1,757 research outputs found
Analytic linearization of nonlinear perturbations of Fuchsian systems
Nonlinear perturbation of Fuchsian systems are studied in regions including
two singularities. Such systems are not necessarily analytically equivalent to
their linear part (they are not linearizable). Nevertheless, it is shown that
in the case when the linear part has commuting monodromy, and the eigenvalues
have positive real parts, there exists a unique correction function of the
nonlinear part so that the corrected system becomes analytically linearizable
Evolution of a model quantum system under time periodic forcing: conditions for complete ionization
We analyze the time evolution of a one-dimensional quantum system with an
attractive delta function potential whose strength is subjected to a time
periodic (zero mean) parametric variation . We show that for generic
, which includes the sum of any finite number of harmonics, the
system, started in a bound state will get fully ionized as . This
is irrespective of the magnitude or frequency (resonant or not) of .
There are however exceptional, very non-generic , that do not lead to
full ionization, which include rather simple explicit periodic functions. For
these the system evolves to a nontrivial localized stationary state
which is related to eigenfunctions of the Floquet operator
Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case
We study the time evolution of a three dimensional quantum particle,
initially in a bound state, under the action of a time-periodic zero range
interaction with ``strength'' (\alpha(t)). Under very weak generic conditions
on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t
\to \infty). We prove also that, under the same conditions, all the states of
the system are scattering states.Comment: LaTeX2e, 15 page
Nonlinear Schroedinger equation with two symmetric point interactions in one dimension
We consider a time-dependent one-dimensional nonlinear Schroedinger equation
with a symmetric potential double well represented by two delta interactions.
Among our results we give an explicit formula for the integral kernel of the
unitary semigroup associated with the linear part of the Hamiltonian. Then we
establish the corresponding Strichartz-type estimate and we prove local
existence and uniqueness of the solution to the original nonlinear problem
Ionization in damped time-harmonic fields
We study the asymptotic behavior of the wave function in a simple one
dimensional model of ionization by pulses, in which the time-dependent
potential is of the form ,
where is the Dirac distribution. We find the ionization probability in
the limit for all and . The long pulse limit is
very singular, and, for , the survival probability is , much larger than , the one in the abrupt transition
counterpart, where
is the Heaviside function
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