Non-perturbative double scaling limits

Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path) integrals by gauge theory or non-linear sigma model (path) integrals. We explain how this solves one of the most fundamental limitation of the classic approach: we automatically obtain non-perturbative definitions in non-Borel summable cases. This is exemplified on the simplest possible examples involving O(N) symmetric non-linear sigma models with N-dimensional target spaces, for which we construct (multi)critical metrics. The non-perturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path) integrals.Comment: 18 pages, one figur

Raman Fingerprint of Charged Impurities in Graphene

We report strong variations in the Raman spectra for different single-layer graphene samples obtained by micromechanical cleavage, which reveals the presence of excess charges, even in the absence of intentional doping. Doping concentrations up to ~10^13 cm-2 are estimated from the G peak shift and width, and the variation of both position and relative intensity of the second order 2D peak. Asymmetric G peaks indicate charge inhomogeneity on the scale of less than 1 micron.Comment: 3 pages, 5 figure

Multiple merging events in Abell 521

We present a detailed spatial and dynamical analysis of the central $\sim$~2.2~\h~Mpc region of the galaxy cluster Abell~521 (z=0.247), based on 238 spectra obtained at the 3.6~m Telescope of ESO and at the CFHT. From the analysis of the 125 galaxies confirmed members of the cluster, we derive a mean velocity of $74019 ^{+112}_{-125}$ km/s and detect a complex velocity distribution with high velocity dispersion, $1325 ^{+145}_{-100}$ km/s), but clear departure from a single gaussian component. The general structure of the cluster follows a NW/SE direction, crossed by a perpendicular high density ``ridge'' of galaxies in the core region. The northern region of the cluster is characterized by a lower velocity dispersion as compared to the whole cluster value; it hosts the BCG and a dynamically bound complex of galaxies, and it is associated to a group detected in X-ray (Arnaud et al 2000). This region could be in pre-merger stage onto the main cluster nearly in the plane of the sky. These results, taken together with the fact that most of the clumps detected on the isodensity maps, as well as the early type galaxies and the brightest ones are aligned, suggest that this NW/SE direction is the preferred one for the formation of this cluster. The central high dense region shows a lower velocity location ($73625 ^{+344}_{-350}$ km/s) and significantly higher scale ($1780 ^{+234}_{-142}$ km/s) as compared to the whole cluster values. This is due to the presence of a low-velocity group of galaxies with a high fraction of emission line objects. This can be explained in a scenario in which a merging of subclusters has recently occurred along the direction of the ``ridge'' with a significant component along the line of sight.Comment: 21 pages, 32 figures, uses aa.cls style, Latex. Accepted for publication in A&

Speedy motions of a body immersed in an infinitely extended medium

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Psi. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound "runaway effect". Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Psi(r) diverges at short distances like g r^{-a}, g,a>0, by showing that the runaway effect still occurs if a<2.Comment: 15 page

CP(N−1)CP^{(N-1)} model in aether-superspace

In this paper we study the dynamical generation of mass in the Lorentz-violating $CP^{(N-1)}$ model defined in two and three-dimensional aether-superspace. We show that even though the model presents a phase structure similar to the usual, Lorentz invariant case, the dynamically generated mass by quantum corrections has a dependence on the Lorentz violating background properties, except for spacelike LV vector parameter. This is to be contrasted with the behavior of the quantum electrodynamics in the two-dimensional aether-superspace, where the dynamical generation of mass was shown to exhibit an explicit dependence on the aether parameters in every possible case.Comment: 18 pages, 4 figure

On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure