2,315 research outputs found
KAM for the quantum harmonic oscillator
In this paper we prove an abstract KAM theorem for infinite dimensional
Hamiltonians systems. This result extends previous works of S.B. Kuksin and J.
P\"oschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an
application we show that some 1D nonlinear Schr\"odinger equations with
harmonic potential admits many quasi-periodic solutions. In a second
application we prove the reducibility of the 1D Schr\"odinger equations with
the harmonic potential and a quasi periodic in time potential.Comment: 54 pages. To appear in Comm. Math. Phy
Electrostatic pair creation and recombination in quantum plasmas
The collective production of electron-positron pairs by electrostatic waves
in quantum plasmas is investigated. In particular, a semi-classical governing
set of equation for a self-consistent treatment of pair creation by the
Schwinger mechanism in a quantum plasma is derived.Comment: 4 pages, 3 figures, to appear in JETP Letter
New Precision Electroweak Tests in Supergravity Models
We update the analysis of the precision electroweak tests in terms of 4
epsilon parameters, , to obtain more accurate experimental
values of them by taking into account the new LEP data released at the 28th
ICHEP (1996, Poland). We also compute and in the
context of the no-scale supergravity model to obtain the
updated constraints by imposing the correlated constraints in terms of the
experimental ellipses in the plane and also by imposing
the new bound on the lightest chargino mass, .
Upon imposing these new experimental results, we find that the situations in
the no-scale model are much more favorable than those in the standard model,
and if , then the allowed regions at the 95% C.~L. in
the no-scale model are and for , which are in fact much more stringent than in
our previous analysis. Therefore, assuming that , if the
lightest chargino mass bound were to be pushed up only by a few GeV, the sign
on the Higgs mixing term in the no-scale model could well be determined
from the constraint to be positive at the 95% C.~L. At
any rate, better accuracy in the measured from the Tevatron in the near
future combined with the LEP data is most likely to provide a decisive test of
the no-scale supergravity model.Comment: 15 pages, REVTEX, 1 figure (not included but available as a ps file
from [email protected]
Spin induced nonlinearities in the electron MHD regime
We consider the influence of the electron spin on the nonlinear propagation
of whistler waves. For this purpose a recently developed electron two-fluid
model, where the spin up- and down populations are treated as different fluids,
is adapted to the electron MHD regime. We then derive a nonlinear Schrodinger
equation for whistler waves, and compare the coefficients of nonlinearity with
and without spin effects. The relative importance of spin effects depend on the
plasma density and temperature as well as the external magnetic field strength
and the wave frequency. The significance of our results to various plasmas are
discussed.Comment: 5 page
Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example
We study a perturbed Floquet Hamiltonian depending on a coupling
constant . The spectrum is assumed to be pure point and
dense. We pick up an eigen-value, namely , and show the
existence of a function defined on such that
for all , 0 is a point of
density for the set , and the Rayleigh-Schr\"odinger perturbation series
represents an asymptotic series for the function . All ideas
are developed and demonstrated when treating an explicit example but some of
them are expected to have an essentially wider range of application.Comment: Latex, 24 pages, 51
Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula
We consider a perturbation of an ``integrable'' Hamiltonian and give an
expression for the canonical or unitary transformation which ``simplifies''
this perturbed system. The problem is to invert a functional defined on the
Lie- algebra of observables. We give a bound for the perturbation in order to
solve this inversion. And apply this result to a particular case of the control
theory, as a first example, and to the ``quantum adiabatic transformation'', as
another example.Comment: Version 8.0. 26 pages, Latex2e, final version published in J. Phys.
The Maslov index and nondegenerate singularities of integrable systems
We consider integrable Hamiltonian systems in R^{2n} with integrals of motion
F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical
points of F where rank dF = n-1 and which have definite linear stability. The
set of nondegenerate singularities is a codimension-two symplectic submanifold
invariant under the flow. We show that the Maslov index of a closed curve is a
sum of contributions +/- 2 from the nondegenerate singularities it is encloses,
the sign depending on the local orientation and stability at the singularities.
For one-freedom systems this corresponds to the well-known formula for the
Poincar\'e index of a closed curve as the oriented difference between the
number of elliptic and hyperbolic fixed points enclosed. We also obtain a
formula for the Liapunov exponent of invariant (n-1)-dimensional tori in the
nondegenerate singular set. Examples include rotationally symmetric n-freedom
Hamiltonians, while an application to the periodic Toda chain is described in a
companion paper.Comment: 27 pages, 1 figure; published versio
Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain
The n-particle periodic Toda chain is a well known example of an integrable
but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold
singularities of the Toda chain, ie points where there exist k independent
linear relations amongst the gradients of the integrals of motion, coincide
with points where there are k (doubly) degenerate eigenvalues of
representatives L and Lbar of the two inequivalent classes of Lax matrices
(corresponding to degenerate periodic or antiperiodic solutions of the
associated second-order difference equation). The singularities are shown to be
nondegenerate, so that Sigma_k is a codimension-2k symplectic submanifold.
Sigma_k is shown to be of elliptic type, and the frequencies of transverse
oscillations under Hamiltonians which fix Sigma_k are computed in terms of
spectral data of the Lax matrices. If mu(C) is the (even) Maslov index of a
closed curve C in the regular component of R^{2n}, then (-1)^{\mu(C)/2} is
given by the product of the holonomies (equal to +/- 1) of the even- (or odd-)
indexed eigenvector bundles of L and Lmat.Comment: 25 pages; published versio
Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators
We establish sharp results on the modulus of continuity of the distribution
of the spectral measure for one-frequency Schrodinger operators with
Diophantine frequencies in the region of absolutely continuous spectrum. More
precisely, we establish 1/2-Holder continuity near almost reducible energies
(an essential support of absolutely continuous spectrum). For
non-perturbatively small potentials (and for the almost Mathieu operator with
subcritical coupling), our results apply for all energies.Comment: 16 page
Role of phason-defects on the conductance of a 1-d quasicrystal
We have studied the influence of a particular kind of phason-defect on the
Landauer resistance of a Fibonacci chain. Depending on parameters, we sometimes
find the resistance to decrease upon introduction of defect or temperature, a
behavior that also appears in real quasicrystalline materials. We demonstrate
essential differences between a standard tight-binding model and a full
continuous model. In the continuous case, we study the conductance in relation
to the underlying chaotic map and its invariant. Close to conducting points,
where the invariant vanishes, and in the majority of cases studied, the
resistance is found to decrease upon introduction of a defect. Subtle
interference effects between a sudden phason-change in the structure and the
phase of the wavefunction are also found, and these give rise to resistive
behaviors that produce exceedingly simple and regular patterns.Comment: 12 pages, special macros jnl.tex,reforder.tex, eqnorder.tex. arXiv
admin note: original tex thoroughly broken, figures missing. Modified so that
tex compiles, original renamed .tex.orig in source
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