Time-Reversal Symmetry in Non-Hermitian Systems

For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when \Theta^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.Comment: 40 pages, 2 figures; typos fixed, references adde

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

Performance evaluation of novel square-bordered position-sensitive silicon detectors with four-corner readout

We report on a recently developed novel type of large area (62 mm x 62 mm) position sensitive silicon detector with four-corner readout. It consists of a square-shaped ion-implanted resistive anode framed by additional low-resistivity strips with resistances smaller than the anode surface resistance by a factor of 2. The detector position linearity, position resolution, and energy resolution were measured with alpha-particles and heavy ions. In-beam experimental results reveal a position resolution below 1 mm (FWHM) and a very good non-linearity of less than 1% (rms). The energy resolution determined from 228Th alpha source measurements is around 2% (FWHM).Comment: 13 pages, 10 figures, submitted to Nucl. Instr. and Meth.

Validation of HRDI MLT winds with meteor radars

International audienceA 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 t-tests 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 6ms?1 for the Shigaraki meteor radar, 15ms?1 for the Jakarta meteor radar, and 20ms?1 for HRDI at 90-km altitude. These values can be used to confirm the statistical significance of the wind field obtained by averaging the observed winds

A flexible sample selection model: A GTL-copula approach

In this paper, we propose a new approach to estimating sample selection models that combines Generalized Tukey Lambda (GTL) distributions with copulas. The GTL distribution is a versatile univariate distribution that permits a wide range of skewness and thick- or thin-tailed behavior in the data that it represents. Copulas help create versatile representations of bivariate distribution. The versatility arising from inserting GTL marginal distributions into copula-constructed bivariate distributions reduces the dependence of estimated parameters on distributional assumptions in applied research. A thorough Monte Carlo study illustrates that our proposed estimator performs well under normal and nonnormal settings, both with and without an instrument in the selection equation that fulfills the exclusion restriction that is often considered to be a requisite for implementation of sample selection models in empirical research. Five applications ranging from wages and health expenditures to speeding tickets and international disputes illustrate the value of the proposed GTL-copula estimator

Radial Bargmann representation for the Fock space of type B

Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the Gaussian process of type B) over the $(\alpha,q)$-Fock space (the Fock space of type B). The main purpose of this paper is to find the radial Bargmann representation of $\nu_{\alpha,q}$. Our main results cover not only the representation of $q$-Gaussian distribution by \cite{LM95}, but also of $q^2$-Gaussian and symmetric free Meixner distributions on $\mathbb R$. In addition, non-trivial commutation relations satisfied by $(\alpha,q)$-operators are presented.Comment: 13 pages, minor changes have been mad

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

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