New four-dimensional integrals by Mellin-Barnes transform

This paper is devoted to the calculation by Mellin-Barnes transform of a especial class of integrals. It contains double integrals in the position space in d = 4-2e dimensions, where e is parameter of dimensional regularization. These integrals contribute to the effective action of the N = 4 supersymmetric Yang-Mills theory. The integrand is a fraction in which the numerator is a logarithm of ratio of spacetime intervals, and the denominator is the product of powers of spacetime intervals. According to the method developed in the previous papers, in order to make use of the uniqueness technique for one of two integrations, we shift exponents in powers in the denominator of integrands by some multiples of e. As the next step, the second integration in the position space is done by Mellin-Barnes transform. For normalizing procedure, we reproduce first the known result obtained earlier by Gegenbauer polynomial technique. Then, we make another shift of exponents in powers in the denominator to create the logarithm in the numerator as the derivative with respect to the shift parameter delta. We show that the technique of work with the contour of the integral modified in this way by using Mellin-Barnes transform repeats the technique of work with the contour of the integral without such a modification. In particular, all the operations with a shift of contour of integration over complex variables of two-fold Mellin-Barnes transform are the same as before the delta modification of indices, and even the poles of residues coincide. This confirms the observation made in the previous papers that in the position space all the Green function of N = 4 supersymmetric Yang-Mills theory can be expressed in terms of UD functions.Comment: Talk at El Congreso de Matematica Capricornio, COMCA 2009, Antofagasta, Chile and at DMFA seminar, UCSC, Concepcion, Chile, 24 pages; revised version, Introduction is modified, Conclusion is added, five Appendices are added, Appendix E is ne

Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates

We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time-evolution of optical and matter-wave fields is performed in the framework of the semiclassical Maxwell-Schroedinger equations. Our theory is not only able to explain many of the known experimental observations, e.g., the behavior of the atomic side-mode distributions, but also provides further detailed insights into the coupled dynamics of optical and matter-wave fields. To work out the significance of propagation effects, we compare our results to other theoretical models in which these effects are neglected.Comment: 14 pages, 13 figure

Description of paramagnetic--spin glass transition in Edwards-Anderson model in terms of critical dynamics

Possibility of description of the glass transition in terms of critical dynamics considering a hierarchy of the intermodal relaxation time is shown. The generalized Vogel-Fulcher law for the system relaxation time is derived in terms of this approach. It is shown that the system satisfies the fluctuating--dissipative theorem in case of the absence of the intermodal relaxation time hierarchy.Comment: 10 pages, 6 figure

A multiloop improvement of non-singlet QCD evolution equations

An approach is elaborated for calculation of "all loop" contributions to the non-singlet evolution kernels from the diagrams with renormalon chain insertions. Closed expressions are obtained for sums of contributions to kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the "nonforward" ER-BL equation from these diagrams that dominate for a large value of $b_0$, the first $\beta$-function coefficient. Calculations are performed in the covariant $\xi$-gauge in a MS-like scheme. It is established that a special choice of the gauge parameter $\xi=-3$ generalizes the standard "naive nonabelianization" approximation. The solutions are obtained to the ER-BL evolution equation (taken at the "all loop" improved kernel), which are in form similar to one-loop solutions. A consequence for QCD descriptions of hard processes and the benefits and incompleteness of the approach are briefly discussed.Comment: 13 pages, revtex, 2 figures are enclosed as eps-file, the text style and figures are corrected following version, accepted for publication to Phys. Rev.

High frequency dielectric and magnetic anomaly at the phase transition in NaV2O5

We found anomalies in the temperature dependence of the dielectric and the magnetic susceptibiliy of NaV_2O_5 in the microwave and far infrared frequency ranges. The anomalies occur at the phase transition temperature T_c, at which the spin gap opens. The real parts of the dielectric constants epsilon_a and epsilon_c decrease below T_c. The decrease of epsilon_a (except for the narrow region close to T_c) is proportional to the intensity of the x-ray reflection appearing at T_c. The dielectric constant anomaly can be explained by the zigzag charge ordering in the ab-plane appearing below T_c. The anomaly of the microwave magnetic losses is probably related to the coupling between the spin and charge degrees of freedom in vanadium ladders.Comment: 3 PS-figures, LATEX-text, new experimental data added, typos correcte

Critical exponents from two-particle irreducible 1/N expansion

We calculate the critical exponent $\nu$ in the 1/N expansion of the two-particle-irreducible (2PI) effective action for the O(N) symmetric $\phi ^4$ model in three spatial dimensions. The exponent $\nu$ controls the behavior of a two-point function $$ {\it near} the critical point $T\neq T_c$, but can be evaluated on the critical point $T=T_c$ by the use of the vertex function $\Gamma^{(2,1)}$. We derive a self-consistent equation for $\Gamma^{(2,1)}$ within the 2PI effective action, and solve it by iteration in the 1/N expansion. At the next-to-leading order in the 1/N expansion, our result turns out to improve those obtained in the standard one-particle-irreducible calculation.Comment: 18 page

Effects of Turbulent Mixing on the Critical Behavior

Effects of strongly anisotropic turbulent mixing on the critical behavior are studied by means of the renormalization group. Two models are considered: the equilibrium model A, which describes purely relaxational dynamics of a nonconserved scalar order parameter, and the Gribov model, which describes the nonequilibrium phase transition between the absorbing and fluctuating states in a reaction-diffusion system. The velocity is modelled by the d-dimensional generalization of the random shear flow introduced by Avellaneda and Majda within the context of passive scalar advection. Existence of new nonequilibrium types of critical regimes (universality classes) is established.Comment: Talk given in the International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (Moscow-Dubna, 21-27 August 2009

Sequential superradiant scattering from atomic Bose-Einstein condensates

We theoretically discuss several aspects of sequential superradiant scattering from atomic Bose-Einstein condensates. Our treatment is based on the semiclassical description of the process in terms of the Maxwell-Schroedinger equations for the coupled matter-wave and optical fields. First, we investigate sequential scattering in the weak-pulse regime and work out the essential mechanisms responsible for bringing about the characteristic fan-shaped side-mode distribution patterns. Second, we discuss the transition between the Kapitza-Dirac and Bragg regimes of sequential scattering in the strong-pulse regime. Finally, we consider the situation where superradiance is initiated by coherently populating an atomic side mode through Bragg diffraction, as in studies of matter-wave amplification, and describe the effect on the sequential scattering process.Comment: 9 pages, 4 figures. Submitted to Proceedings of LPHYS'06 worksho

A simple analytical model for dark matter halo structure and adiabatic contraction

A simple analytical model for describing inner parts of dark matter halo is considered. It is assumed that dark matter density is power-law. The model deals with dark matter distribution function in phase space of adiabatic invariants (radial action and angular momentum). Two variants are considered for the angular part of the distribution function: narrow and broad distribution. The model allows to describe explicitly the process of adiabatic contraction of halo due to change of gravitational potential caused by condensation of baryonic matter in the centre. The modification of dark matter density in the centre is calculated, and is it shown that the standard algorithm of adiabatic contraction calculation overestimates the compressed halo density, especially in the case of strong radial anisotropy.Comment: 5 pages, 3 figures. v3 - major improvements, another halo model introduced, discussion extende