Related papers: Estimates for the scattering map associated to a t…
The semi-classical limit of quantum-mechanical scattering in two dimensions (2D) is developed. We derive the Wentzel-Kramers-Brillouin and Eikonal results for 2D scattering. No backward or forward glory scattering is present in 2D. Other…
We discuss scattering from pairs of isospectral quantum graphs constructed using the method described in [1, 2]. It was shown in [3] that scattering matrices of such graphs have the same spectrum and polar structure, provided that infinite…
We propose an effectively nonperturbative approach to calculating scattering amplitudes in the perturbative regime. We do this in a discretized momentum space by using the QSE method to calculate all the contributions (to all orders in…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…
We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann-Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation…
Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
Effective Hamiltonians can explain in a much simpler way the physics behind a scattering process. Chaotic scattering is directly related to Lorentzian Hamiltonians which, because of their properties, can be reduced to a $2\times 2$ matrix…
We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its…
Using the properties of random M\"{o}bius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the…
We study forward and backward pi-pi scattering within a QCD model based on the Dyson--Schwinger, Bethe--Salpeter equations truncated to the rainbow-ladder level. Our microscopic relativistic quark formulation preserves chiral symmetry and…
We present an iterative algorithm to compute numerical approximations of the potential for the Schr\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle,…
When the spatial dimensions $n$=2, the initial data $u_0\in H^1$ and the Hamiltonian $H(u_0)\leq 1$, we prove that the scattering operator is well-defined in the whole energy space $H^1(\mathbb{R}^2)$ for nonlinear Schr\"{o}dinger equation…
We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are $n$ barriers and wells with statistically independent intensities and with a spatial extension $\l_c$ which may contain an…
As a step toward satisfactory understanding of the quantum dynamics of Dirichlet \break (D-) particles, the amplitude for the basic process describing the scattering of two quantized D-particles is computed in bosonic string theory. The…
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…