DD-dimensional Arrays of Josephson Junctions, Spin Glasses and qq-deformed Harmonic Oscillators

We study the statistical mechanics of a $D$-dimensional array of Josephson junctions in presence of a magnetic field. In the high temperature region the thermodynamical properties can be computed in the limit $D \to \infty$, where the problem is simplified; this limit is taken in the framework of the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e. to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the $q$-deformed harmonic oscillator

Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Internationalisation of service firms through corporate social entrepreneurship and networking

Findings: The findings reveal that, by engaging in social entrepreneurship, these MNCs have focused on the neglected needs of the BOP population, developed sustainable solutions and empowerment, and started with social value creation and postponed value capturing. The pursuit of corporate social entrepreneurship has paved the way for them to establish relationships with NGOs. While the MNCs have mainly had the technical knowledge and financial resources required, collaboration with NGOs have allowed them to learn about the BOP’s specific needs and benefit from the NGOs’ knowledge, human resources and good relationships in this market.Originality/value: This research unravels how service firms can seize opportunities at the BOP. The authors build on social entrepreneurship theory and bring new insights to the field of international business. In addition, the authors broaden the network view and show how networking with social actors such as NGOs enables the mobilisation of resources, actors and activities in emerging markets.Design/methodology/approach: This research adopts an exploratory approach employing qualitative multiple case studies. Three service firms that have targeted the BOP markets in India were studied. In total, 25 in-depth interviews were conducted with multinational corporations (MNCs) and their NGO partners. Data analysis was facilitated through pattern matching and systematic case comparison.Purpose: The purpose of this paper is to explore how employing corporate social entrepreneurship and developing a network of relationships with non-governmental organisations (NGOs) can support and contribute towards the internationalisation of service firms into the base of the pyramid (BOP) markets in emerging markets

Extreme events driven glassy behaviour in granular media

Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator [Nature 413 (2001) 407], we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: (1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the relaxation time. The model draws a parallel between macroscopic rearrangements in the system and extreme events whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed as well as the existence of other regimes.Comment: 7 pages, to appear in Europhys. Let

Current Distribution in the Three-Dimensional Random Resistor Network at the Percolation Threshold

We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth moments of the current distribution, finding {\it e.g.\/} that $t/\nu=2.282(5)$ where $t$ is the conductivity exponent and $\nu$ is the correlation length exponent.Comment: 10 pages, latex, 8 figures in separate uuencoded fil

Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?

The motion of driven interfaces in random media at finite temperature $T$ and small external force $F$ is usually described by a linear displacement $h_G(t) \sim V(F,T) t$ at large times, where the velocity vanishes according to the creep formula as $V(F,T) \sim e^{-K(T)/F^{\mu}}$ for $F \to 0$. In this paper, we question this picture on the specific example of the directed polymer in a two dimensional random medium. We have recently shown (C. Monthus and T. Garel, arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong disorder renormalization procedure, where the distribution of renormalized barriers flows towards some "infinite disorder fixed point". In the present paper, we obtain that for small $F$, this "infinite disorder fixed point" becomes a "strong disorder fixed point" with an exponential distribution of renormalized barriers. The corresponding distribution of trapping times then only decays as a power-law $P(\tau) \sim 1/\tau^{1+\alpha}$, where the exponent $\alpha(F,T)$ vanishes as $\alpha(F,T) \propto F^{\mu}$ as $F \to 0$. Our conclusion is that in the small force region $\alpha(F,T)<1$, the divergence of the averaged trapping time $\bar{\tau}=+\infty$ induces strong non-self-averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value. We find instead that the motion is only sub-linearly in time $h_G(t) \sim t^{\alpha(F,T)}$, i.e. the asymptotic velocity vanishes V=0. This analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape. We moreover obtain that the roughness exponent, which is governed by the equilibrium value $\zeta_{eq}=2/3$ up to some large scale, becomes equal to $\zeta=1$ at the largest scales.Comment: v3=final versio

Structure of the superconducting state in a fully frustrated wire network with dice lattice geometry

The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy functional projected on its unstable supspace as an effective model on the triangular lattice of sixfold coordinated sites. For this latter model, we obtain a large class of degenerate equilibrium configurations in one to one correspondence with those previously constructed for the pure XY model on the maximally frustrated dice lattice. The entropy of these states is proportional to the linear size of the system. Finally we show that magnetic interactions between currents provide a degeneracy lifting mechanism.Comment: The final version (as published in Phys. Rev. B). Substantial corrections have been made to Sec.

Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity

A new version of the invariant imbedding theory for the propagation of coupled waves in inhomogeneous media is applied to the mode conversion of high frequency electromagnetic waves into electrostatic modes in cold, magnetized and stratified plasmas. The cases where the external magnetic field is applied perpendicularly to the direction of inhomogeneity and the electron density profile is linear are considered. Extensive and numerically exact results for the mode conversion coefficients, the reflectances and the wave electric and magnetic field profiles inside the inhomogeneous plasma are obtained. The dependences of mode conversion phenomena on the magnitude of the external magnetic field, the incident angle and the wave frequency are explored in detail.Comment: 11 figures, to be published in Physics of Plasma

Exact transmission moments in one-dimensional weak localization and single-parameter scaling

We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection coefficients to fourth order in the weakly disordered site energies. These results confirm the validity of single-parameter scaling theory in a domain where the higher transmission cumulants may be neglected. We compare our results with earlier results for transmission cumulants in the weak localization domain based on the phase randomization hypothesis