14,242 research outputs found
The application of a numerical integration procedure developed by erwin fehlberg to the restricted problem of three bodies
Application of numerical integration procedures to restricted three-body proble
Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator
A Lindblad master equation for a harmonic oscillator, which describes the
dynamics of an open system, is formally solved. The solution yields the
spectral resolution of the Liouvillian, that is, all eigenvalues and
eigenprojections are obtained. This spectral resolution is discussed in depth
in the context of the biorthogonal system and the rigged Hilbert space, and the
contribution of each eigenprojection to expectation values of physical
quantities is revealed. We also construct the ladder operators of the
Liouvillian, which clarify the structure of the spectral resolution.Comment: 22pages, no figure; title changed, minor corrections, references
added; minor correction
Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux
We study the dynamics of a quantum particle moving in a plane under the
influence of a constant magnetic field and driven by a slowly time-dependent
singular flux tube through a puncture. The known adiabatic results do not cover
these models as the Hamiltonian has time dependent domain. We give a meaning to
the propagator and prove an adiabatic theorem. To this end we introduce and
develop the new notion of a propagator weakly associated to a time-dependent
Hamiltonian.Comment: Title and Abstract changed, will appear in Journal of Mathematical
Physic
A Number-Theoretic Error-Correcting Code
In this paper we describe a new error-correcting code (ECC) inspired by the
Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the
proposed ECC happens to be more efficient than some established ECCs for
certain sets of parameters. The new ECC adds an appendix to the message. The
appendix is the modular product of small primes representing the message bits.
The receiver recomputes the product and detects transmission errors using
modular division and lattice reduction
Boundary effect of a partition in a quantum well
The paper wishes to demonstrate that, in quantum systems with boundaries,
different boundary conditions can lead to remarkably different physical
behaviour. Our seemingly innocent setting is a one dimensional potential well
that is divided into two halves by a thin separating wall. The two half wells
are populated by the same type and number of particles and are kept at the same
temperature. The only difference is in the boundary condition imposed at the
two sides of the separating wall, which is the Dirichlet condition from the
left and the Neumann condition from the right. The resulting different energy
spectra cause a difference in the quantum statistically emerging pressure on
the two sides. The net force acting on the separating wall proves to be nonzero
at any temperature and, after a weak decrease in the low temperature domain, to
increase and diverge with a square-root-of-temperature asymptotics for high
temperatures. These observations hold for both bosonic and fermionic type
particles, but with quantitative differences. We work out several analytic
approximations to explain these differences and the various aspects of the
found unexpectedly complex picture.Comment: LaTeX (with iopart.cls, iopart10.clo and iopart12.clo), 28 pages, 17
figure
Resonances Width in Crossed Electric and Magnetic Fields
We study the spectral properties of a charged particle confined to a
two-dimensional plane and submitted to homogeneous magnetic and electric fields
and an impurity potential. We use the method of complex translations to prove
that the life-times of resonances induced by the presence of electric field are
at least Gaussian long as the electric field tends to zero.Comment: 3 figure
Physical properties and radius variations in the HAT-P-5 planetary system from simultaneous four-colour photometry
The radii of giant planets, as measured from transit observations, may vary
with wavelength due to Rayleigh scattering or variations in opacity. Such an
effect is predicted to be large enough to detect using ground-based
observations at multiple wavelengths. We present defocussed photometry of a
transit in the HAT-P-5 system, obtained simultaneously through Stromgren u,
Gunn g and r, and Johnson I filters. Two more transit events were observed
through a Gunn r filter. We detect a substantially larger planetary radius in
u, but the effect is greater than predicted using theoretical model atmospheres
of gaseous planets. This phenomenon is most likely to be due to systematic
errors present in the u-band photometry, stemming from variations in the
transparency of Earth's atmosphere at these short wavelengths. We use our data
to calculate an improved orbital ephemeris and to refine the measured physical
properties of the system. The planet HAT-P-5b has a mass of 1.06 +/- 0.11 +/-
0.01 Mjup and a radius of 1.252 +/- 0.042 +/- 0.008 Rjup (statistical and
systematic errors respectively), making it slightly larger than expected
according to standard models of coreless gas-giant planets. Its equilibrium
temperature of 1517 +/- 29 K is within 60K of that of the extensively-studied
planet HD 209458b.Comment: Version 2 corrects the accidental omission of one author in the arXiv
metadata. Accepted for publication in MNRAS. 9 pages, 4 figures, 7 tables.
The properties of HAT-P-5 have been added to the Transiting Extrasolar Planet
Catalogue at http://www.astro.keele.ac.uk/~jkt/tepcat
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
Self-Adjointness of Generalized MIC-Kepler System
We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian,
obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We
have shown that for \tilde l=0, the system admits a 1-parameter family of
self-adjoint extensions and for \tilde l \neq 0 but \tilde l <{1/2}, it has
also a 1-parameter family of self-adjoint extensions.Comment: 11 pages, Latex, no figur
Quantum oscillator on complex projective space (Lobachewski space) in constant magnetic field and the issue of generic boundary conditions
We perform a 1-parameter family of self-adjoint extensions characterized by
the parameter . This allows us to get generic boundary conditions for
the quantum oscillator on dimensional complex projective
space() and on its non-compact version i.e., Lobachewski
space() in presence of constant magnetic field. As a result, we
get a family of energy spectrums for the oscillator. In our formulation the
already known result of this oscillator is also belong to the family. We have
also obtained energy spectrum which preserve all the symmetry (full hidden
symmetry and rotational symmetry) of the oscillator. The method of self-adjoint
extensions have been discussed for conic oscillator in presence of constant
magnetic field also.Comment: Accepted in Journal of Physics
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