensional setup of two interacting particles in a box.…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
In this paper, we consider the quantum version of the hamiltonian model describing friction introduced in [BDB]. This model consists of a particle which interacts with a bosonic reservoir representing a homogeneous medium through which the…
We consider a quantum particle in a waveguide which consists of an infinite straight Dirichlet strip divided by a thin semitransparent barrier on a line parallel to the walls which is modeled by a $\delta$ potential. We show that if the…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…