5,607 research outputs found
Vacuum polarization induced by a uniformly accelerated charge
We consider a point charge fixed in the Rindler coordinates which describe a
uniformly accelerated frame. We determine an integral expression of the induced
charge density due to the vacuum polarization at the first order in the fine
structure constant. In the case where the acceleration is weak, we give
explicitly the induced electrostatic potential.Comment: 13 pages, latex, no figures, to appear in Int. J. Theor. Phys
On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain
A generalization of Jacobi's elliptic functions is introduced as inversions
of hyperelliptic integrals. We discuss the special properties of these
functions, present addition theorems and give a list of indefinite integrals.
As a physical application we show that periodic kink solutions (kink chains) of
the double sine-Gordon model can be described in a canonical form in terms of
generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table
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 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.
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
Spacetime Encodings II - Pictures of Integrability
I visually explore the features of geodesic orbits in arbitrary stationary
axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst
potential. Some of the geometric features of integrable and chaotic orbits are
highlighted. The geodesic problem for these SAV spacetimes is rewritten as a
two degree of freedom problem and the connection between current ideas in
dynamical systems and the study of two manifolds sought. The relationship
between the Hamilton-Jacobi equations, canonical transformations, constants of
motion and Killing tensors are commented on. Wherever possible I illustrate the
concepts by means of examples from general relativity. This investigation is
designed to build the readers' intuition about how integrability arises, and to
summarize some of the known facts about two degree of freedom systems. Evidence
is given, in the form of orbit-crossing structure, that geodesics in SAV
spacetimes might admit, a fourth constant of motion that is quartic in momentum
(by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure
Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages
In a previous work a random matrix average for the Laguerre unitary ensemble,
generalising the generating function for the probability that an interval at the hard edge contains eigenvalues, was evaluated in terms of
a Painlev\'e V transcendent in -form. However the boundary conditions
for the corresponding differential equation were not specified for the full
parameter space. Here this task is accomplished in general, and the obtained
functional form is compared against the most general small behaviour of
the Painlev\'e V equation in -form known from the work of Jimbo. An
analogous study is carried out for the the hard edge scaling limit of the
random matrix average, which we have previously evaluated in terms of a
Painlev\'e \IIId transcendent in -form. An application of the latter
result is given to the rapid evaluation of a Hankel determinant appearing in a
recent work of Conrey, Rubinstein and Snaith relating to the derivative of the
Riemann zeta function
Family memories in the home: contrasting physical and digital mementos
We carried out fieldwork to characterise and compare physical and digital mementos in the home. Physical mementos are highly valued, heterogeneous and support different types of recollection. Contrary to expectations, we found physical mementos are not purely representational, and can involve appropriating common objects and more idiosyncratic forms. In contrast, digital mementos were initially perceived as less valuable, although participants later reconsidered this. Digital mementos were somewhat limited in function and expression, largely involving representational photos and videos, and infrequently accessed. We explain these digital limitations and conclude with design guidelines for digital mementos, including better techniques for accessing and integrating these into everyday life, allowing them to acquire the symbolic associations and lasting value that characterise their physical counterparts
Dynamics of Energy Transport in a Toda Ring
We present results on the relationships between persistent currents and the
known conservation laws in the classical Toda ring. We also show that
perturbing the integrability leads to a decay of the currents at long times,
with a time scale that is determined by the perturbing parameter. We summarize
several known results concerning the Toda ring in 1-dimension, and present new
results relating to the frequency, average kinetic and potential energy, and
mean square displacement in the cnoidal waves, as functions of the wave vector
and a parameter that determines the non linearity.Comment: 34 pages, 11 figures. Small changes made in response to referee's
comment
Angular distribution of photoluminescence as a probe of Bose Condensation of trapped excitons
Recent experiments on two-dimensional exciton systems have shown the excitons
collect in shallow in-plane traps. We find that Bose condensation in a trap
results in a dramatic change of the exciton photoluminescence (PL) angular
distribution. The long-range coherence of the condensed state gives rise to a
sharply focussed peak of radiation in the direction normal to the plane. By
comparing the PL profile with and without Bose Condensation we provide a simple
diagnostic for the existence of a Bose condensate. The PL peak has strong
temperature dependence due to the thermal order parameter phase fluctuations
across the system. The angular PL distribution can also be used for imaging
vortices in the trapped condensate. Vortex phase spatial variation leads to
destructive interference of PL radiation in certain directions, creating nodes
in the PL distribution that imprint the vortex configuration.Comment: 4 pages, 3 figure
On the mechanistic difference between in-phase and out-of-phase thermo-mechanical fatigue crack growth
The crack driving mechanisms in a coarse grained nickel-base superalloy RR1000 when subjected to in- and out of phase thermo mechanical fatigue are investigated. It is found that the difference in fatigue crack growth rate between these two load conditions is accounted for by the different mechanical conditions at the crack tip region, rather than oxidation effects. This is based on digital image correlation and finite element analyses of the mechanical strain field at the crack tip, which demonstrate that in phase leads to larger crack tip deformation and crack opening. Notably, it is demonstrated that in- and out of phase crack growth rates coincide when correlated to the crack tip opening displacement
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