Landau analog levels for dipoles in non-commutative space and phase space - Landau analog levels for dipoles

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov-Casher and He-McKellar-Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

In situ X-ray diffraction studies of phase transition in Pb1-x La x Zr0.40Ti0.60O3 ferroelectric ceramics

The temperature dependence of the crystalline structure and the lattice parameters of Pb1-xLaxZr0.40Ti0.60O3 ferroelectric ceramic system with 0.00 x 0.21 was determined. The samples with x 0.11 show a cubic-to-tetragonal phase transition at the maximum dielectric permittivity, Tmax. Above this amount and especially for the x = 0.12 sample, a spontaneous phase transition from a relaxor ferroelectric state (cubic phase) to a ferroelectric state (tetragonal phase) is observed upon cooling below the Tmax. Unlike what has been reported in other studies, the x = 0.13, 0.14, and 0.15 samples, which present a more pronounced relaxor behavior, also presents a spontaneous normal-to-relaxor transition, indicated by a cubic to tetragonal symmetry below the Tmax. The origin of this anomaly has been associated with an increase in the degree of tetragonality, confirmed by the measurements of the X-ray diffraction patterns. The differential thermal analysis (DSC) measurements also confirm the existence of these phase transitions.

Compressibility of electron liquid in the quantized Hall phase of GaAs/AlGaAs multi-layers

Magneto-capacitance was studied in narrow miniband GaAs/AlGaAs superlattices where quasi-two dimensional electrons revealed the integer quantum Hall effect. The interwell tunneling was shown to reduce the effect of the quantization of the density of states on the capacitance of the superlattices. In such case the minimum of the capacitance observed at the filling factor nu = 2 was attributed to the decrease of the electron compressibility due to the formation of the incompressible quantized Hall phase. In accord with the theory this phase was found strongly inhomogeneous. The incompressible fraction of the quantized Hall phase was demonstrated to rapidly disappear with the increasing temperature. (C) 2008 Elsevier B.V. All rights reserved.

Spectroscopic evidence of extended states in quantized Hall phase of weakly coupled GaAs/AlGaAs multi-layers

The influence of the interlayer coupling on formation of the quantized Hall conductor phase at the filling factor v = 2 was studied in the multi-layer GaAs/AlGaAs heterostructures. The disorder broadened Gaussian photoluminescence line due to the localized electrons was found in the quantized Hall phase of the isolated multi-quantum well structure. On the other hand, the quantized Hall phase of the weakly coupled multi-layers emitted an unexpected asymmetrical line similar to that one observed in the metallic electron systems. We demonstrated that the observed asymmetry is caused by a partial population of the extended electron states formed in the quantized Hall conductor phase due to the interlayer percolation. A sharp decrease of the single-particle scattering time associated with these extended states was observed at the filling factor v = 2. (c) 2007 Elsevier B.V. All rights reserved.

Structural Phase Transition Studies on PMN-0.35PT using Infrared Spectroscopy

The purpose of the present work is to report studies on structural phase transition for PMN-xPT ferroelectric, with melt PbTiO3 composition around the MPB (x = 0.35 mol %), using infrared spectroscopy technique. The study was centered on monitoring the behavior of the 1-(NbO), 1-(TiO) and 1-(MgO) stretching modes as a function of temperature. The increasing as a function of temperature for 1-(TiO) and 1-(MgO) modes, observed between 230 and 300 K, can be related to the monoclinic (MC) + tetragonal (T) phase coexistence in the PMN-PT.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Phase-transition studies of Ba(0.90)Ca(0.10)(Ti(1-x)Zr(x))O(3) ferroelectric ceramic compounds

Perovskite-structured Ba(0.90)Ca(0.10)(Ti(1-x)Zr(x))O(3) ceramics were prepared in this work and subsequently studied in terms of composition-dependent dielectric and high-resolution long-range order structural properties from 30 to 450 K. The dielectric response of these materials was measured at several frequencies in the range from 1 kHz to 1 MHz. Combining both techniques, including Rietveld refinement of the X-ray diffraction data, allowed observing that, when increasing Zr(4+) content, the materials change from conventional to diffuse and relaxor ferroelectric compounds, the transition occurring spontaneously at the x = 0.18 composition. Interestingly, this spontaneous transition turned out to be prevented for a further increase of Zr(4+). On the basis of all the dielectric and structural results processed, a phase diagram of this system is presented. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Evidence for magnetic phase separation in La(0.86)Sr(0.14)Mn(1-x)Cu(x)O(3+delta) manganites from NMR and magnetic measurements

Polycrystalline La(0.86)Sr(0.14)Mn(1-x)Cu(x)O(3+delta) (x = 0, 0.05, 0.10, 0.15, 0.20) manganites were investigated by means of magnetic measurements and zero-field (139)La and (55)Mn nuclear magnetic resonance (NMR) spectroscopy. Magnetization versus temperature measurements revealed a paramagnetic to ferromagnetic transition in most samples, with lower Curie temperatures and broader transitions for samples with higher Cu contents. The details of the magnetization measurements suggested a phase-separated scenario, with ferromagnetic clusters embedded in an antiferromagnetic matrix, especially for the samples with large Cu contents (x = 0.15 and 0.20). Zero-field (139)La NMR measurements confirmed this finding, since the spectral features remained almost unchanged for all Cu-doped samples, whereas the bulk magnetization was drastically reduced with increasing Cu content. (55)Mn NMR spectra were again typical of ferromagnetic regions, with a broadening of the resonance line caused by the disorder introduced by the Cu doping. The results indicate a coexistence of different magnetic phases in the manganites studied, with the addition of Cu contributing to the weakening of the double-exchange interaction in most parts of the material.

Tunneling among rotation tori

We consider an integrable Hamiltonian system generated by the resonant normal form in order to study a particular mechanism of tunneling. We isolated near doublets of energy corresponding to rotation tori of the classical dynamics counterpart and the degeneracies breakdown is attributed to rotation-rotation tunneling. (C) 2008 Elsevier B.V. All rights reserved.

Cellular automaton model for molecular traffic jams

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally asymmetric simple exclusion process with sublattice parallel update and thus may serve as a model for studying traffic jams in systems of self-driven particles. We study the emergence of shocks from the microscopic dynamics of the model. In particular, we introduce shock measures whose time evolution we can compute explicitly, both in the thermodynamic limit and for open boundaries where a boundary-induced phase transition driven by the motion of a shock occurs. The motion of the shock, which results from the collective dynamics of the exclusion particles, is a random walk with an internal degree of freedom that determines the jump direction. This type of hopping dynamics is reminiscent of some transport phenomena in biological systems.

An information-theoretic approach to statistical dependence: Copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.