A Non-Crossing Approximation for the Study of Intersite Correlations

We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a self-consistently embedded periodic cluster of size $N_c$. It is a fully causal and systematic approximation to the full lattice problem, with corrections ${\cal{O}}(1/N_c)$ in two dimensions. The NCA we develop is a systematic approximation with corrections ${\cal{O}}(1/N_c^3)$. The method will be discussed in detail and results for the one-particle properties of the Hubbard model are shown. Near half filling, the spectra display pronounced features including a pseudogap and non-Fermi-liquid behavior due to short-ranged antiferromagnetic correlations.Comment: 12 pages, 11 figures, EPJB styl

Light scattering from mesoscopic objects in diffusive media

The diffuse intensity propagating in turbid media is sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects can be described by a stationary diffusion equation, the effect of any single object being parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object (capacitance $Q$ or effective radius $R_{\rm eff}$, polarizability $P$) can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is radiative transfer theory. This formalism is worked out in detail for spheres and cylinders of the following kinds: totally absorbing (black), transparent, and totally reflecting.Comment: 31 pages, 2 tables, 7 figures. To appear in Eur. J. Phys.

Thermodynamic description of a dynamical glassy transition

For the dynamical glassy transition in the $p$-spin mean field spin glass model a thermodynamic description is given. The often considered marginal states are not the relevant ones for this purpose. This leads to consider a cooling experiment on exponential timescales, where lower states are accessed. The very slow configurational modes are at quasi-equilibrium at an effective temperature. A system independent law is derived that expresses their contribution to the specific heat. $t/t_w$-scaling in the aging regime of two-time quantities is explained.Comment: 5 pages revte

Solvable glassy system: static versus dynamical transition

A directed polymer is considered on a flat substrate with randomly located parallel ridges. It prefers to lie inside wide regions between the ridges. When the transversel width $W=\exp(\lambda L^{1/3})$ is exponential in the longitudinal length $L$, there can be a large number $\sim \exp L^{1/3}$ of available wide states. This ``complexity'' causes a phase transition from a high temperature phase where the polymer lies in the widest lane, to a glassy low temperature phase where it lies in one of many narrower lanes. Starting from a uniform initial distribution of independent polymers, equilibration up to some exponential time scale induces a sharp dynamical transition. When the temperature is slowly increased with time, this occurs at a tunable temperature. There is an asymmetry between cooling and heating. The structure of phase space in the low temperature non-equilibrium glassy phase is of a one-level tree.Comment: 4 pages revte

Ginzburg-Landau theory of the cluster glass phase

On the basis of a recent field theory for site-disordered spin glasses a Ginzburg-Landau free energy is proposed to describe the low temperatures glassy phase(s) of site-disordered magnets. The prefactors of the cubic and dominant quartic terms change gradually along the transition line in the concentration-temperature phase diagram. Either of them may vanish at certain points $(c_*, T_*)$, where new transition lines originate. The new phases are classifiedComment: 6 pages Revtex, 5 figures. To appear in J. Phys. A. Let

Relation between trees of fragmenting granules and supergranulation evolution

Context: The determination of the underlying mechanisms of the magnetic elements diffusion over the solar surface is still a challenge. Understanding the formation and evolution of the solar network (NE) is a challenge, because it provides a magnetic flux over the solar surface comparable to the flux of active regions at solar maximum. Aims: We investigate the structure and evolution of interior cells of solar supergranulation. From Hinode observations, we explore the motions on solar surface at high spatial and temporal resolution. We derive the main organization of the flows inside supergranules and their effect on the magnetic elements. Method: To probe the superganule interior cell, we used the Trees of Fragmenting Granules (TFG) evolution and their relations to horizontal Results: Evolution of TFG and their mutual interactions result in cumulative effects able to build horizontal coherent flows with longer lifetime than granulation (1 to 2 hours) over a scale up to 12\arcsec. These flows clearly act on the diffusion of the intranetwork (IN) magnetic elements and also on the location and shape of the network. Conclusions: From our analysis during 24 hours, TFG appear as one of the major elements of the supergranules which diffuse and advect the magnetic field on the Sun's surface. The strongest supergranules contribute the most to magnetic flux diffusion in the solar photosphere.Comment: 13 pages, 17 figures, accepted in Astronomy and Astrophysics movie : http://www.lesia.obspm.fr/perso/jean-marie-malherbe/Hinode2007/hinode2007.htm