1,114 research outputs found
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 for the DGLAP equation and for the "nonforward" ER-BL
equation from these diagrams that dominate for a large value of , the
first -function coefficient. Calculations are performed in the covariant
-gauge in a MS-like scheme. It is established that a special choice of the
gauge parameter 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 in the 1/N expansion of the
two-particle-irreducible (2PI) effective action for the O(N) symmetric model in three spatial dimensions. The exponent controls the behavior
of a two-point function {\it near} the critical point , but can be evaluated on the critical point by the use of the
vertex function . We derive a self-consistent equation for
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
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