17,206 research outputs found
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
We consider massive Dirac fields evolving in the exterior region of a
5-dimensional Myers-Perry black hole and study their propagation properties.
Our main result states that the local energy of such fields decays in a weak
sense at late times. We obtain this result in two steps: first, using the
separability of the Dirac equation, we prove the absence of a pure point
spectrum for the corresponding Dirac operator; second, using a new form of the
equation adapted to the local rotations of the black hole, we show by a Mourre
theory argument that the spectrum is absolutely continuous. This leads directly
to our main result.Comment: 40 page
Ionization of Atoms by Intense Laser Pulses
The process of ionization of a hydrogen atom by a short infrared laser pulse
is studied in the regime of very large pulse intensity, in the dipole
approximation. Let denote the integral of the electric field of the pulse
over time at the location of the atomic nucleus. It is shown that, in the limit
where , the ionization probability approaches unity and the
electron is ejected into a cone opening in the direction of and of
arbitrarily small opening angle. Asymptotics of various physical quantities in
is studied carefully. Our results are in qualitative agreement with
experimental data reported in \cite{1,2}.Comment: 27 pages, 1 figure
The Berry-Keating operator on L^2(\rz_>, x) and on compact quantum graphs with general self-adjoint realizations
The Berry-Keating operator H_{\mathrm{BK}}:=
-\ui\hbar(x\frac{
\phantom{x}}{
x}+{1/2}) [M. V. Berry and J. P. Keating,
SIAM Rev. 41 (1999) 236] governing the Schr\"odinger dynamics is discussed in
the Hilbert space L^2(\rz_>,
x) and on compact quantum graphs. It is
proved that the spectrum of defined on L^2(\rz_>,
x) is
purely continuous and thus this quantization of cannot yield
the hypothetical Hilbert-Polya operator possessing as eigenvalues the
nontrivial zeros of the Riemann zeta function. A complete classification of all
self-adjoint extensions of acting on compact quantum graphs
is given together with the corresponding secular equation in form of a
determinant whose zeros determine the discrete spectrum of .
In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue
counting function are derived. Furthermore, we introduce the "squared"
Berry-Keating operator which is a special case of the
Black-Scholes operator used in financial theory of option pricing. Again, all
self-adjoint extensions, the corresponding secular equation, the trace formula
and the Weyl asymptotics are derived for on compact quantum
graphs. While the spectra of both and on
any compact quantum graph are discrete, their Weyl asymptotics demonstrate that
neither nor can yield as eigenvalues the
nontrivial Riemann zeros. Some simple examples are worked out in detail.Comment: 33p
Whirling Waves and the Aharonov-Bohm Effect for Relativistic Spinning Particles
The formulation of Berry for the Aharonov-Bohm effect is generalized to the
relativistic regime. Then, the problem of finding the self-adjoint extensions
of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background
potential, is solved in a novel way. The same treatment also solves the problem
of finding the self-adjoint extensions of the Dirac Hamiltonian in a background
Aharonov-Casher
Determination of cobalt in seawater
Cobalt has been isolated from seawater by cocrystallization with α-nitroso-β-naphthol. Quantitative determination by a nitroso-R-salt method for each of two sea.water samples has indicated the cobalt content to be 0.038 µg/l after radiometric correction for losses incurred in the isolation process
Observables and a Hilbert Space for Bianchi IX
We consider a quantization of the Bianchi IX cosmological model based on
taking the constraint to be a self-adjoint operator in an auxiliary Hilbert
space. Using a WKB-style self-consistent approximation, the constraint chosen
is shown to have only continuous spectrum at zero. Nevertheless, the auxiliary
space induces an inner product on the zero-eigenvalue generalized eigenstates
such that the resulting physical Hilbert space has countably infinite
dimension. In addition, a complete set of gauge-invariant operators on the
physical space is constructed by integrating differential forms over the
spacetime. The behavior of these operators indicates that this quantization
preserves Wald's classical result that the Bianchi IX spacetimes expand to a
maximum volume and then recollapse.Comment: 23 pages, ReVTeX, CGPG-94/6-3, UCSBTH-94-3
Homogenization of the planar waveguide with frequently alternating boundary conditions
We consider Laplacian in a planar strip with Dirichlet boundary condition on
the upper boundary and with frequent alternation boundary condition on the
lower boundary. The alternation is introduced by the periodic partition of the
boundary into small segments on which Dirichlet and Neumann conditions are
imposed in turns. We show that under the certain condition the homogenized
operator is the Dirichlet Laplacian and prove the uniform resolvent
convergence. The spectrum of the perturbed operator consists of its essential
part only and has a band structure. We construct the leading terms of the
asymptotic expansions for the first band functions. We also construct the
complete asymptotic expansion for the bottom of the spectrum
Weyl asymptotics for magnetic Schr\"odinger operators and de Gennes' boundary condition
This paper is concerned with the discrete spectrum of the self-adjoint
realization of the semi-classical Schr\"odinger operator with constant magnetic
field and associated with the de Gennes (Fourier/Robin) boundary condition. We
derive an asymptotic expansion of the number of eigenvalues below the essential
spectrum (Weyl-type asymptotics). The methods of proof relies on results
concerning the asymptotic behavior of the first eigenvalue obtained in a
previous work [A. Kachmar, J. Math. Phys. Vol. 47 (7) 072106 (2006)].Comment: 28 pages (revised version). to appear in Rev Math Phy
A linear-time algorithm for finding a complete graph minor in a dense graph
Let g(t) be the minimum number such that every graph G with average degree
d(G) \geq g(t) contains a K_{t}-minor. Such a function is known to exist, as
originally shown by Mader. Kostochka and Thomason independently proved that
g(t) \in \Theta(t*sqrt{log t}). This article shows that for all fixed \epsilon
> 0 and fixed sufficiently large t \geq t(\epsilon), if d(G) \geq
(2+\epsilon)g(t) then we can find this K_{t}-minor in linear time. This
improves a previous result by Reed and Wood who gave a linear-time algorithm
when d(G) \geq 2^{t-2}.Comment: 6 pages, 0 figures; Clarification added in several places, no change
to arguments or result
Conceptual inconsistencies in finite-dimensional quantum and classical mechanics
Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012);
arXiv:1105.4014], we demonstrate that any finite-dimensional representation of
quantum and classical dynamics violates the Ehrenfest theorems. Other
peculiarities are also revealed, including the nonexistence of the free
particle and ambiguity in defining potential forces. Non-Hermitian mechanics is
shown to have the same problems. This work compromises a popular belief that
finite-dimensional mechanics is a straightforward discretization of the
corresponding infinite-dimensional formulation.Comment: 5 pages, 2 figure
- …