Related papers: Adiabatic Approximation, Semiclassical Scattering,…
Most discussions of chaotic scattering systems are devoted to two-dimensional systems. It is of considerable interest to extend these studies to the, in general, more realistic case of three dimensions. In this context, it is conceptually…
Propagation of light through media with a complex refractive index in which gain and loss are engineered to be $PT$ symmetric has many remarkable features. In particular the usual unitarity relations are not satisfied, so that the…
We explore the absorption and scattering properties of one dimensional parity-time ($\mathcal{PT}$)-symmetric photonic crystal. In addition to the familiar transmittance and reflectance, we give the definition of the generalized absorptance…
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The…
In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between…
We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a non-adiabatic scattering problem. In particular, we consider scattering on a magnetic field…
Non-Hermitian, one-dimensional potentials which are also non-local, allow for scattering asymmetries, namely, asymmetric transmission or reflection responses to the incidence of a particle from left or right. The symmetries of the potential…
We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
Proceeding from optical analogy we propose a new physical interpretation of unitarity saturation leading to antishadowing as a reflective scattering. This interpretation of antishadowing is related to the non-perturbative aspects of strong…
For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special…
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010)], and on the formulation of the degenerate adiabatic theorem, along with its…
The multi-channel Coulomb scattering problem in the adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-zero asymptotic behavior at large internuclear separations. The asymptotic solutions at…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
To understand the recently observed mysterious non-adiabatic energy transfer for hyperthermal H atom scattering from a semiconductor surface, Ge(111)c(2*8), we present a mixed quantum-classical non-adiabatic molecular dynamics model based…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed matter physics to high-energy physics because of its non-perturbative…