Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.     

Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

Stability of rocksalt (111) polar surfaces: beyond the octopole

Stable polar oxide surfaces must be simultaneously electrostatically compensated and in thermodynamic equilibrium with the environment. As a paradigm, the MgO(111)-p(2x2) reconstructed surface is shown to involve combinations of Mg-covered terminations with peculiar insulating electronic structure, favored in O-poor conditions, and the O-terminated octopole, stabler in more O-rich environments. Such a picture, which could not have been foreseen by either experiments or simulations separately, goes beyond the Wolf model and reconciles the theory with the experimental data taken in variable thermodynamic conditions.     

Upward and downward heat and mass transfer with miniature periodically operating loop thermosyphons

Upward and downward two-phase heat and mass transfer has been considered in the present paper. The heat and mass transfer with the condenser located below the evaporator has been obtained by inserting an accumulator tank in the liquid line of a loop thermosyphon and enforcing a pressure pulsation. In previous papers these heat transfer devices have been called pulsated two phase thermosyphons (PTPT). A mini PTPT has been experimentally investigated. It has shown a stable periodic heat transfer regime weakly influenced by the position of the condenser with respect to the evaporator. In contrast a classical loop mini thermosyphon (diameter of connecting pipes 4 mm) did not achieve a stable functioning for the investigated level differences between evaporator and condenser lower than 0.37 m. The present study shows that the functioning of a PTPT device does not directly depend on the level difference or the presence of noncondensable gas. In order to obtain a natural circulation in mini or micro loops, a periodically operating heat transfer regime should therefore be considered.     

Boosts in an Arbitrary Direction and Maximal Causal Velocities in a Deformed Minkowski Space

We discuss boosts in a deformed Minkowski space, i.e., a four-dimensional spacetime with metric coefficients depending on nonmetric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal trivector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts.     

High peak power operation and harmonic generation of a single-polarization, Yb-doped photonic crystal fiber amplifier

We report on the use of a single-polarization, 41 μm core-diameter, intrinsically single-mode photonic crystal fiber (PCF) to obtain high peak power (up to 800 kW), 1 ns-duration pulses in a 100:1 linearly polarized, intrinsically single-mode (M²  1.2) output. By transmitting the PCF output through nonlinear crystals, we also obtained efficient second, third, and fourth harmonic generation resulting in peak power >400 kW in the visible (green, 531 nm) and 200 kW in the UV (265.5 nm). To our knowledge these results represent the highest peak power obtained in a linearly polarized output from a fiber and the highest peak power in the visible and UV obtained through harmonic generation of the direct fiber output.     

Electrochemical characterization of LiCoO2 as rechargeable electrode in aqueous LiNO3 electrolyte

The development of lithium ion aqueous batteries is getting renewed interest due to their safety and low cost. We have demonstrated that the layer-structure LiCoO₂ phase, the most commonly used electrode material in organic systems, can be successful delithiated and lithiated again in a water-based electrolyte at currents up to 2.70 A/g. The capacity is about 100 mAh/g at 0.135 A/g and can be tuned by cycling the electrode in different potential ranges. In fact, increasing the high cut-off voltage leads to higher specific capacity (up to 135 mAh/g) but the Coulomb efficiency is reduced (from 99.9% to 98.5%). The very good electrode kinetic is probably due to the high conductivity of the electrolyte solution (0.17 Scm^− 1 at 25 °C) but this behavior is affected by the electrode load.     

Braiding structures on formal Poisson groups and classical solutions of the QYBE

If is a quasitriangular Lie bialgebra, the formal Poisson group can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G=SL₂) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.     

Precision and sensitivity optimization of quantitative measurements in solid state NMR

This work presents a methodology for optimizing the precision, accuracy and sensitivity of quantitative solid state NMR measurements based on the external reference method. It is shown that the sample must be exclusively located within and completely span the coil region where the NMR response is directly proportional to the sample amount. We describe two methods to determine this "quantitative" coil volume, based on whether the probe is equipped or not with a gradient coil. In addition, to improve the sensitivity and the accuracy, an optimum rotor packing design is described, which allows the sample volume of the rotor to be matched to the quantitative coil volume. Experiments conducted on adamantane and NaCl, which are representative of a soft and hard material, respectively, show that one order of magnitude increase in experimental precision can be achieved with this methodology. Interestingly, the precision can be further improved by using the ERETIC method in order to compensate for most instrumental instabilities.