513 research outputs found
Cooperative quantum jumps for three dipole-interacting atoms
We investigate the effect of the dipole-dipole interaction on the quantum
jump statistics of three atoms. This is done for three-level systems in a V
configuration and in what may be called a D configuration. The transition rates
between the four different intensity periods are calculated in closed form.
Cooperative effects are shown to increase by a factor of 2 compared to two of
either three-level systems. This results in transition rates that are, for
distances of about one wavelength of the strong transition, up to 100% higher
than for independent systems. In addition the double and triple jump rates are
calculated from the transition rates. In this case cooperative effects of up to
170% for distances of about one wavelength and still up to 15% around 10
wavelengths are found. Nevertheless, for the parameters of an experiment with
Hg+ ions the effects are negligible, in agreement with the experimental data.
For three Ba+ ions this seems to indicate that the large cooperative effects
observed experimentally cannot be explained by the dipole-dipole interaction.Comment: 9 pages, 9 figures. Revised version, to be published in PR
Causality, particle localization and positivity of the energy
Positivity of the Hamiltonian alone is used to show that particles, if
initially localized in a finite region, immediately develop infinite tails.Comment: To appear in: Irreversibility and Causality in Quantum Theory --
Semigroups and Rigged Hilbert Spaces, edited by A. Bohm, H.-D. Doebner and P.
Kielanowski, Springer Lecture Notes in Physics, Vol. 504 (1998
Localization and Causality for a free particle
Theorems (most notably by Hegerfeldt) prove that an initially localized
particle whose time evolution is determined by a positive Hamiltonian will
violate causality. We argue that this apparent paradox is resolved for a free
particle described by either the Dirac equation or the Klein-Gordon equation
because such a particle cannot be localized in the sense required by the
theorems.Comment: 9 pages,no figures,new section adde
Causality, delocalization and positivity of energy
In a series of interesting papers G. C. Hegerfeldt has shown that quantum
systems with positive energy initially localized in a finite region,
immediately develop infinite tails. In our paper Hegerfeldt's theorem is
analysed using quantum and classical wave packets. We show that Hegerfeldt's
conclusion remains valid in classical physics. No violation of Einstein's
causality is ever involved. Using only positive frequencies, complex wave
packets are constructed which at are real and finitely localized and
which, furthemore, are superpositions of two nonlocal wave packets. The
nonlocality is initially cancelled by destructive interference. However this
cancellation becomes incomplete at arbitrary times immediately afterwards. In
agreement with relativity the two nonlocal wave packets move with the velocity
of light, in opposite directions.Comment: 14 pages, 5 figure
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