Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

TeV Scale Lee-Wick Fields out of Large Extra Dimensional Gravity

We study the gravitational corrections to the Maxwell, Dirac and Klein-Gorden theories in the large extra dimension model in which the gravitons propagate in the (4+n)-dimensional bulk, while the gauge and matter fields are confined to the four-dimensional world. The corrections to the two-point Green's functions of the gauge and matter fields from the exchanges of virtual Kaluza-Klein gravitons are calculated in the gauge independent background field method. In the framework of effective field theory, we show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a TeV scale Lee-Wick partner of every gauge and matter field as extra degrees of freedom in the theory. Thus the large extra dimension model of gravity provides a natural mechanism to the emergence of these exotic particles which were recently used to construct an extension of the Standard Model.Comment: 17 pages, 3 figures, references added, to appear in Phys. Rev.

Spin entanglement induced by spin-orbit interactions in coupled quantum dots

We theoretically explore the possibility of creating spin quantum entanglement in a system of two electrons confined respectively in two vertically coupled quantum dots in the presence of Rashba type spin-orbit coupling. We find that the system can be described by a generalized Jaynes - Cummings model of two modes bosons interacting with two spins. The lower excitation states of this model are calculated to reveal the underlying physics of the far infrared absorption spectra. The analytic perturbation approach shows that an effective transverse coupling of spins can be obtained by eliminating the orbital degrees of freedom in the large detuning limit. Here, the orbital degrees of freedom of the two electrons, which are described by two modes of bosons, serve as a quantized data bus to exchange the quantum information between two electrons. Then a nontrivial two-qubit logic gate is realized and spin entanglement between the two electrons is created by virtue of spin-orbit coupling.Comment: 7 pages, 5 figure

Self-similarity under inflation and level statistics: a study in two dimensions

Energy level spacing statistics are discussed for a two dimensional quasiperiodic tiling. The property of self-similarity under inflation is used to write a recursion relation for the level spacing distributions defined on square approximants to the perfect quasiperiodic structure. New distribution functions are defined and determined by a combination of numerical and analytical calculations.Comment: Latex, 13 pages including 6 EPS figures, paper submitted to PR