Neutrino Observatories Can Characterize Cosmic Sources and Neutrino Properties

Neutrino telescopes that measure relative fluxes of ultrahigh-energy $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ can give information about the location and characteristics of sources, about neutrino mixing, and can test for neutrino instability and for departures from CPT invariance in the neutrino sector. We investigate consequences of neutrino mixing for the neutrino flux arriving at Earth, and consider how terrestrial measurements can characterize distant sources. We contrast mixtures that arise from neutrino oscillations with those signaling neutrino decays. We stress the importance of measuring $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ fluxes in neutrino observatories.Comment: 9 RevTeX pages, 4 figure

Test of renormalization predictions for universal finite-size scaling functions

We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular epsilon-expansion, where epsilon is the distance to the upper critical dimension. Subsequently, we check the results by numerical simulations of spin models in the same universality class. Our systems offer the essential advantage that epsilon can be varied continuously, allowing an accurate examination of the region where epsilon is small. The numerical calculations turn out to be in striking disagreement with the predicted singularity.Comment: 6 pages, including 3 EPS figures. To appear in Phys. Rev. E. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Critical structure factor in Ising systems

We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L^3 with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernicke expression of Puglielli and Ford.Comment: 16 page

Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the $\eta$ exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent $z$ are recovered and several new results are obtained. The equilibrium two-point scaling functions are obtained. The nonequilibrium, finite momentum, two-time $t,t'$ response and correlations are computed. They are shown to exhibit scaling forms, characterized by novel exponents $\lambda_R \neq \lambda_C$, as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be non trivial and of the form $X(q^z (t-t'), t/t')$. Analogies and differences with pure critical models are discussed.Comment: 33 pages, RevTe

Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension

We present exact results for the density profile of the one dimensional array of N hard spheres of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquid-solid transition occurs at zero temperature, because the close-pakced density, $\phi_c$, is one. However, if we relax this condition slightly such that $phi_c=1-\delta$, we find a series of critical temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th particle undergoes the liquid-solid transition. The functional form of the onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom

Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model

The low energy behaviour of the 2d antiferromagnetic Heisenberg model is studied in the sector with total spins $S=0,1,2$ by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix $\Delta_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$, $n=1,2,3,...$ from the corresponding quantities $\Delta_S^{(n)}$. Conservation of total spin $S$ is implemented explicitly and plays an important role. It is shown, how the ground state energies $E_S^{(n+1)}$, $S=0,1,2$ approach each other for increasing $n$, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions $$ between the ground states $|S,m;n+1>$ ($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated by the staggered spin operator $S_q^*$Comment: 18 pages, 8 figures, RevTe

Two-particle pairing and phase separation in a two-dimensional Bose-gas with one or two sorts of bosons

We present a phase diagram for a dilute two-dimensional Bose-gas on a lattice. For one sort of boson we consider a realistic case of the van der Waals interaction between particles with a strong hard-core repulsion $U$ and a van der Waals attractive tail $V$. For $V< 2 t$, $t$ being a hopping amplitude, the phase diagram of the system contains regions of the usual one-particle Bose-Einstein condensation (BEC). However for $V>2t$ we have total phase separation on a Mott-Hubbard Bose solid and a dilute Bose gas. For two sorts of structureless bosons described by the two band Hubbard model an s-wave pairing of the two bosons of different sort $\neq 0$ is possible. The results we obtained should be important for different Bose systems, including submonolayers of $^4$He, excitons in semiconductors, Schwinger bosons in magnetic systems and holons in HTSC. In the HTSC case a possibility of two-holon pairing in the slave-bosons theories of superconductivity can restore a required charge $2e$ of a Cooper pair.Comment: 10 pages, 2 figure

Soft lepton-flavor violation in a multi-Higgs-doublet seesaw model

We consider the Standard Model with an arbitrary number n_H of Higgs doublets and enlarge the lepton sector by adding to each lepton family \ell a right-handed neutrino singlet \nu_{\ell R}. We assume that all Yukawa-coupling matrices are diagonal, but the Majorana mass matrix M_R of the right-handed neutrino singlets is an arbitrary symmetric matrix, thereby introducing an explicit but soft violation of all lepton numbers. We investigate lepton-flavor-violating processes within this model. We pay particular attention to the large-m_R behavior of the amplitudes for these processes, where m_R is the order of magnitude of the matrix elements of M_R. While the amplitudes for processes like tau^- --> mu^- gamma and Z --> tau^+ mu^- drop as 1/m_R^2 for arbitrary n_H, processes like tau^- --> mu^- e^+ e^- and mu^- --> e^- e^+ e^- obey this power law only for n_H = 1. For n_H \geq 2, on the contrary, those amplitudes do not fall off when m_R increases, rather they converge towards constants. This non-decoupling of the right-handed scale occurs because of the sub-process ell^- --> ell'^- {S_b^0}^*, where S_b^0 is a neutral scalar which subsequently decays to e^+ e^-. That sub-process has a contribution from charged-scalar exchange which, for n_H \geq 2, does not decrease when m_R tends to infinity. We also perform a general study of the non-decoupling and argue that, after performing the limit m_R --> \infty and removing the \nu_R from the Lagrangian, our model becomes a multi-Higgs-doublet Standard Model with suppressed flavor-changing Yukawa couplings. Finally, we show that, with the usual assumptions about the mass scales in the seesaw mechanism, the branching ratios of all lepton-flavor-changing processes are several orders of magnitude smaller than present experimental limits.Comment: 46 pages, 2 figures, Revte

Dual Vortex Theory of Strongly Interacting Electrons: Non-Fermi Liquid to the (Hard) Core

As discovered in the quantum Hall effect, a very effective way for strongly-repulsive electrons to minimize their potential energy is to aquire non-zero relative angular momentum. We pursue this mechanism for interacting two-dimensional electrons in zero magnetic field, by employing a representation of the electrons as composite bosons interacting with a Chern-Simons gauge field. This enables us to construct a dual description in which the fundamental constituents are vortices in the auxiliary boson fields. The resulting formalism embraces a cornucopia of possible phases. Remarkably, superconductivity is a generic feature, while the Fermi liquid is not -- prompting us to conjecture that such a state may not be possible when the interactions are sufficiently strong. Many aspects of our earlier discussions of the nodal liquid and spin-charge separation find surprising incarnations in this new framework.Comment: Modified dicussion of the hard-core model, correcting several mistake

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.