2,808,960 research outputs found
A semi-empirical stability criterion for real planetary systems
We test a crossing orbit stability criterion for eccentric planetary systems,
based on Wisdom's criterion of first order mean motion resonance overlap
(Wisdom, 1980).
We show that this criterion fits the stability regions in real exoplanet
systems quite well. In addition, we show that elliptical orbits can remain
stable even for regions where the apocenter distance of the inner orbit is
larger than the pericenter distance of the outer orbit, as long as the initial
orbits are aligned.
The analytical expressions provided here can be used to put rapid constraints
on the stability zones of multi-planetary systems. As a byproduct of this
research, we further show that the amplitude variations of the eccentricity can
be used as a fast-computing stability indicator.Comment: 11 pages, 11 figures. MNRAS accepte
Coulomb-Modified Fano Resonance in a One-Lead Quantum Dot
We investigate a tunable Fano interferometer consisting of a quantum dot
coupled via tunneling to a one-dimensional channel. In addition to Fano
resonance, the channel shows strong Coulomb response to the dot, with a single
electron modulating channel conductance by factors of up to 100. Where these
effects coexist, lineshapes with up to four extrema are found. A model of
Coulomb-modified Fano resonance is developed and gives excellent agreement with
experiment.Comment: related papers available at http://marcuslab.harvard.ed
Level Crossings in Complex Two-Dimensional Potentials
Two-dimensional PT-symmetric quantum-mechanical systems with the complex
cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential
V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and
perturbative methods, energy spectra are obtained to high levels. Although both
potentials respect the PT symmetry, the complex energy eigenvalues appear when
level crossing happens between same parity eigenstates.Comment: 9 pages, 4 figures. Submitted as a conference proceeding of PHHQP
Radiative pressure feedback by a quasar in a galactic bulge
We show that Eddington-limited black hole luminosities can be sufficient to
deplete a galaxy bulge of gas through radiation pressure, when the ionization
state of the gas and the presence of dust are properly taken into account. Once
feedback starts to be effective it can consistently drive all the gas out of
the whole galaxy. We estimate the amount by which the effect of radiation
pressure on dusty gas boosts the mass involved in the Eddington limit and
discuss the expected column density at which the gas is ejected. An example is
shown of the predicted observed nuclear spectrum of the system at the end of an
early, obscured phase of growth when the remaining column density NH ~ f * 1e24
cm^-2 where f is the gas fraction in the bulge.Comment: correct corrupted figures in pdf version, MNRAS accepted, 5 pages, 3
figure
Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Conventional weak-coupling perturbation theory suffers from problems that
arise from resonant coupling of successive orders in the perturbation series.
Multiple-scale perturbation theory avoids such problems by implicitly
performing an infinite reordering and resummation of the conventional
perturbation series. Multiple-scale analysis provides a good description of the
classical anharmonic oscillator. Here, it is extended to study the Heisenberg
operator equations of motion for the quantum anharmonic oscillator. The
analysis yields a system of nonlinear operator differential equations, which is
solved exactly. The solution provides an operator mass renormalization of the
theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm
Quantum tunneling as a classical anomaly
Classical mechanics is a singular theory in that real-energy classical
particles can never enter classically forbidden regions. However, if one
regulates classical mechanics by allowing the energy E of a particle to be
complex, the particle exhibits quantum-like behavior: Complex-energy classical
particles can travel between classically allowed regions separated by potential
barriers. When Im(E) -> 0, the classical tunneling probabilities persist.
Hence, one can interpret quantum tunneling as an anomaly. A numerical
comparison of complex classical tunneling probabilities with quantum tunneling
probabilities leads to the conjecture that as ReE increases, complex classical
tunneling probabilities approach the corresponding quantum probabilities. Thus,
this work attempts to generalize the Bohr correspondence principle from
classically allowed to classically forbidden regions.Comment: 12 pages, 7 figure
Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation
Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact
and connected manifold and let u be a semi-concave function defined on M. If E
(u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian
flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact
Lagrangian Lipschitz graph. This provides a geometric
interpretation/explanation of a regularization tool that was introduced by
P.~Bernard to prove the existence of C 1,1 subsolutions
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