Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.Comment: 20 pages, 4 figure

Rotating black rings on Taub-NUT

In this paper, we construct new solutions describing rotating black rings on Taub-NUT using the inverse-scattering method. These are five-dimensional vacuum space-times, generalising the Emparan-Reall and extremal Pomeransky-Sen'kov black rings to a Taub-NUT background space. When reduced to four dimensions in Kaluza-Klein theory, these solutions describe (possibly rotating) electrically charged black holes in superposition with a finitely separated magnetic monopole. Various properties of these solutions are studied, from both a five- and four-dimensional perspective.Comment: 33 pages, 3 figures, LaTe

Propagation of Bose-Einstein condensates in a magnetic waveguide

Gaseous Bose-Einstein condensates of 2-3 million atoms were loaded into a microfabricated magnetic trap using optical tweezers. Subsequently, the condensates were released into a magnetic waveguide and propagated 12 mm. Single-mode propagation was observed along homogeneous segments of the waveguide. Inhomogeneities in the guiding potential arose from geometric deformations of the microfabricated wires and caused strong transverse excitations. Such deformations may restrict the waveguide physics that can be explored with propagating condensates.Comment: 5 pages, 4 figure

Axisymmetric metrics in arbitrary dimensions

We consider axially symmetric static metrics in arbitrary dimension, both with and without a cosmological constant. The most obvious such solutions have an SO(n) group of Killing vectors representing the axial symmetry, although one can also consider abelian groups which represent a flat `internal space'. We relate such metrics to lower dimensional dilatonic cosmological metrics with a Liouville potential. We also develop a duality relation between vacuum solutions with internal curvature and those with zero internal curvature but a cosmological constant. This duality relation gives a solution generating technique permitting the mapping of different spacetimes. We give a large class of solutions to the vacuum or cosmological constant spacetimes. We comment on the extension of the C-metric to higher dimensions and provide a novel solution for a braneworld black hole.Comment: 36 pages, LaTeX (JHEP), 4 figures, section added (published version

Topological superfluid 3^3He-B: fermion zero modes on interfaces and in the vortex core

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which are robust to perturbation and interaction. We discuss the nodeless 3D system, such as superfluid $^3$He-B, vacuum of Dirac fermions, and relativistic singlet and triplet supercondutors which may arise in quark matter. The systems, which have nonzero value of topological invariant, have gapless fermions on the boundary and in the core of quantized vortices. We discuss the index theorem which relates fermion zero modes on vortices with the topological invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi, Finlan

Kaluza-Klein Pistons with non-Commutative Extra Dimensions

We calculate the scalar Casimir energy and Casimir force for a $R^3\times N$ Kaluza-Klein piston setup in which the extra dimensional space $N$ contains a non-commutative 2-sphere, $S_{FZ}$. The cases to be studied are $T^d\times S_{FZ}$ and $S_{FZ}$ respectively as extra dimensional spaces, with $T^d$ the $d$ dimensional commutative torus. The validity of the results and the regularization that the piston setup offers are examined in both cases. Finally we examine the 1-loop corrected Casimir energy for one piston chamber, due to the self interacting scalar field in the non-commutative geometry. The computation is done within some approximations. We compare this case for the same calculation done in Minkowski spacetime $M^D$. A discussion on the stabilization of the extra dimensional space within the piston setup follows at the end of the article.Comment: 22 page

The control parameterization method for nonlinear optimal control: A survey

The control parameterization method is a popular numerical technique for solving optimal control problems. The main idea of control parameterization is to discretize the control space by approximating the control function by a linear combination of basis functions. Under this approximation scheme, the optimal control problem is reduced to an approximate nonlinear optimization problem with a finite number of decision variables. This approximate problem can then be solved using nonlinear programming techniques. The aim of this paper is to introduce the fundamentals of the control parameterization method and survey its various applications to non-standard optimal control problems. Topics discussed include gradient computation, numerical convergence, variable switching times, and methods for handling state constraints. We conclude the paper with some suggestions for future research

The unusual electronic structure of the "pseudo-ladder" compound CaCu2O3

Experimental and theoretical studies of the unoccupied electronic structure of CaCu2O3 single crystals have been performed using polarization-dependent x-ray absorption spectroscopy and band structure calculations. The measured hole distribution shows an unusual large number of holes in orbitals parallel to the interlayer direction which is in agreement with the theoretical analysis. CaCu2O3 deviates significantly from the standard pd-sigma cuprate picture. The corresponding strong interlayer exchange is responsible for the missing spin gap generic for other two-leg ladder cuprates.Comment: 4 pages, 3 figures include

Quantum (in)stability of 2D charged dilaton black holes and 3D rotating black holes

The quantum properties of charged black holes (BHs) in 2D dilaton-Maxwell gravity (spontaneously compactified from heterotic string) with $N$ dilaton coupled scalars are studied. We first investigate 2D BHs found by McGuigan, Nappi and Yost. Kaluza-Klein reduction of 3D gravity with minimal scalars leads also to 2D dilaton-Maxwell gravity with dilaton coupled scalars and the rotating BH solution found by Ba\~nados, Teitelboim and Zanelli (BTZ) which can be also described by 2D charged dilatonic BH. Evaluating the one-loop effective action for dilaton coupled scalars in large $N$ (and s-wave approximation for BTZ case), we show that quantum-corrected BHs may evaporate or else anti-evaporate similarly to 4D Nariai BH as is observed by Bousso and Hawking. Higher modes may cause the disintegration of BH in accordance with recent observation by Bousso.Comment: LaTeX file and ps files for figures, new section is added, title is change

Two-dimensional Dirac fermions in a topological insulator: transport in the quantum limit

Pulsed magnetic fields of up to 55T are used to investigate the transport properties of the topological insulator Bi_2Se_3 in the extreme quantum limit. For samples with a bulk carrier density of n = 2.9\times10^16cm^-3, the lowest Landau level of the bulk 3D Fermi surface is reached by a field of 4T. For fields well beyond this limit, Shubnikov-de Haas oscillations arising from quantization of the 2D surface state are observed, with the \nu =1 Landau level attained by a field of 35T. These measurements reveal the presence of additional oscillations which occur at fields corresponding to simple rational fractions of the integer Landau indices.Comment: 5 pages, 4 figure