Related papers: Wave-packet continuum discretization for quantum s…
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation…
We present a general formalism describing a propagation of an arbitrary multiparticle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism…
Formalism based on complex-scaling method is developed for solving the few particle scattering problem by employing only trivial boundary conditions. Several applications are presented proving efficiency of the method in describing elastic…
We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
Quantum theoretical treatment of coherent forward scattering of light in a polarized atomic ensemble with an arbitrary angular momentum is developed. We consider coherent forward scattering of a weak radiation field interacting with a…
We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…
The wave scattering by moving particles (dynamic scattering) is a well known physical problem routinely occurring in practice. For the particles which are much smaller than the incident wavelength, the static scattering problem can be…
Understanding dynamics of localized quantum systems embedded in engineered bosonic environments is a central problem in quantum optics and open quantum system theory. We present a formalism for studying few-particle scattering from a…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. The equation is solved through Pad\'e summation,…
A proposal is made for reducing the solution of the N-particle Lippmann-Schwinger equation to that of smaller sets of particles. This consists of first writing the N-particle equation in terms of all possible $N/2$-particle…
Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…
Within the class of Derezi{\'n}ski-Enss pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known \cite{De}, we show that all entries of the $N$-body quantum scattering matrix have a well-defined…
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation…
The Lippmann-Schwinger equation for the nucleon-nucleon $t$-matrix as well as the corresponding Bethe-Goldstone equation to determine the Brueckner reaction matrix in nuclear matter are reformulated in terms of the resolvents for the total…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…