Indirect RKKY interaction in any dimensionality

We present an analytical method which enables one to find the exact spatial dependence of the indirect RKKY interaction between the localized moments via the conduction electrons for the arbitrary dimensionality $n$. The corresponding momentum dependence of the Lindhard function is exactly found for any $n$ as well. Demonstrating the capability of the method we find the RKKY interaction in a system of metallic layers weakly hybridized to each other. Along with usual $2k_F$ in-plane oscillations the RKKY interaction has the sign-reversal character in a direction perpendicular to layers, thus favoring the antiferromagnetic type of layers' stacking.Comment: 3 pages, REVTEX, accepted to Phys.Rev.

Modified spontaneous symmetry breaking pattern by brane-bulk interaction terms

We show how translational invariance can be broken by the vacuum that drives the spontaneous symmetry breaking of extra-dimensional extensions of the Standard Model, when delta-like interactions between brane and bulk scalar fields are present. We explicitly build some examples of vacuum configurations, which induce the spontaneous symmetry breaking, and have non trivial profile in the extra coordinate.Comment: 13 pages, two figure

RKKY interaction in the nearly-nested Fermi liquid

We present the results of analytical evaluation of the indirect RKKY interaction in a layered metal with nearly nested (almost squared) Fermi surface. The final expressions are obtained in closed form as a combination of Bessel functions. We discuss the notion of the ``2k_F'' oscillations and show that they occur as the far asymptote of our expressions. We show the existence of the intermediate asymptote of the interaction which is of the sign-reversal antiferromagnetic type and is the only term surviving in the limit of exact nesting. A good accordance of our analytical formulas with numerical findings is demonstrated until the interatomic distances. The obtained expressions for the Green's functions extend the previous analytical results into the region of intermediate distances as well.Comment: 9 pages, REVTEX, 3 .eps figures, to appear in PRB 1 Oct 199

Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves

Field theories on the plane wave background are considered. We discuss that for such field theories one can only form 1+1 dimensional freely propagating wave packets. We analyze tree level four point functions of scalar field theory as well as scalars coupled to gauge fields in detail and show that these four point functions are well-behaved so that they can be interpreted as S-matrix elements for 2 particle $\to$ 2 particle scattering amplitudes. Therefore, at least classically, field theories on the plane wave background have S-matrix formulation.Comment: Latex file, 26 pages, 4 eps figures. v3: In the end of paper there is a "Note Added" as an update of the result

Susceptibility Amplitude Ratios Near a Lifshitz Point

The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz point is calculated at one-loop level using field-theoretic and $\epsilon_{L}$-expansion methods. We use the Schwinger parametrization of the propagator in order to split the quadratic and quartic part of the momenta, as well as a new special symmetry point suitable for renormalization purposes. For a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.Comment: 7 pages, late

Bubble fluctuations in Ω<1\Omega<1 inflation

In the context of the open inflationary universe, we calculate the amplitude of quantum fluctuations which deform the bubble shape. These give rise to scalar field fluctuations in the open Friedman-Robertson-Walker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the perturbations behave as tensor modes (gravitational waves of very long wavelength). For $(1-\Omega)<<1$, where $\Omega$ is the density parameter, the microwave temperature anisotropies produced by these modes are of order $\delta T/T\sim H(R_0\mu l)^{-1/2} (1-\Omega)^{l/2}$. Here, $H$ is the expansion rate during inflation, $R_0$ is the intrinsic radius of the bubble at the time of nucleation, $\mu$ is the bubble wall tension and $l$ labels the different multipoles ($l>1$). The gravitational backreaction of the bubble has been ignored. In this approximation, $G\mu R_0<<1$, and the new effect can be much larger than the one due to ordinary gravitational waves generated during inflation (unless, of course, $\Omega$ gets too close to one, in which case the new effect disappears).Comment: 17 pages, 3 figs, LaTeX, epsfig.sty, available at ftp://ftp.ifae.es/preprint/ft/uabft387.p

Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics

Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $\sigma$--model approach, in combination with the saddle--point method. The LDOS distribution is found to have the logarithmically normal asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D sample, the result is confirmed by the exact solution. In 2D case a perfect agreement with an earlier renormalization group calculation is found. In 3D the found asymptotics is of somewhat different type: P(\rho)\sim \exp(-\mbox{const}\,|\ln^3\rho|).Comment: REVTEX, 14 pages, no figure

Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of a nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate is suggested which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur

Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter $g_{NL}$. The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of $g_{NL}$ and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for $g_{NL}>0$ and less of both for $g_{NL}<0$. The deviation increases linearly with $g_{NL}$ and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of $g_{NL}$ that are clearly distinct from the quadratic order perturbations, encoded in the parameter $f_{NL}$. Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between $g_{NL}$ and $f_{NL}$ type non-Gaussianities.Comment: 18+1 page

Regular particle acceleration in relativistic jets

Exact solution is obtained for electromagnetic field around a conducting cylinder of infinite length and finite radius, with a periodical axial current, when the wave length is much larger than the radius of the cylinder. The solution describes simultaneously the fields in the near zone close to the cylinder, and transition to the wave zone. Proper long-wave oscillations of such cylinder are studied. The electromagnetic energy flux from the cylinder is calculated. These solutions could be applied for description of the electromagnetic field around relativistic jets from active galactic nuclei and quasars and particle acceleration inside jets.Comment: 12 pages, 1 figure. To appear in Proc. of the Workshop The Multiwavelength Approach To Unidentified Gamma Ray Sources. The University of Hong Kong - Hong Kong, China, 1-4 June 200