Heat Capacity in Magnetic and Electric Fields Near the Ferroelectric Transition in Tri-Glycine Sulfate

Specific-heat measurements are reported near the Curie temperature ($T_C$~= 320 K) on tri-glycine sulfate. Measurements were made on crystals whose surfaces were either non-grounded or short-circuited, and were carried out in magnetic fields up to 9 T and electric fields up to 220 V/cm. In non-grounded crystals we find that the shape of the specific-heat anomaly near $T_C$ is thermally broadened. However, the anomaly changes to the characteristic sharp $\lambda$-shape expected for a continuous transition with the application of either a magnetic field or an electric field. In crystals whose surfaces were short-circuited with gold, the characteristic $\lambda$-shape appeared in the absence of an external field. This effect enabled a determination of the critical exponents above and below $T_C$, and may be understood on the basis that the surface charge originating from the pyroelectric coefficient, $dP/dT$, behaves as if shorted by external magnetic or electric fields.Comment: 4 Pages, 4 Figures. To Appear in Applied Physics Letters_ January 200

Majorana Spin Liquids, Topology and Superconductivity in Ladders

We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin liquid phases or Anderson resonating valence bond (RVB) states can be understood, as an effective model, in terms of p-wave superconductivity and Majorana fermions. We derive a generalized phase diagram for the two-leg ladder system with tunable interaction strengths between chains allowing us to vary the shape of the lattice (from square to honeycomb ribbon or brickwall ladder). We evaluate the winding number associated with possible emergent (topological) gapless modes at the edges. In the Az phase, as a result of the emergent Z2 gauge fields and pi-flux ground state, one may build spin-1/2 (loop) qubit operators by analogy to the toric code. In addition, we show how the intermediate gapless B phase evolves in the generalized ladder model. For the brickwall ladder, the $B$ phase is reduced to one line, which is analyzed through perturbation theory in a rung tensor product states representation and bosonization. Finally, we show that doping with a few holes can result in the formation of hole pairs and leads to a mapping with the Su-Schrieffer-Heeger model in polyacetylene; a superconducting-insulating quantum phase transition for these hole pairs is accessible, as well as related topological properties.Comment: 25 pages, 10 figures, final version - to be published in PR

A two-step learning approach for solving full and almost full cold start problems in dyadic prediction

Dyadic prediction methods operate on pairs of objects (dyads), aiming to infer labels for out-of-sample dyads. We consider the full and almost full cold start problem in dyadic prediction, a setting that occurs when both objects in an out-of-sample dyad have not been observed during training, or if one of them has been observed, but very few times. A popular approach for addressing this problem is to train a model that makes predictions based on a pairwise feature representation of the dyads, or, in case of kernel methods, based on a tensor product pairwise kernel. As an alternative to such a kernel approach, we introduce a novel two-step learning algorithm that borrows ideas from the fields of pairwise learning and spectral filtering. We show theoretically that the two-step method is very closely related to the tensor product kernel approach, and experimentally that it yields a slightly better predictive performance. Moreover, unlike existing tensor product kernel methods, the two-step method allows closed-form solutions for training and parameter selection via cross-validation estimates both in the full and almost full cold start settings, making the approach much more efficient and straightforward to implement

The electron lifetime in Luttinger liquids

We investigate the decoherence of the electron wavepacket in purely ballistic one-dimensional systems described through the Luttinger liquid (LL). At a finite temperature $T$ and long times $t$, we show that the electron Green's function for a fixed wavevector close to one Fermi point decays as $\exp(-t/\tau_F)$, as opposed to the power-law behavior occurring at short times, and the emerging electron lifetime obeys $\tau_F^{-1}\propto T$ for spinful as well as spinless electrons. For strong interactions, $(T\tau_F)\ll 1$, reflecting that the electron is not a good Landau quasiparticle in LLs. We justify that fractionalization is the main source of electron decoherence for spinful as well as spinless electrons clarifying the peculiar electron mass renormalization close to the Fermi points. For spinless electrons and weak interactions, our intuition can be enriched through a diagrammatic approach or Fermi Golden rule and through a Johnson-Nyquist noise picture. We stress that the electron lifetime (and the fractional quasiparticles) can be revealed from Aharonov-Bohm experiments or momentum resolved tunneling. We aim to compare the results with those of spin-incoherent and chiral LLs.Comment: 20 pages, 1 column, 6 figures, 1 Table; expands cond-mat/0110307 and cond-mat/0503652; final version to appear in PR

Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.Comment: 18 RevTeX pages, 5 figure

Stretching of polymers around the Kolmogorov scale in a turbulent shear flow

We present numerical studies of stretching of Hookean dumbbells in a turbulent Navier-Stokes flow with a linear mean profile, =Sy. In addition to the turbulence features beyond the viscous Kolmogorov scale \eta, the dynamics at the equilibrium extension of the dumbbells significantly below eta is well resolved. The variation of the constant shear rate S causes a change of the turbulent velocity fluctuations on all scales and thus of the intensity of local stretching rate of the advecting flow. The latter is measured by the maximum Lyapunov exponent lambda_1 which is found to increase as \lambda_1 ~ S^{3/2}, in agreement with a dimensional argument. The ensemble of up to 2 times 10^6 passively advected dumbbells is advanced by Brownian dynamics simulations in combination with a pseudospectral integration for the turbulent shear flow. Anisotropy of stretching is quantified by the statistics of the azimuthal angle $\phi$ which measures the alignment with the mean flow axis in the x-y shear plane, and the polar angle theta which determines the orientation with respect to the shear plane. The asymmetry of the probability density function (PDF) of phi increases with growing shear rate S. Furthermore, the PDF becomes increasingly peaked around mean flow direction (phi= 0). In contrast, the PDF of the polar angle theta is symmetric and less sensitive to changes of S.Comment: 16 pages, 14 Postscript figures (2 with reduced quality

A Bethe lattice representation for sandpiles

Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments are reconciled. Critical behavior is here expressed troughout the critical properties of percolation phenomena.Comment: 5 pages, 4 figures, submitted for publicatio

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic