10,169 research outputs found
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
Comment on "Nonlinear eigenvalue problems"
The asymptotic behaviour of solutions to was investigated by Bender, Fring and Komijani (2014). They found, for example, a relation between the initial value and the number of maxima that the solution exhibited. We present an alternative derivation of the asymptotic results that looks at the solutions in the regions , and confirms the behaviour found previously for larger values of . This method uses the small amplitude and high frequency of the oscillatory behaviour in the region
Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space
One of the atom interferometer gravitational wave missions proposed by
Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested
gravitational wave sensitivity set by the atom state detection shot noise level
that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20
mHz, and had better sensitivity from 20 to 500 mHz. The separation between the
spacecraft was 1,000 km, with atom interferometers 200 m long and shades from
sunlight used at each end. A careful analysis of many error sources was
included, but requirements on the time-stability of both the laser wavefront
aberrations and the atom temperatures in the atom clouds were not investigated.
After including these considerations, the laser wavefront aberration stability
requirement to meet the quoted sensitivity level is about 1\times10-8
wavelengths, and is far tighter than for LISA. Also, the temperature
fluctuations between atom clouds have to be less than 1 pK. An alternate atom
interferometer GW mission in Earth orbit called AGIS-LEO with 30 km satellite
separation has been suggested recently. The reduction of wavefront aberration
noise by sending the laser beam through a high-finesse mode-scrubbing optical
cavity is discussed briefly, but the requirements on such a cavity are not
given. Unfortunately, such an Earth-orbiting mission seems to be considerably
more difficult to design than a non-geocentric mission and does not appear to
have comparably attractive scientific goals.Comment: Submitted to Proc. 46th Rencontres de Moriond: Gravitational Waves
and Experimental Gravity, March 20 - 27, 2011, La Thuile, Ital
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