7,024 research outputs found
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
A miniaturized 3 dimensional bandpass frequency selective surface
A planar bandpass frequency selective surface
(FSS) is proposed along with an alternative 3D element design
with the intent of miniaturizing the unit cell. The two structures
are simulated in CST and compared. Such techniques show the
potential of using 3D elements in FSS design to miniaturize the
structure for space constrained applications
Particles in a magnetic field and plasma analogies: doubly periodic boundary conditions
The -particle free fermion state for quantum particles in the plane
subject to a perpendicular magnetic field, and with doubly periodic boundary
conditions, is written in a product form. The absolute value of this is used to
formulate an exactly solvable one-component plasma model, and further motivates
the formulation of an exactly solvable two-species Coulomb gas. The large
expansion of the free energy of both these models exhibits the same O(1) term.
On the basis of a relationship to the Gaussian free field, this term is
predicted to be universal for conductive Coulomb systems in doubly periodic
boundary conditions.Comment: 12 page
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.
Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type
We discuss a family of multi-term addition formulae for Weierstrass functions
on specialized curves of genus one and two with many automorphisms. In the
genus one case we find new addition formulae for the equianharmonic and
lemniscate cases, and in genus two we find some new addition formulae for a
number of curves, including the Burnside curve.Comment: 19 pages. We have extended the Introduction, corrected some typos and
tidied up some proofs, and inserted extra material on genus 3 curve
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
From angle-action to Cartesian coordinates: A key transformation for molecular dynamics
The transformation from angle-action variables to Cartesian coordinates is a
crucial step of the (semi) classical description of bimolecular collisions and
photo-fragmentations. The basic reason is that dynamical conditions
corresponding to experiments are ideally generated in angle-action variables
whereas the classical equations of motion are ideally solved in Cartesian
coordinates by standard numerical approaches. To our knowledge, the previous
transformation is available in the literature only for triatomic systems. The
goal of the present work is to derive it for polyatomic ones.Comment: 10 pages, 11 figures, submitted to J. Chem. Phy
Absolute spacetime: the twentieth century ether
All gauge theories need ``something fixed'' even as ``something changes.''
Underlying the implementation of these ideas all major physical theories make
indispensable use of an elaborately designed spacetime model as the ``something
fixed,'' i.e., absolute. This model must provide at least the following
sequence of structures: point set, topological space, smooth manifold,
geometric manifold, base for various bundles. The ``fine structure'' of
spacetime inherent in this sequence is of course empirically unobservable
directly, certainly when quantum mechanics is taken into account. This issue is
at the basis of the difficulties in quantizing general relativity and has been
approached in many different ways. Here we review an approach taking into
account the non-Boolean properties of quantum logic when forming a spacetime
model. Finally, we recall how the fundamental gauge of diffeomorphisms (the
issue of general covariance vs coordinate conditions) raised deep conceptual
problems for Einstein in his early development of general relativity. This is
clearly illustrated in the notorious ``hole'' argument. This scenario, which
does not seem to be widely known to practicing relativists, is nevertheless
still interesting in terms of its impact for fundamental gauge issues.Comment: Contribution to Proceedings of Mexico Meeting on Gauge Theories of
Gravity in honor of Friedrich Heh
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