Abstract:
Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: Level number k is split into k+1 sublevels that render the $k$th oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our observations are relevant for quantum Hall configurations whenever electric field effects should be taken into account.

Abstract:
Paramagnetic, dipolar Hund's case-a radicals are considered in the presence of arbitrary, non-collinear combinations of electric and magnetic fields. The field-dependent part of the Hamiltonian is found to be exactly diagonalizable, and described by quantum numbers given by the projection of the molecule's total angular momentum along a space-fixed axis that is determined by both the fields and the electric and magnetic dipole moments of the molecule. In cases of strong fields, this procedure identifies a set of quantum numbers for the molecule in crossed fields. We dub this set a "Hund's case-X" basis.

Abstract:
It is shown that the renormalizability of the zero-range interaction in the two-dimensional space is always followed by the existence of a bound state, which is not true for odd-dimensional spaces. A renormalization procedure is defined and the exact retarded Green's function for electrons moving in two dimensions and interacting with both crossed magnetic and electric fields and an attractive zero-range interaction is constructed. Imaginary parts of poles of this Green's function determine lifetimes of quasi-bound (resonance) states. It is shown that for some particular parameters the stabilization against decay occurs even for strong electric fields.

Abstract:
Crossed electric and magnetic fields influence dipolar neutral particles in the same way as the magnetic field influences charged particles. The effect of crossed fields is proportional to the dipole moment of particles (inherent or induced). We show that the effect of crossed fields is quite spectacular in a multilayer system of polar molecules with dipole moments perpendicular to the layers. In this system the dipoles are coupled into chains, with a very large dipole moment of a given chain. The crossed fields may then induce a large number of vortices in the superfluid gas of chains. This effect can be used for monitoring the formation and dissociation of chains in multilayer dipolar structures.

Abstract:
We present the first observations of cylindrical symmetry breaking in highly excited diamagnetic hydrogen with a small crossed electric field, and we give a semiclassical interpretation of this effect. As the small perpendicular electric field is added, the recurrence strengths of closed orbits decrease smoothly to a minimum, and revive again. This phenomenon, caused by interference among the electron waves that return to the nucleus, can be computed from the azimuthal dependence of the classical closed orbits.

Abstract:
We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.

Abstract:
A two-dimensional electron system interacting with an impurity and placed in crossed magnetic and electric fields is under investigation. Since it is assumed that an impurity center interacts as an attractive $\delta$-like potential a renormalization procedure for the retarded Green's function has to be carried out. For the vanishing electric field we obtain a close analytical expression for the Green's function and we find one bound state localized between Landau levels. It is also shown by numerical investigations that switching on the electric field new long-living resonance states localized in the vicinity of Landau levels can be generated.

Abstract:
Multi-electron giant dipole resonances of atoms in crossed electric and magnetic fields are investigated. Stationary configurations corresponding to a highly symmetric arrangement of the electrons on a decentered circle are derived, and a normal-mode and stability analysis are performed. A classification of the various modes, which are dominated by the magnetic field or the Coulomb interactions, is provided. Based on the MCTDH approach, we carry out a six-dimensional wave-packet dynamical study for the two-electron resonances, yielding in particular lifetimes of more than 0.1 $\mu$s for strong electric fields.

Abstract:
The S-matrix theory formulation of closed-orbit theory recently proposed by Granger and Greene is extended to atoms in crossed electric and magnetic fields. We then present a semiclassical quantization of the hydrogen atom in crossed fields, which succeeds in resolving individual lines in the spectrum, but is restricted to the strongest lines of each n-manifold. By means of a detailed semiclassical analysis of the quantum spectrum, we demonstrate that it is the abundance of bifurcations of closed orbits that precludes the resolution of finer details. They necessitate the inclusion of uniform semiclassical approximations into the quantization process. Uniform approximations for the generic types of closed-orbit bifurcation are derived, and a general method for including them in a high-resolution semiclassical quantization is devised.

Abstract:
We study the quantum dynamics of localized impurity states created by a point interaction for an electron moving in two dimensions under the influence of a perpendicular magnetic field and an in-plane weak electric field. All impurity states are unstable in presence of the electric field. Their lifetimes are computed and shown to grow in a Gaussian way as the electric field tends to zero.