3,546 research outputs found
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
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
PT-symmetric square well and the associated SUSY hierarchies
The PT-symmetric square well problem is considered in a SUSY framework. When
the coupling strength lies below the critical value
where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY
partner potentials, depicting an unbroken SUSY situation and reducing to the
family of -like potentials in the limit. For above
, there is a rich diversity of SUSY hierarchies, including
some with PT-symmetry breaking and some with partial PT-symmetry restoration.Comment: LaTeX, 18 pages, no figure; broken PT-symmetry case added (Sec. 6
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
- …