Related papers: Adiabatic Approximation, Semiclassical Scattering,…
We compare the coupled channels procedure to the semiclassical approach to describe two-body emission processes, in particular $\alpha$-decay, from deformed nuclei within the propagator method. We express the scattering amplitudes in terms…
In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched…
We develop an adiabatic formalism to study the Hawking phenomenon from the perspective of Unruh-DeWitt detectors moving along non-stationary, non-asymptotic trajectories. When applied to geodesic trajectories, this formalism yields the…
We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary…
While the hydrogen molecular ion is the simplest molecule in nature and very well studied in all of its properties, it remains an interesting system to use for explorations of fundamental questions. One such question treated in this study…
Scattering by an isolated defect embedded in a dielectric medium of two dimensional periodicity is of interest in many sub-fields of electrodynamics. Present approaches to compute this scattering rely either on the Born approximation and…
Invisibility devices exploit ambiguities in the inverse scattering problem of light in media. Scattering also serves as an important general tool to infer information about the structure of matter. We elucidate the nature of scattering…
We introduce a perturbative approach to solving the time dependent Schroedinger equation, named adiabatic perturbation theory (APT), whose zeroth order term is the quantum adiabatic approximation. The small parameter in the power series…
We study smooth, caustic-free, chaotic semiclassical dynamics on two-dimensional phase space and find that the dynamics can be approached by an iterative procedure which constructs an approximation to the exact long-time semiclassical…
Employing tight-binding approximation we derive a transfer matrix formalism for one-dimensional single photon transport through a composite scattering center, which consists of parallel connected resonator optical waveguides. By solving the…
We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered…
In non-Hermitian scattering problems the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and…
We formulate a hyperspherical approach within standard configuration interaction calculations aiming at a description of large-scale dynamics of $N$-particle system. The channel wave function and the adiabatic channel energy are determined…
A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…
In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In…
A general formalism is worked out for the description of one-dimensional scattering by non-local separable potentials and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term…
$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by…
Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…
We introduce a new class of $\mathcal{PT}$-symmetric complex crystals which are almost transparent and one-way reflectionless over a broad frequency range around the Bragg frequency, i.e. unidirectionally invisible, regardless of the…