Self-Consistent Mean-Field Theory for Frustrated Josephson Junction Arrays

We review the self-consistent mean-field theory for charge-frustrated Josephson junction arrays. Using (\phi is the phase of the superconducting wavefunction) as order parameter and imposing the self-consistency condition, we compute the phase boundary line between the superconducting region ( not equal to zero) and the insulating one ( = 0). For a uniform offset charge q=e the superconducting phase increases with respect to the situation in which q=0. Here, we generalize the self-consistent mean-field theory to include the effects induced by a random distribution of offset charges and/or of diagonal self-capacitances. For most of the phase diagram, our results agree with the outcomes of Quantum Monte Carlo simulations as well as with previous studies using the path-integral approach.Comment: Presented by F. P. Mancini at the Conference "Highlights in Condensed Matter Physics", May 9-11 2003, Salerno, Ital

Superconducting Topological Fluids in Josephson Junction Arrays

We argue that the frustrated Josephson junction arrays may support a topologically ordered superconducting ground state, characterized by a non-trivial ground state degeneracy on the torus. This superconducting quantum fluid provides an explicit example of a system in which superconductivity arises from a topological mechanism rather than from the usual Landau-Ginzburg mechanism.Comment: 4 page

Topology Induced Spatial Bose-Einstein Condensation for Bosons on Star-Shaped Optical Networks

New coherent states may be induced by pertinently engineering the topology of a network. As an example, we consider the properties of non-interacting bosons on a star network, which may be realized with a dilute atomic gas in a star-shaped deep optical lattice. The ground state is localized around the star center and it is macroscopically occupied below the Bose-Einstein condensation temperature T_c. We show that T_c depends only on the number of the star arms and on the Josephson energy of the bosonic Josephson junctions and that the non-condensate fraction is simply given by the reduced temperature T/T_c.Comment: 20 Pages, 5 Figure

Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations

We study the class of generalized Korteweg-DeVries equations derivable from the Lagrangian: L(l,p) = \int \left( \frac{1}{2} \vp_{x} \vp_{t} - { {(\vp_{x})^{l}} \over {l(l-1)}} + \alpha(\vp_{x})^{p} (\vp_{xx})^{2} \right) dx, where the usual fields $u(x,t)$ of the generalized KdV equation are defined by u(x,t) = \vp_{x}(x,t). This class contains compactons, which are solitary waves with compact support, and when $l=p+2$, these solutions have the feature that their width is independent of the amplitude. We consider the Hamiltonian structure and integrability properties of this class of KdV equations. We show that many of the properties of the solitary waves and compactons are easily obtained using a variational method based on the principle of least action. Using a class of trial variational functions of the form $u(x,t) = A(t) \exp \left[-\beta (t) \left|x-q(t) \right|^{2n} \right]$ we find soliton-like solutions for all $n$, moving with fixed shape and constant velocity, $c$. We show that the velocity, mass, and energy of the variational travelling wave solutions are related by $c = 2 r E M^{-1}$, where $r = (p+l+2)/(p+6-l)$, independent of $n$.\newline \newline PACS numbers: 03.40.Kf, 47.20.Ky, Nb, 52.35.SbComment: 16 pages. LaTeX. Figures available upon request (Postscript or hard copy

Lattice Gauge Theories and the Heisenberg Antiferromagnetic Chain

We study the strongly coupled 2-flavor lattice Schwinger model and the SU(2)-color QCD_2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.Comment: Proceedings LATTICE99 (spin models), 3 page

Finite-temperature corrections to the Lorenz ratio at the N = 3 topological Kondo fixed point

We analyze the finite-temperature scaling of the Lorenz ratio at the topological Kondo fixed point realized at a junction of three interacting quantum wires connected to a floating superconducting island. Using the Tomonaga-Luttinger liquid approach to the quantum wires, we derive the full functional dependence of the finite-temperature correction on the Luttinger parameter g

Propagation of Discrete Solitons in Inhomogeneous Networks

In many physical applications solitons propagate on supports whose topological properties may induce new and interesting effects. In this paper, we investigate the propagation of solitons on chains with a topological inhomogeneity generated by the insertion of a finite discrete network on the chain. For networks connected by a link to a single site of the chain, we derive a general criterion yielding the momenta for perfect reflection and transmission of traveling solitons and we discuss solitonic motion on chains with topological inhomogeneities