Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudo-potential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.Comment: 14 pages, contribution to the proceedings of the Group 27 conference, Yerevan, Armenia, August 13-19, 2008, published versio

Exact shock solution of a coupled system of delay differential equations: a car-following model

In this paper, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called {\it the car-following model}. We use the Hirota method, originally developed in order to solve soliton equations. %While, with a periodic boundary condition, this system has % a traveling-wave solution given by elliptic functions. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with a periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure

Harmonic Superspace Gaugeon Formalism for the ABJM Theory

In this paper we will analyse the ABJM theory in harmonic superspace. The harmonic superspace variables will be parameterized by the coset $SU(2)/U(1)$ and thus will have manifest $\mathcal{N} =3$ supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical sub-space from the total Hilbert space. We will also show that the evolution of the $\mathcal{S}$-matrix is unitary for this ABJM theory in harmonic superspace.Comment: 11, pages, 0 figures, accepted for publication in Mod. Phys. Lett.

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration

We discuss four off-shell N=4 D=1 supersymmetry transformations, their associated one-dimensional sigma-models and their mutual relations. They are given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of R^4), II) the (3,4,1)_{lin} linear supermultiplet (supersymmetric extension of R^3), III) the (3,4,1)_{nl} non-linear supermultiplet living on S^3 and IV) the (2,4,2)_{nl} non-linear supermultiplet living on S^2. The I -> II map is the supersymmetric extension of the R^4 -> R^3 bilinear map, while the II -> IV map is the supersymmetric extension of the S^3 -> S^2 first Hopf fibration. The restrictions on the S^3, S^2 spheres are expressed in terms of the stereographic projections. The non-linear supermultiplets, whose supertransformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The sigma-models are determined in terms of an unconstrained prepotential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the prepotential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N<=8.Comment: 24 page

Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models

A system of first-order differential-difference equations with time lag describes the formation of density waves, called as quasi-solitons for dissipative systems in this paper. For co-moving density waves, the system reduces to some exactly solvable lattice models. We construct a shock-wave solution as well as one-quasi-soliton solution, and argue that there are pseudo-conserved quantities which characterize the formation of the co-moving waves. The simplest non-trivial one is given to discuss the presence of a cascade phenomena in relaxation process toward the pattern formation.Comment: REVTeX, 4 pages, 1 figur

In situ observations of "cold trap" dehydration in the western tropical Pacific

International audienceWater vapor sonde observations were conducted at Bandung, Indonesia (6.90 S, 107.60 E) and Tarawa, Kiribati (1.35 N, 172.91 E) in December 2003 to examine the efficiency of the "cold trap'' dehydration in the tropical tropopause layer (TTL). Trajectory analysis based on bundles of trajectories suggest that the modification of air parcels' identity due to irreversible mixing by the branching-out and merging-in of nearby trajectories is found to be an important factor, in addition to the routes air parcels are supposed to follow, for interpreting the water vapor concentrations observed by radiosondes in the TTL. Clear correspondence between the observed water vapor concentration and the estimated temperature history of air parcels is found showing that dry air parcels are exposed to low temperatures while humid air parcels do not experience cold conditions during advection, in support of the "cold trap'' hypothesis. It is suggested that the observed air parcel retained the water vapor by roughly twice as much as the minimum saturation mixing ratio after its passage through the "cold trap,'' although appreciable uncertainties remain

Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems

Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of $N$-component electrons at the integer filling factor $\nu=k\leq N$. The basic algebra is the SU(N)-extended W$_{\infty}$. A specific feature is that noncommutative geometry leads to a spontaneous development of SU(N) quantum coherence by generating the exchange Coulomb interaction. The effective Hamiltonian is the Grassmannian $G_{N,k}$ sigma model, and the dynamical field is the Grassmannian $G_{N,k}$ field, describing $k(N-k)$ complex Goldstone modes and one kind of topological solitons (Grassmannian solitons).Comment: 15 pages (no figures

Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of the set describes a density wave with definite number of car-bunches in the circuit. By the numerical simulation, we observe a transition process from a uniform flow to the one-bunch analytic solution, which seems to be an attractor of the system. In the process, the system shows a series of cascade transitions visiting the configurations closely similar to the higher multi-bunch solutions in the set.Comment: revtex, 7 pages, 5 figure

Validation of HRDI MLT winds with meteor radars

A validation study of the mesospheric and lower-thermospheric (MLT) wind velocities measured by the High-Resolution Doppler Imager (HRDI) on board the Upper-Atmosphere Research Satellite (UARS) has been carried out, comparing with observations by meteor radars located at Shigaraki, Japan and Jakarta, Indonesia. The accuracy of the HRDI winds relative to the meteor radars is obtained by a series of simultaneous wind measurements at the time of UARS overpasses. Statistical tests on the difference in the wind vectors observed by HRDI and the meteor radars are applied to determine whether the wind speed has been overestimated by HRDI (or underestimated by the MF radars) as previously noticed in HRDI vs. MF radar comparisons. The techniques employed are the conventional t -test applied to the mean values of the paired wind vector components as well as wind speeds, and two nonparametric tests suitable for testing the paired wind speed. The square-root transformation has been applied before the Mests of the wind speed in order to fit the wind-speed distribution function to the normal distribution. The overall results show little evidence of overestimation by HRDI (underestimation by meteor radars) of wind velocities in the MLT region. Some exceptions are noticed, however, at the altitudes around 88 km, where statistical differences occasionally reach a level of significance of 0.01. The validation is extended to estimate the precision of the wind velocities by both HRDI and meteor radars. In the procedure, the structure function defined by the mean square difference of the observed anomalies is applied in the vertical direction for the profile data. This method assumes the isotropy and the homogeneity of variance for the physical quantity and the homogeneity of variance for the observational errors. The estimated precision is about 6m s − for the Shigaraki meteor radar, 15 m s −1 for the Jakarta meteor radar, and 20 m s −1 for HRDI at 90-km altitude. These values can be used ot confirm the statistical significance of the wind field obtained by averaging the observed winds.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47860/1/585_1997_Article_70151142.pd