Related papers: Spectral Singularities and Zero Energy Bound State…
A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{PT}$-symmetric Schr\"odinger equations that exhibit spontaneous $\mathcal{PT}$ symmetry breaking despite…
It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials…
The scattering of a nonrelativistic electron on a narrow solenoid of finite length is considered. In this case, the magnetic field outside the solenoid is not zero. Using the eikonal approximation, the differential and total cross sections…
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…
Bound state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss…
Non-Hermitian systems characterized by suitable spatial distributions of gain and loss can exhibit "spectral singularities" in the form of zero-width resonances associated to real-frequency poles in the scattering operator. Here, we study…
We theoretically study a non-magnetic impurity effect on the vortex bound states of a multi-quantum vortex. The zero-energy peak of the local density of states is investigated for vortex cores with the winding numbers 2 and 4 within the…
The large values of the singlet and triplet two-nucleon scattering lengths locate the nuclear system close to the unitary limit. This particular position strongly constrains the low-energy observables in the three-nucleon system as…
Scattering theory for p-forms on manifolds with cylindrical ends has a direct interpretation in terms of cohomology. Using the Hodge isomorphism,the scattering matrix at low energy may be regarded as operator on the cohomology of the…
We calculate the energy spectrum of quasiparticles trapped by a domain wall separating different time reversal symmetry-breaking ground states in a hexagonal superconductor, such as UPt$_3$. The bound state energy is found to be strongly…
In hadron physics, molecular-like multihadron states can interact with compact multiquark states. The latter are modeled as bare states in the Hilbert space of a potential model. In this work, we study several potential models relevant to…
Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states $\nu_F$ and the resistivity $\rho$, occurring when the Fermi level $E$ crosses a bottom $E_N$ of some subband of transverse quantization. We…
A grain boundary which separates domains with different orientation along the c-axis is analyzed. The coupling of two parallel superconducting planes whose order parameters are rotated leads to interesting properties which are expected to…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
We perform a large suite of $N=4$ numerical scattering experiments between two identical binaries consisting of identical point particles in a (continuous) background potential. For investigative purposes, albeit without loss of generality,…
Three-boson Efimov physics is well known in the bound-state regime, but far less in the three-particle continuum at negative two-particle scattering length where Efimov states evolve into resonances. They are studied solving rigorous…
In this work we investigate the quantum dynamics of an electric dipole in a $(2+1)$-dimensional conical spacetime. For specific conditions, the Schr\"odinger equation is solved and bound states are found with the energy spectrum and…
Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high temperature…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
We consider the effects of bound atomic electrons scattered by solar neutrinos due to the electromagnetic properties of neutrinos. This necessiate considering the recoil of atomic nucleus, which should be considered in the momentum…