1,402 research outputs found
Ehrenfest theorem, Galilean invariance and nonlinear Schr\"odinger equations
Galilean invariant Schr\"odinger equations possessing nonlinear terms
coupling the amplitude and the phase of the wave function can violate the
Ehrenfest theorem. An example of this kind is provided. The example leads to
the proof of the theorem: A Galilean invariant Schr\"odinger equation derived
from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for
any linear or nonlinear lagrangian.Comment: Latex format, no figures, submitted to journal of physics
Momentum transferred to a trapped Bose-Einstein condensate by stimulated light scattering
The response of a trapped Bose-Einstein condensed gas to a density
perturbation generated by a two-photon Bragg pulse is investigated by solving
the time-dependent Gross-Pitaevskii equation. We calculate the total momentum
imparted to the condensate as a function of both the time duration of the pulse
and the frequency difference of the two laser beams. The role of the dynamic
response function in characterizing the time evolution of the system is pointed
out, with special emphasis to the phonon regime. Numerical simulations are
compared with the predictions of local density approximation. The relevance of
our results for the interpretation of current experiments is also discussed.Comment: 7 pages, 3 postscript figure
How to measure the Bogoliubov quasiparticle amplitudes in a trapped condensate
We propose an experiment, based on two consecutive Bragg pulses, to measure
the momentum distribution of quasiparticle excitations in a trapped Bose gas at
low temperature. With the first pulse one generates a bunch of excitations
carrying momentum , whose Doppler line is measured by the second pulse. We
show that this experiment can provide direct access to the amplitudes
and characterizing the Bogoliubov transformations from particles to
quasiparticles. We simulate the behavior of the nonuniform gas by numerically
solving the time dependent Gross-Pitaevskii equation.Comment: 12 pages, 4 figures include
Quantum Evaporation from Superfluid Helium at Normal Incidence
We study the scattering of atoms, rotons and phonons at the free surface of
He at normal incidence and calculate the evaporation, condensation and
reflection probabilities. Assuming elastic one-to-one processes and using
general properties of the scattering matrix, such as unitarity and time
reversal, we argue that all nonzero probabilities can be written in terms of a
single energy-dependent parameter. Quantitative predictions are obtained using
linearized time dependent density functional theory.Comment: 12 pages, REVTeX, 2 postscript figures, available also at
http://anubis.science.unitn.it/~dalfovo/papers/papers.htm
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