Related papers: An Introduction to Scattering Theory
For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schr\"{o}dinger operator $H=H_0+V$, where $H_0=(-\Delta)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We…
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…
Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert…
We consider the scalar wave equation $\square_g \phi$ and the linearized Einstein-scalar field system around generalized Kasner spacetimes with spatial topology $\mathbb{T}^D$. In suitable regimes for the Kasner exponents, it is known that…
Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different…
In a recent Letter, Cummer et al. give a description of material parameters for acoustic wave propagation giving rise to a 3D spherical cloak, and verify the cloaking phenomenon on the level of scattering coefficients. A similar…
The transfer matrix ${\mathbf{M}}$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system with a time-dependent non-Hermitian Hamiltonian. This leads to a dynamical…
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…
We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…
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…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is…
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
The object of study in this paper is the on-shell scattering matrix $S(E)$ of the Schr\"odinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of $S(E)$ in the…
The scattering theory of Lax and Phillips, originally developed to describe resonances associated with classical wave equations, has been recently extended to apply as well to the case of the Schroedinger equation in the case that the wave…