A symmetry breaking mechanism for selecting the speed of relativistic solitons

We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point of view, the mechanism allows one to select the speed of a SG soliton just by tuning elastic couplings constants and kinematical parameters. From a fundamental, field-theoretical point of view we show that the characterizing features of relativistic SG solitons (existence of conserved topological charges and stability) may be still preserved even if the Lorentz symmetry is broken and a soliton of a given speed is selected.Comment: 23 pages, no figure

Superfluidity and dimerization in a multilayered system of fermionic polar molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce inter-layer pairing. Due to competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every-other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light scattering experiments to detect dimerization.Comment: 4 pages main text + 3 pages supplemental Appendices, 4 figure

Superfluid-insulator transition of disordered bosons in one-dimension

We study the superfluid-insulator transition in a one dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong randomness real space renormalization group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid insulator transition is always Kosterlitz- Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a non universal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. {\bf 3}, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott glass phase. If both integer and half integer filling factors are allowed then the corresponding phase is a random singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.Comment: 16 page

Interface growth in two dimensions: A Loewner-equation approach

The problem of Laplacian growth in two dimensions is considered within the Loewner-equation framework. Initially the problem of fingered growth recently discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77, 041602 (2008)] is revisited and a new exact solution for a three-finger configuration is reported. Then a general class of growth models for an interface growing in the upper-half plane is introduced and the corresponding Loewner equation for the problem is derived. Several examples are given including interfaces with one or more tips as well as multiple growing interfaces. A generalization of our interface growth model in terms of ``Loewner domains,'' where the growth rule is specified by a time evolving measure, is briefly discussed.Comment: To appear in Physical Review

R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz

We review some of the strategies that can be implemented to infer an $R$-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in arXiv:1306.6303, on three state $U(1)$-invariant Hamiltonians solvable by CBA, focusing on models for which the $S$-matrix is not trivial. For the 19-vertex solutions, we recover the $R$-matrices of the well-known Zamolodchikov--Fateev and Izergin--Korepin models. We point out that the generalized Bariev Hamiltonian is related to both main and special branches studied by Martins in arXiv:1303.4010, that we prove to generate the same Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we are able to state some no-go theorems on its $R$-matrix. For 17-vertex Hamiltonians, we produce a new $R$-matrix.Comment: 22 page

A coarse-grained, ``realistic'' model for Protein Folding

A phenomenological model hamiltonian to describe the folding of a protein with any given sequence is proposed. The protein is thought of as a collection of pieces of helices; as a consequence its configuration space increases with the number of secondary structure elements rather than with the number of residues. The hamiltonian presents both local (i.e. single helix, accounting for the stiffness of the chain) and non local (interactions between hydrophobically-charged helices) terms, and is expected to provide a first tool for studying the folding of real proteins. The partition function for a simplified, but by no means trivial, version of the model is calculated almost completely in an analytical way. The latter simplified model is also applied to the study of a synthetic protein, and some preliminary results are shown.Comment: 21 pages, 5 Postscript figures, RevTex; to be published in J. Chem. Phy

Discrete models of force chain networks

A fundamental property of any material is its response to a localized stress applied at a boundary. For granular materials consisting of hard, cohesionless particles, not even the general form of the stress response is known. Directed force chain networks (DFCNs) provide a theoretical framework for addressing this issue, and analysis of simplified DFCN models reveal both rich mathematical structure and surprising properties. We review some basic elements of DFCN models and present a class of homogeneous solutions for cases in which force chains are restricted to lie on a discrete set of directions.Comment: 17 pages, 6 figures, dcds-B.cls; Minor corrections to version 2, but including an important factor of 2; Submitted to Discrete and Continuous Dynamical Systems B for special issue honoring David Schaeffe