Hierarchies of R-violating interactions from Family Symmetries

We investigate the possibility of constructing models of R-violating LQD Yukawa couplings using a single U(1) flavour-symmetry group and supermultiplet charge assignments that are compatible with the known hierarchies of quark and lepton masses. The mismatch of mass and current eigenstates inferred from the known charged-current mixing induces the propagation of strong phenomenological constraints on some R-violating couplings to many others. Applying these constraints, we look for flavour-symmetry models that are consistent with different squark-production hypotheses devised to explain the possible HERA large-Q^2 anomaly. The e^+ d -> stop interpretation of the HERA data is accommodated relatively easily, at the price of postulating an extra parity. The e^+ s -> stop interpretation of the events requires models to have only small (2,3) mixing in the down quark sector. The e^+ d -> scharm mechanism cannot be accommodated without large violations of squark-mass universality, due to the very strong experimental constraints on R-violating operators. We display a model in which baryon decay due to dangerous dimension-five operators is automatically suppressed.Comment: 21 pages, Latex file, no figure

On magnetic catalysis in even-flavor QED3

In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scaling logarithmically with the external field. We also confirm this type of scaling behavior through quenched lattice calculations using the non-compact version for the gauge field. Both the zero and finite temperature cases are examined. A preliminary study of the fermion condensate in the presence of magnetic flux tubes on the lattice is also included.Comment: 38 pages latex, 18 figures and a style file (axodraw) incorporated (some clarifying remarks concerning the validity of the approximations made and some references were added correcting an earlier version; no effect on conclusions; version to appear in Phys. Rev. D.

Stochastic six-vertex model

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit shape as the mesh size tends to 0. We further prove that the one-point fluctuations around the limit shape are asymptotically governed by the GUE Tracy-Widom distribution. We also explain an equivalent formulation of our model as an interacting particle system, which can be viewed as a discrete time generalization of ASEP started from the step initial condition. Our results confirm an earlier prediction of Gwa and Spohn (1992) that this system belongs to the KPZ universality class.Comment: 45 pages, 8 figure

U(1)A_A Models of Fermion Masses Without a μ\mu Problem

We discuss the connection between models of fermion masses and mixing involving a string-motivated flavor/generation U(1)$_A$ gauge symmetry and the $\mu$ term. We point out that in a certain class of such models the flavor physics can provide an appealing solution to the $\mu$ problem, naturally yielding a $\mu \sim O(m_{_W})$. A simple relationship between the $U(1)_A$ charge $q_{H}$ of the $\mu$-term and the average generational $U(1)_A$ charges of the down quark and leptonic sectors is derived. Finally, we construct an explicit model illustrating our results.Comment: 12 pages, Latex Fil

Distribution of G-concurrence of random pure states

Average entanglement of random pure states of an N x N composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant we characterize the probability distribution P(D). Similar results are obtained for the rescaled N-th root of the determinant, called G-concurrence. We show that in the limit $N\to\infty$ this quantity becomes concentrated at a single point G=1/e. The position of the concentration point changes if one consider an arbitrary N x K bipartite system, in the joint limit $N,K\to\infty$, K/N fixed.Comment: RevTeX4, 11 pages, 4 Encapsuled PostScript figures - Introduced new results, Section II and V have been significantly improved - To appear on PR

Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux

We introduce a new family of noncommutative analogues of the Hall-Littlewood symmetric functions. Our construction relies upon Tevlin's bases and simple q-deformations of the classical combinatorial Hopf algebras. We connect our new Hall-Littlewood functions to permutation tableaux, and also give an exact formula for the q-enumeration of permutation tableaux of a fixed shape. This gives an explicit formula for: the steady state probability of each state in the partially asymmetric exclusion process (PASEP); the polynomial enumerating permutations with a fixed set of weak excedances according to crossings; the polynomial enumerating permutations with a fixed set of descent bottoms according to occurrences of the generalized pattern 2-31.Comment: 37 pages, 4 figures, new references adde

Diffusion-Annihilation in the Presence of a Driving Field

We study the effect of an external driving force on a simple stochastic reaction-diffusion system in one dimension. In our model each lattice site may be occupied by at most one particle. These particles hop with rates $(1\pm\eta)/2$ to the right and left nearest neighbouring site resp. if this site is vacant and annihilate with rate 1 if it is occupied. We show that density fluctuations (i.e. the $m^{th}$ moments $\langle N^m \rangle$ of the density distribution at time $t$) do not depend on the spatial anisotropy $\eta$ induced by the driving field, irrespective of the initial condition. Furthermore we show that if one takes certain translationally invariant averages over initial states (e.g. random initial conditions) even local fluctuations do not depend on $\eta$. In the scaling regime $t \sim L^2$ the effect of the driving can be completely absorbed in a Galilei transformation (for any initial condition). We compute the probability of finding a system of $L$ sites in its stationary state at time $t$ if it was fully occupied at time $t_0 = 0$.Comment: 17 pages, latex, no figure