Related papers: Multipoint scatterers with zero-energy bound state…
We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions $d=2$ and $d=3$. We show that for these scatterers: 1) each positive energy $E$ is a transmission…
We investigate the low-energy behavior of the resolvent of Schrodinger operators with finitely many point interactions in three dimensions. We also discuss the occurrence and the multiplicity of zero energy obstructions.
We study the existence of bound states in the continuum for a system of n two-level quantum emitters, coupled with a one-dimensional boson field, in which a single excitation is shared among different components of the system. The emitters…
We propose a criterion to determine the existence of zero-energy edge states for a class of particle-hole symmetric systems. A loop is assigned for each system, and its topology and a symmetry play an essential role. Applications to d-wave…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering state is not in the form of the Bethe eigenstate in the sense that the wave-number set of the incoming plane wave is not conserved during the…
The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3->3 scattering amplitude for spinless particles, which contains an…
The renormalized energy density of a massless scalar field defined in a D-dimensional flat spacetime is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the…
We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the 2-dimensional case, we show that in the weak coupling regime the eigenvalue spacing distribution coincides with that of the spectrum of…
Under certain restrictions on pair--potentials it is proved that the eigenvalues in the three--particle system are absorbed at zero energy threshold if there is no negative energy bound states and zero energy resonances in particle pairs.
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary…
We consider 1-equivariant wave maps from \R \times (\R^3 \setminus B) to S^3 where B is a ball centered at 0, and the boundary of B gets mapped to a fixed point on S^3. We show that 1-equivariant maps of degree zero scatter to zero…
We investigate localization of low-energy modes of the Laplacian with a point scatterer on a rectangular plate. We observe that the point scatterer acts as a barrier confining the low-level modes to one side of the plate while assuming the…
We introduce the concept of multi-point propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a non-linearly evolved Fourier mode depends on…
We study kinetics of electrons, scattered by heavy particles undergoing slow diffusive motion. In a three-dimensional space we claim the existence of the crossover region (on the energy axis), which separates the states with fast diffusion…
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting…
We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in…
In the three-body problem with positive energy, solutions which avoid triple collision have the property that the size of the triangle formed by the bodies tends to infinity as $t\rightarrow \pm\infty$. Furthermore, the triangles have…
We generalize the concept of parity-time symmetric structures with the goal to create meta-atoms exhibiting extraordinary abilities to overcome the presumed limitations in the scattering of overall lossless particles, such as non-zero…
The PXP model is paradigmatic in the field of quantum many-body scars. This model has a number of zero-energy eigenstates that is exponentially large in system size. Lower bounds on the number of zero-energy eigenstates are obtained for…