Related papers: Time delay and Calabi invariant in classical scatt…
We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, $n$-site cluster. For a particle wavepacket with small wavenumber, an expression for the time…
The Wigner-Smith time-delay of flux conserving systems is a real quantity that measures how long an excitation resides in an interaction region. The complex generalization of time-delay to non-Hermitian systems is still under development,…
We study and develop the stationary scattering theory for a class of one-body Stark Hamiltonians with short-range potentials, including the Coulomb potential, continuing our study in [AIIS1,AIIS2]. The classical scattering orbits are…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
We derive a Hamiltonian formulation of the theory of gauge invariant, linear perturbations in anisotropic Bianchi I spacetimes, and describe how to quantize this system. The matter content is assumed to be a minimally coupled scalar field…
The scattering phase-shifts are invariant under unitary transformations of the Hamiltonian. However, the numerical solution of the scattering problem that requires to discretize the continuum violates this phase-shift invariance among…
We propose a definition of a Poincar\'e algebra for a two dimensional space--time with one discretized dimension. This algebra has the structure of a Hopf algebra. We use the link between Onsager's uniformization of the Ising model and the…
We study the correlations of time delays in a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between…
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…
Based on our previous study [IS2] we develop fully the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic…
We present a theoretical framework for electromagnetic scattering by particles with a permittivity that is periodically varying in time, based on a perturbative approach. Within this framework, we derive explicit expressions for the…
We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum…
Using the concept of minimal chaotic cavities, we give the distribution of the proper delay times of $Q=-i\hbar S^\dagger \frac{\partial S}{\partial E}$ at the spectrum edge with a scattering matrix $S$ belonging to circular ensembles CE.…
Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the…
We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We calculate the leading-order scattering for a conformally massless…
Delay time is defined as a time that a wave spent in a scattering medium before it escapes, and this can be derived by the energy derivative of the phase of the scattering wave. Considering the complex reflection amplitude…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
Starting with a time-independent Hamiltonian $h$ and an appropriately chosen solution of the von Neumann equation $i\dot\rho(t)=[ h,\rho(t)]$ we construct its binary-Darboux partner $h_1(t)$ and an exact scattering solution of…
Different from the usual harmonic oscillator, the time-decaying harmonic oscillator accelerates particles and generates scattering states. We study one of the multidimensional inverse scatterings in this two-body quantum system perturbed by…
A causality problem in the time-dependent scattering of classical waves from point scatterers is pointed out and analyzed. Based on an alternative model, the leading pole approximation of the exact scattering matrix of the square well…