Related papers: Finite Energy Sum Rules in Potential Scattering
The multichannel scattering problem for the stationary Schr\"{o}dinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the…
We present a possible way of computing resonance poles and modes in scattering theory. Numerical examples are given for the scattering of electromagnetic waves by finite-size photonic crystals.
We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In the…
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $\phi^3$-theory. This formalism greatly facilitates the…
The analytic properties of the Jost functions are fundamental in quantum scattering theory and in the analytic continuation of the scattering matrix into the complex energy plane. In this work, the analyticity of the Jost functions is…
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
In this work, we discuss the scattering theory of local, relativistic quantum fields with indefinite metric. Since the results of Haag--Ruelle theory do not carry over to the case of indefinite metric, we propose an axiomatic framework for…
Transition to the reflective scattering mode results in the increasing role of the multiplicity fluctuations of quantum origin and its asymptotic dominance. We note here the feasibility to experimentally detect presence of quantum…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…
We construct the exact position representation of a deformed quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and scattering from a step potential, among others. In…
We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering…
The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the…
We analyze the results of an experimental setup that consist of two statistically independent laser beams that cross, interfere and end at detectors. At the beam intersection we place a thin wire at the center of a dark interference fringe…
Integrable boundary Toda theories are considered. We use boundary one-point functions and boundary scattering theory to construct the explicit solutions corresponding to classical vacuum configurations. The boundary ground state energies…
We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on…
We present an exact procedure that allows one to calculate the scattering lenth for any potential expressed as an algebraic sum of inverse powers of the interatomic distance. We apply it to (12, $s$) Lennard-Jones potentials, with different…
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…