The propagation of the electromagnetic field of a laser through a dense Bose gas is examined and nonlinear operator equations for the motion of the center of mass of the atoms are derived. The goal is to present a self-consistent set of coupled Maxwell-Bloch equations for atomic and electromagnetic fields generalized to include the atomic center-of-mass motion. Two effects are considered: The ultracold gas forms a medium for the Maxwell field which modifies its propagation properties. Combined herewith is the influence of the dipole-dipole interaction between atoms which leads to a density dependent shift of the atomic transition frequency. It is expressed in a position dependent detuning and is the reason for the nonlinearity. This results in a direct and physically transparent way from the quantum field theoretical version of the local-field approach to electrodynamics in quantum media. The equations for the matter fields are general. Previously published nonlinear equations are obtained as limiting cases. As an atom optical application the scattering of a dense beam of a Bose gas is studied in the Raman-Nath regime. The main conclusion is that for increasing density of the gas the dipole-dipole interaction suppresses or enhances the scattering depending on the sign of the detuning.
The Schrödinger equation in higher dimensions is considered. It consists of the kinetic energy part given by the corresponding Laplace operator, and a term describing the interaction with the electrostatic field of a point charge. From Rutherford-type scattering experiments one can conclude that the potential of a point charge is ∼1/r irrespective of the dimension of the space where the experiment is carried through. Also the structure of the kinetic energy is unchanged in higher dimensions so that one is lead to the result that there exist stable atoms in higher spatial dimensions d⩾4. The solutions and energy eigenvalues to this Schrödinger equation in higher dimensions are presented. As a consequence, the dimensionality of space can be read off from the spectral scheme of atoms: The three-dimensionality of space is a consequence of the existence of the Lyman series. Another consequence is that the Maxwell equations in higher dimensions must be modified in order to have the 1/r-potential as solution for a point charge.
DNA-PK directly phosphorylates NOR-1 and, this way, modulates SMC proliferation. These data add to our understanding of vascular remodelling processes and opens new avenues for treatment of vascular proliferative diseases.
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