6,573 research outputs found

### Penrose Limit and String Theories on Various Brane Backgrounds

We investigate the Penrose limit of various brane solutions including
Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings.
We obtain special null geodesics with the fixed radial coordinate (critical
radius), along which the Penrose limit gives string theories with constant
mass. We also study string theories with time-dependent mass, which arise from
the Penrose limit of the brane backgrounds. We examine equations of motion of
the strings in the asymptotic flat region and around the critical radius. In
particular, for (p,q) fivebranes, we find that the string equations of motion
in the directions with the B field are explicitly solved by the spheroidal wave
functions.Comment: 41 pages, Latex, minor correction

### Integral D-Finite Functions

We propose a differential analog of the notion of integral closure of
algebraic function fields. We present an algorithm for computing the integral
closure of the algebra defined by a linear differential operator. Our algorithm
is a direct analog of van Hoeij's algorithm for computing integral bases of
algebraic function fields

### Nonlocal symmetries of Riccati and Abel chains and their similarity reductions

We study nonlocal symmetries and their similarity reductions of Riccati and
Abel chains. Our results show that all the equations in Riccati chain share the
same form of nonlocal symmetry. The similarity reduced $N^{th}$ order ordinary
differential equation (ODE), $N=2, 3,4,...$, in this chain yields $(N-1)^{th}$
order ODE in the same chain. All the equations in the Abel chain also share the
same form of nonlocal symmetry (which is different from the one that exist in
Riccati chain) but the similarity reduced $N^{th}$ order ODE, $N=2, 3,4,$, in
the Abel chain always ends at the $(N-1)^{th}$ order ODE in the Riccati chain.
We describe the method of finding general solution of all the equations that
appear in these chains from the nonlocal symmetry.Comment: Accepted for publication in J. Math. Phy

### Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave
functions is reviewed as based on a proper modification of the scalar product
in Hilbert space. Bound states are then studied in a deep-square-well model
where spectrum is roughly equidistant and where a fine-tuning of the levels is
mediated by PT-symmetric interactions composed of imaginary delta functions
which mimic creation/annihilation processes.Comment: Int. Worskhop "Pseudo-Hermitian Hamiltonians in Quantum Physics III"
(June 20 - 22, 2005, Koc Unversity,
Istanbul(http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.htm) a part
of talk (9 pages

### MHD Memes

The celebration of Allan Kaufman's 80th birthday was an occasion to reflect
on a career that has stimulated the mutual exchange of ideas (or memes in the
terminology of Richard Dawkins) between many researchers. This paper will
revisit a meme Allan encountered in his early career in magnetohydrodynamics,
the continuation of a magnetohydrodynamic mode through a singularity, and will
also mention other problems where Allan's work has had a powerful
cross-fertilizing effect in plasma physics and other areas of physics and
mathematics.Comment: Submitted for publication in IOP Journal of Physics: Conference
Series for publication in "Plasma Theory, Wave Kinetics, and Nonlinear
Dynamics", Proceedings of KaufmanFest, 5-7 October 2007, University of
California, Berkeley, US

### Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential

We present an analytical calculation of periodic orbits in the homogeneous
quartic oscillator potential. Exploiting the properties of the periodic
Lam{\'e} functions that describe the orbits bifurcated from the fundamental
linear orbit in the vicinity of the bifurcation points, we use perturbation
theory to obtain their evolution away from the bifurcation points. As an
application, we derive an analytical semiclassical trace formula for the
density of states in the separable case, using a uniform approximation for the
pitchfork bifurcations occurring there, which allows for full semiclassical
quantization. For the non-integrable situations, we show that the uniform
contribution of the bifurcating period-one orbits to the coarse-grained density
of states competes with that of the shortest isolated orbits, but decreases
with increasing chaoticity parameter $\alpha$.Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear
in J. Phys. A final version 3; error in eq. (33) corrected and note added in
prin

### Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain

### Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

We report an alternative method to solve second order differential equations
which have at most four singular points. This method is developed by changing
the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU)
method. This is called extended NU method for this paper. The eigenvalue
solutions of Heun equation and confluent Heun equation are obtained via
extended NU method. Some quantum mechanical problems such as Coulomb problem on
a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic
double-well potential are investigated by this method

### The Pseudothreshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

The values at pseudothreshold of two loop sunrise master amplitudes with
arbitrary masses are obtained by solving a system of differential equations.
The expansion at pseudothreshold of the amplitudes is constructed and some
lowest terms are explicitly presented.Comment: 1+22 pages, Latex, no figures, changes in Eq.(41),(44),(47

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