The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics

We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a random walk X on Z^d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time L_t(X,Y)=\int_0^t \ind_{X_s=Y_s}\dd s: the weight of the path under the new measure is exp(beta L_t(X,Y)), beta in R. As beta increases, the system exhibits a delocalization/localization transition: there is a critical value beta_c, such that if beta>beta_c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d larger or equal to three 3, the presence of disorder makes the phase transition at least of second order. This, in dimension larger or equal to 4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.Comment: 18 page

Thickness Estimation of Epitaxial Graphene on SiC using Attenuation of Substrate Raman Intensity

A simple, non-invasive method using Raman spectroscopy for the estimation of the thickness of graphene layers grown epitaxially on silicon carbide (SiC) is presented, enabling simultaneous determination of thickness, grain size and disorder using the spectra. The attenuation of the substrate Raman signal due to the graphene overlayer is found to be dependent on the graphene film thickness deduced from X-ray photoelectron spectroscopy and transmission electron microscopy of the surfaces. We explain this dependence using an absorbing overlayer model. This method can be used for mapping graphene thickness over a region and is capable of estimating thickness of multilayer graphene films beyond that possible by XPS and Auger electron spectroscopy (AES).Comment: 14 pages, 9 figure

Observing Nucleon Decay in Lead Perchlorate

Lead perchlorate, part of the OMNIS supernova neutrino detector, contains two nuclei, 208Pb and 35Cl, that might be used to study nucleon decay. Both would produce signatures that will make them especially useful for studying less-well-studied neutron decay modes, e.g., those in which only neutrinos are emitted.Comment: 6 pages, 2 figure

Observable Neutron-Antineutron Oscillations in Seesaw Models of Neutrino Mass

We show that in a large class of supersymmetric models with spontaneously broken B-L symmetry, neutron--antineutron oscillations occur at an observable level even though the scale of B-L breaking is very high, v_{B-L} ~ 2 x 10^{16} GeV, as suggested by gauge coupling unification and neutrino masses. We illustrate this phenomenon in the context of a recently proposed class of seesaw models that solves the strong CP problem and the SUSY phase problem using parity symmetry. We obtain an upper limit on N-\bar{N} oscillation time in these models, \tau_{N-\bar{N}} < 10^{9} -10^{10} sec. This suggests that a modest improvement in the current limit on \tau_{N-\bar{N}} of 0.86 x 10^8 sec will either lead to the discovery of N-\bar{N} oscillations, or will considerably restrict the allowed parameter space of an interesting class of neutrino mass models.Comment: 11 pages RevTeX, 1 figur

Signatures of Nucleon Disappearance in Large Underground Detectors

For neutrons bound inside nuclei, baryon instability can manifest itself as a decay into undetectable particles (e.g., $\it n \to \nu \nu \bar{\nu}$), i.e., as a disappearance of a neutron from its nuclear state. If electric charge is conserved, a similar disappearance is impossible for a proton. The existing experimental lifetime limit for neutron disappearance is 4-7 orders of magnitude lower than the lifetime limits with detectable nucleon decay products in the final state [PDG2000]. In this paper we calculated the spectrum of nuclear de-excitations that would result from the disappearance of a neutron or two neutrons from $^{12}$C. We found that some de-excitation modes have signatures that are advantageous for detection in the modern high-mass, low-background, and low-threshold underground detectors, where neutron disappearance would result in a characteristic sequence of time- and space-correlated events. Thus, in the KamLAND detector [Kamland], a time-correlated triple coincidence of a prompt signal, a captured neutron, and a $\beta^{+}$ decay of the residual nucleus, all originating from the same point in the detector, will be a unique signal of neutron disappearance allowing searches for baryon instability with sensitivity 3-4 orders of magnitude beyond the present experimental limits.Comment: 13 pages including 6 figures, revised version, to be published in Phys.Rev.

Models of electron transport in single layer graphene

The main features of the conductivity of doped single layer graphene are analyzed, and models for different scattering mechanisms are presented.Comment: 15 pages. Submitted to the Proceedings of the ULTI symposium on Quantum Phenomena and Devices at Low Temperatures, Espoo, Finland, to be published in the Journ. of Low. Temp. Phy

Constraints on Three-Neutrino Mixing from Atmospheric and Reactor Data

Observations of atmospheric neutrinos are usually analyzed using the simplifying approximation that either $\nu_\mu \leftrightarrow \nu_\tau$ or $\nu_e \leftrightarrow \nu_\mu$ two-flavor mixing is relevant. Here we instead consider the data using the simplifying approximation that only one neutrino mass scale is relevant. This approximation is the minimal three-flavor notation that includes the two relevant two-flavor approximations. The constraints in the parameter space orthogonal to the usual, two-flavor analyses are studied.Comment: 15 pages, preprint IUHET-26

Measuring Atmospheric Neutrino Oscillations with Neutrino Telescopes

Neutrino telescopes with large detection volumes can demonstrate that the current indications of neutrino oscillation are correct or if a better description can be achieved with non-standard alternatives. Observations of contained muons produced by atmospheric neutrinos can better constrain the allowed region for oscillations or determine the relevant parameters of non-standard models. We analyze the possibility of neutrino telescopes measuring atmospheric neutrino oscillations. We suggest adjustments to improve this potential. An addition of four densely-instrumented strings to the AMANDA II detector makes observations feasible. Such a configuration is competitive with current and proposed experiments.Comment: 36 pages, 21 figures, revte

Leptogenesis and neutrino parameters

We calculate the baryonic asymmetry of the universe in the baryogenesis-via-leptogenesis framework, assuming first a quark-lepton symmetry and then a charged-neutral lepton symmetry. We match the results with the experimentally favoured range. In the first case all the oscillation solutions to the solar neutrino problem, except the large mixing matter solution, can lead to the allowed range, but with fine tuning of the parameters. In the second case the general result is quite similar. Some related theoretical hints are discussed.Comment: RevTex, 21 pages with 8 figure

Transport Properties through Double Barrier Structure in Graphene

The mode-dependent transmission of relativistic ballistic massless Dirac fermion through a graphene based double barrier structure is being investigated for various barrier parameters. We compare our results with already published work and point out the relevance of these findings to a systematic study of the transport properties in double barrier structures. An interesting situation arises when we set the potential in the leads to zero, then our 2D problem reduces effectively to a 1D massive Dirac equation with an effective mass proportional to the quantized wave number along the transverse direction. Furthermore we have shown that the minimal conductivity and maximal Fano factor remain insensitive to the ratio between the two potentials V_2/V_1=\alpha.Comment: 18 pages, 12 figures, clarifications and reference added, misprints corrected. Version to appear in JLT