Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs

This paper presents a novel approach to wave propagation inside the Fabry-Perot framework. It states that the time-averaged Poynting vector modulus could be nonequivalent with the squared-field amplitude modulus. This fact permits the introduction of a new kind of nonlinear medium whose nonlinearity is proportional to the time-averaged Poynting vector modulus. Its transmittance is calculated and found to differ with that obtained for the Kerr medium, whose nonlinearity is proportional to the squared-field amplitude modulus. The latter emphasizes the nonequivalence of these magnitudes. A space-time symmetry analysis shows that the Poynting nonlinearity should be only possible in noncentrosymmetric materials.Comment: 5 pages, 4 figures, added space-time symmetry analysis and reference

Strongly localized polaritons in an array of trapped two-level atoms interacting with a light field

We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a transition results in the appearance of a macroscopic polarization of the atomic medium at non-zero frequency. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array.Comment: 16 pages, 6 figure

Holographic Renormalization for z=2 Lifshitz Space-Times from AdS

Lifshitz space-times with critical exponent z=2 can be obtained by dimensional reduction of Schroedinger space-times with critical exponent z=0. The latter space-times are asymptotically AdS solutions of AdS gravity coupled to an axion-dilaton system and can be uplifted to solutions of type IIB supergravity. This basic observation is used to perform holographic renormalization for 4-dimensional asymptotically z=2 locally Lifshitz space-times by Scherk-Schwarz dimensional reduction of the corresponding problem of holographic renormalization for 5-dimensional asymptotically locally AdS space-times coupled to an axion-dilaton system. We can thus define and characterize a 4-dimensional asymptotically locally z=2 Lifshitz space-time in terms of 5-dimensional AdS boundary data. In this setup the 4-dimensional structure of the Fefferman-Graham expansion and the structure of the counterterm action, including the scale anomaly, will be discussed. We find that for asymptotically locally z=2 Lifshitz space-times obtained in this way there are two anomalies each with their own associated nonzero central charge. Both anomalies follow from the Scherk--Schwarz dimensional reduction of the 5-dimensional conformal anomaly of AdS gravity coupled to an axion-dilaton system. Together they make up an action that is of the Horava-Lifshitz type with nonzero potential term for z=2 conformal gravity.Comment: 32 pages, v2: modified discussion of the central charge

de Sitter Thick Brane Solution in Weyl Geometry

In this paper, we consider a de Sitter thick brane model in a pure geometric Weyl integrable five-dimensional space-time, which is a generalization of Riemann geometry and is invariant under a so-called Weyl rescaling. We find a solution of this model via performing a conformal transformation to map the Weylian structure into a familiar Riemannian one with a conformal metric. The metric perturbations of the model are discussed. For gravitational perturbation, we get the effective modified P$\ddot{\text{o}}$schl-Teller potential in corresponding Schr$\ddot{\text{o}}$dinger equation for Kaluza-Klein (KK) modes of the graviton. There is only one bound state, which is a normalizable massless zero mode and represents a stable 4-dimensional graviton. Furthermore, there exists a mass gap between the massless mode and continuous KK modes. We also find that the model is stable under the scalar perturbation in the metric. The correction to the Newtonian potential on the brane is proportional to $e^{-3 r \beta/2}/r^2$, where $\beta$ is the de Sitter parameter of the brane. This is very different from the correction caused by a volcano-like effective potential.Comment: 24 pages, 13 figures, published versio