197 research outputs found
Buoyancy driven planetary flows
The large scale flow patterns driven by surface buoyancy flux are obtained as numerical solutions of the planetary geostrophic equations to which dissipation and diffusion have been appended. Within a cartesian β plane, square box geometry, the solution is made of gyres of the largest possible size with western and northern intensification, anticyclonic above the main thermocline, cyclonic below. Within regions of heat gain, the classical equilibrium between downward eddy diffusion and vertical upwelling is approximately observed in the main thermocline. As a consequence the abyssal circulation (southern interior and western boundary current) behave according to the early Stommel-Arons\u27 ideas. The situation is rather different in regions of heat losses where convection is active: the flow patterns consist of swift zonal flows with horizontal divergence whose dynamics involve lateral diffusion of density and vorticity. The solutions are mostly sensitive to the choice of the vertical diffusion coefficient whose value between 1 and 2 cm2 s–1 produces realistic bottom water formation rates and meridional heat fluxes. The bulk of the heat accumulated in the Tropics is transported poleward by a direct Hadley cell (northward at the surface, southward at depth) obtained through a zonal averaging of the meridional circulation: horizontal rotational recirculations are less important for the heat transport
The efficient computation of transition state resonances and reaction rates from a quantum normal form
A quantum version of a recent formulation of transition state theory in {\em
phase space} is presented. The theory developed provides an algorithm to
compute quantum reaction rates and the associated Gamov-Siegert resonances with
very high accuracy. The algorithm is especially efficient for
multi-degree-of-freedom systems where other approaches are no longer feasible.Comment: 4 pages, 3 figures, revtex
Eigenfunction statistics for a point scatterer on a three-dimensional torus
In this paper we study eigenfunction statistics for a point scatterer (the
Laplacian perturbed by a delta-potential) on a three-dimensional flat torus.
The eigenfunctions of this operator are the eigenfunctions of the Laplacian
which vanish at the scatterer, together with a set of new eigenfunctions
(perturbed eigenfunctions). We first show that for a point scatterer on the
standard torus all of the perturbed eigenfunctions are uniformly distributed in
configuration space. Then we investigate the same problem for a point scatterer
on a flat torus with some irrationality conditions, and show uniform
distribution in configuration space for almost all of the perturbed
eigenfunctions.Comment: Revised according to referee's comments. Accepted for publication in
Annales Henri Poincar
Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area
We consider a magnetic Laplacian on a
noncompact hyperbolic surface \mM with finite area. is a real one-form
and the magnetic field is constant in each cusp. When the harmonic
component of satifies some quantified condition, the spectrum of
is discrete. In this case we prove that the counting function of
the eigenvalues of satisfies the classical Weyl formula, even
when $dA=0.
Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs
We consider weighted graphs, we equip them with a metric structure given by a
weighted distance, and we discuss essential self-adjointness for weighted graph
Laplacians and Schr\"odinger operators in the metrically non complete case.Comment: Revisited version: Ognjen Milatovic wrote to us that he had
discovered a gap in the proof of theorem 4.2 of our paper. As a consequence
we propose to make an additional assumption (regularity property of the
graph) to this theorem. A new subsection (4.1) is devoted to the study of
this property and some details have been changed in the proof of theorem 4.
Quantum breaking time near classical equilibrium points
By using numerical and semiclassical methods, we evaluate the quantum
breaking, or Ehrenfest time for a wave packet localized around classical
equilibrium points of autonomous one-dimensional systems with polynomial
potentials. We find that the Ehrenfest time diverges logarithmically with the
inverse of the Planck constant whenever the equilibrium point is exponentially
unstable. For stable equilibrium points, we have a power law divergence with
exponent determined by the degree of the potential near the equilibrium point.Comment: 4 pages, 5 figure
Topological properties of quantum periodic Hamiltonians
We consider periodic quantum Hamiltonians on the torus phase space
(Harper-like Hamiltonians). We calculate the topological Chern index which
characterizes each spectral band in the generic case. This calculation is made
by a semi-classical approach with use of quasi-modes. As a result, the Chern
index is equal to the homotopy of the path of these quasi-modes on phase space
as the Floquet parameter (\theta) of the band is varied. It is quite
interesting that the Chern indices, defined as topological quantum numbers, can
be expressed from simple properties of the classical trajectories.Comment: 27 pages, 14 figure
Semiclassical transmission across transition states
It is shown that the probability of quantum-mechanical transmission across a
phase space bottleneck can be compactly approximated using an operator derived
from a complex Poincar\'e return map. This result uniformly incorporates
tunnelling effects with classically-allowed transmission and generalises a
result previously derived for a classically small region of phase space.Comment: To appear in Nonlinearit
Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy
Fractional Hamiltonian Monodromy is a generalization of the notion of
Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A.
Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a
particular type of non-isolated singularities. In this paper, we analyze the
notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin
Monodromy of a Riemann surface constructed from the energy-momentum map and
associated to a loop in complex space which bypasses the line of singularities.
We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n
and m:-n resonant systems.Comment: 39 pages, 24 figures. submitted to J. Math. Phy
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