Related papers: Emergence of Classical Orbits in Few-Cycle Above-T…
The electron localization in the dissociation of the asymmetric charged molecular ion HeH$^{2+}$ exposed to an intense few-cycle laser pulse is studied by solving numerically the 3D time-dependent Schr\"odinger equation. By varying the…
We analyze the solutions of the Schr\"odinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that…
We consider relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry. We utilise Fermi coordinates adapted to the time-like geodesic to describe the low-energy physics in…
We discuss the use of a class of exact finite energy solutions to the vacuum source-free Maxwell equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged point particles. These compact…
The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to yield agreement with the probability density distribution of…
The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters.…
Classical electrodynamics including classical electromagnetic zero-point radiation leads to a ground state and resonant excited states for a charged particle in a Coulomb potential. These resonant states correspond to integer values of the…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
A unitary model describing the electronic transitions in an atom subject to a strong high frequency laser pulse is proposed. The model fully accounts for the initial state coupling with the continuum spectrum. Continuum-continuum as well as…
When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical…
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and…
Several gage-equivalent forms (including some novel ones) of the Schroedinger equation for a hydrogenlike atom in a time-dependent electric field of a laser pulse are presented. These forms allow to develop a perturbation theory for both…
Developing an analytical theory for atomic coherence driven by ultrashort laster pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate, closed-form…
We study here a number of mathematical problems related to our recently introduced neoclassical theory for the electromagnetic phenomena in which charges are represented by complex valued wave functions as in the Schrodinger wave mechanics.…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
Semiclassical approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in phase space, but it is not available for chaotic systems. An analogous evolution surface underlies semiclassical…
We study the ionization of atomic hydrogen in the direction of polarization due to a linearly polarized XUV pulse in the presence a strong field IR. We describe the photoelectron spectra as an interference problem in the time domain.…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…