Quarkonia Disintegration due to time dependence of the qqˉq \bar{q} potential in Relativistic Heavy Ion Collisions

Rapid thermalization in ultra-relativistic heavy-ion collisions leads to fast changing potential between a heavy quark and antiquark from zero temperature potential to the finite temperature one. Time dependent perturbation theory can then be used to calculate the survival probability of the initial quarkonium state. In view of very short time scales of thermalization at RHIC and LHC energies, we calculate the survival probability of $J/\psi$ and $\Upsilon$ using sudden approximation. Our results show that quarkonium decay may be significant even when temperature of QGP remains low enough so that the conventional quarkonium melting due to Debye screening is ineffective.Comment: 3 pages, 4 figure

What role for smart-card data from bus systems?

This paper examines whether data, generated from smart cards used for bus travel, can be put forward as a replacement for, or a complement to, existing transport data sources. Smart-card data possess certain advantages over existing bus ticket machine data and some sample data sources, allowing them to be used for a range of analysis applications that transport service providers may previously have been unable to or found difficult to undertake. To this end, as a new transport data source, the paper firstly reviews the nature of smart-card data. The paper then goes on to examine the impact of smart-card data in relation to two case studies - one concerning its impact on the data collection process and one looking at the impact on travel behaviour analysis

Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass $\wp$ type, one of them being real and the other imaginary and PT symmetric. The latter turns out to be quasiexactly solvable with one known eigenvalue corresponding to a bound state. When the Weierstrass function degenerates to a hyperbolic one, the imaginary potential becomes PT non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int. J. Mod. Phys.

Orientational relaxation in a dispersive dynamic medium : Generalization of the Kubo-Ivanov-Anderson jump diffusion model to include fractional environmental dynamics

Ivanov-Anderson (IA) model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and supercooled liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first and second rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behaviour observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone.Comment: 14 figure

Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics

The continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples.Comment: 16 pages, amssy

Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues

We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the fact that two superpotentials reside naturally in order-two parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes, we complexify their frameworks to successfully account for the three potentials.Comment: LaTeX2e, 28 pages, no figure

A New Class of PT-symmetric Hamiltonians with Real Spectra

We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY Quantum Mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels.Comment: 9 pages, Late