Related papers: Second microlocalization and Fredholm theory for t…
We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvent, and their subspaces consisting of self-adjoint operators. Our main results are the…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized $s$-wave) approximation, and keeping only the leading terms in the…
Basing on analogy between the three-body scattering problem and the diffraction problem of the plane wave (for the case of the short range pair potentials) by the system of six half transparent screens, we presented a new approach to the…
By mapping steady-state nonequilibrium to an effective equilibrium, we formulate nonequilibrium problems within an equilibrium picture where we can apply existing equilibrium many-body techniques to steady-state electron transport problems.…
We study the quantum transport of multi-photon Fock states in one-dimensional Bose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose an optical scheme to probe the underlying many-body states of the system by analyzing…
We apply the renormalisation-group to two-body scattering by a combination of known long-range and unknown short-range forces. A crucial feature is that the low-energy effective theory is regulated by applying a cut-off in the basis of…
Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order…
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…
This paper ascertains the global behavior of the forward and backward branches of solutions provided by the Leray-Schauder continuation theorem for orientable $\mathcal{C}^1$ Fredholm maps, as developed by the authors in [54]. Under…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
In this paper we used the Fredholm method in Schroedinger's integral equation in the investigation of the scattering effect near the center of it between a stationary quantum wave function and an electrostatic potential. Two potentials are…
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics.…
In this paper we show that in two-body scattering the scattering matrix at a fixed energy determines real-valued exponentially decreasing potentials. This result has been proved by Novikov previously, see also the work of Novikov and…
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown…
Consider a Hamiltonian action of a compact connected Lie group on a symplectic manifold $(M,\omega)$. Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten…
The Copenhagen case of the circular restricted three-body problem with oblate primary bodies is numerically investigated by exploring the Newton-Raphson basins of convergence, related to the out-of-plane equilibrium points. The evolution of…
We initiate a novel application of the quantum inverse scattering method for the 20-vertex model, building upon seminal work from Faddeev and Takhtajan on the study of Hamiltonian systems. In comparison to a previous work of the author in…