Phase analysis of the cosmic microwave background from an incomplete sky coverage

Phases of the spherical harmonic analysis of full-sky cosmic microwave background (CMB) temperature data contain useful information complementary to the ubiquitous angular power spectrum. In this letter we present a new method of phase analysis on incomplete sky maps. It is based on Fourier phases of equal-latitude pixel rings of the map, which are related to the mean angle of the trigonometric moments from the full-sky phases. They have an advantage for probing regions of interest without tapping polluted Galactic plane area, and can localize non-Gaussian features and departure from statistical isotropy in the CMB.Comment: 5 pages, 3 figures submitted to MNRAS Letters, replaced with minor change

Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

Magnetization of ballistic quantum dots induced by a linear-polarized microwave field

On a basis of extensive analytical and numerical studies we show that a linear-polarized microwave field creates a stationary magnetization in mesoscopic ballistic quantum dots with two-dimensional electron gas being at a thermal equilibrium. The magnetization is proportional to a number of electrons in a dot and to a microwave power. Microwave fields of moderate strength create in a one dot of few micron size a magnetization which is by few orders of magnitude larger than a magnetization produced by persistent currents. The effect is weakly dependent on temperature and can be observed with existing experimental techniques. The parallels between this effect and ratchets in asymmetric nanostructures are also discussed.Comment: 10 pages, 11 figs, research at http://www.quantware.ups-tlse.f

Dual Projection and Selfduality in Three Dimensions

We discuss the notion of duality and selfduality in the context of the dual projection operation that creates an internal space of potentials. Contrary to the prevailing algebraic or group theoretical methods, this technique is applicable to both even and odd dimensions. The role of parity in the kernel of the Gauss law to determine the dimensional dependence is clarified. We derive the appropriate invariant actions, discuss the symmetry groups and their proper generators. In particular, the novel concept of duality symmetry and selfduality in Maxwell theory in (2+1) dimensions is analysed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and $Z_2$ symmetries, contrary to conventional results.Comment: 20 pages, late

How strong is the evidence for accelerated expansion?

We test the present expansion of the universe using supernova type Ia data without making any assumptions about the matter and energy content of the universe or about the parameterization of the deceleration parameter. We assume the cosmological principle to apply in a strict sense. The result strongly depends on the data set, the light-curve fitting method and the calibration of the absolute magnitude used for the test, indicating strong systematic errors. Nevertheless, in a spatially flat universe there is at least a 5 sigma evidence for acceleration which drops to 1.8 sigma in an open universe.Comment: 16 pages, 3 figure

On Lorentz invariance and supersymmetry of four particle scattering amplitudes in SNR8S^N\R^8 orbifold sigma model

The $S^N\R^8$ supersymmetric orbifold sigma model is expected to describe the IR limit of the Matrix string theory. In the framework of the model the type IIA string interaction is governed by a vertex which was recently proposed by R.Dijkgraaf, E.Verlinde and H.Verlinde. By using this interaction vertex we derive all four particle scattering amplitudes directly from the orbifold model in the large $N$ limit.Comment: Latex, 23 page

Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure