614 research outputs found
Stabilizing quantum metastable states in a time-periodic potential
Metastability of a particle trapped in a well with a time-periodically
oscillating barrier is studied in the Floquet formalism. It is shown that the
oscillating barrier causes the system to decay faster in general. However,
avoided crossings of metastable states can occur with the less stable states
crossing over to the more stable ones. If in the static well there exists a
bound state, then it is possible to stabilize a metastable state by
adiabatically increasing the oscillating frequency of the barrier so that the
unstable state eventually cross-over to the stable bound state. It is also
found that increasing the amplitude of the oscillating field may change a
direct crossing of states into an avoided one.Comment: 7 pages, 6 figure
Generalized Riemann sums
The primary aim of this chapter is, commemorating the 150th anniversary of
Riemann's death, to explain how the idea of {\it Riemann sum} is linked to
other branches of mathematics. The materials I treat are more or less classical
and elementary, thus available to the "common mathematician in the streets."
However one may still see here interesting inter-connection and cohesiveness in
mathematics
On the Number of Facets of Three-Dimensional Dirichlet Stereohedra III: Full Cubic Groups
We are interested in the maximum possible number of facets that Dirichlet
stereohedra for three-dimensional crystallographic groups can have. The problem
for non-cubic groups was studied in previous papers by D. Bochis and the second
author (Discrete Comput. Geom. 25:3 (2001), 419-444, and Beitr. Algebra Geom.,
47:1 (2006), 89-120). This paper deals with ''full'' cubic groups, while
''quarter'' cubic groups are left for a subsequent paper. Here, ''full'' and
''quarter'' refers to the recent classification of three-dimensional
crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston
(math.MG/9911185, Beitr. Algebra Geom. 42.2 (2001), 475-507).
Our main result in this paper is that Dirichlet stereohedra for any of the 27
full groups cannot have more than 25 facets. We also find stereohedra with 17
facets for one of these groups.Comment: 28 pages, 12 figures. Changes from v1: apart of some editing (mostly
at the end of the introduction) and addition of references, an appendix has
been added, which analyzes the case where the base point does not have
trivial stabilize
Selective excitation of metastable atomic states by femto- and attosecond laser pulses
The possibility of achieving highly selective excitation of low metastable
states of hydrogen and helium atoms by using short laser pulses with reasonable
parameters is demonstrated theoretically. Interactions of atoms with the laser
field are studied by solving the close-coupling equations without
discretization. The parameters of laser pulses are calculated using different
kinds of optimization procedures. For the excitation durations of hundreds of
femtoseconds direct optimization of the parameters of one and two laser pulses
with Gaussian envelopes is used to introduce a number of simple schemes of
selective excitation. To treat the case of shorter excitation durations,
optimal control theory is used and the calculated optimal fields are
approximated by sequences of pulses with reasonable shapes. A new way to
achieve selective excitation of metastable atomic states by using sequences of
attosecond pulses is introduced.Comment: To be published in Phys. Rev. A, 10 pages, 3 figure
Amperometric and spectrophotometric determination of carbaryl in natural waters and commercial formulations
The work presented describes the development
and evaluation of two flow-injection analysis (FIA) systems
for the automated determination of carbaryl in spiked
natural waters and commercial formulations. Samples are
injected directly into the system where they are subjected
to alkaline hydrolysis thus forming 1-naphthol. This product
is readily oxidised at a glassy carbon electrode. The
electrochemical behaviour of 1-naphthol allows the development
of an FIA system with an amperometric detector
in which 1-naphthol determination, and thus measurement
of carbaryl concentration, can be performed. Linear response
over the range 1.0×10–7 to 1.0×10–5 mol L–1, with a
sampling rate of 80 samples h–1, was recorded. The detection
limit was 1.0×10–8 mol L–1. Another FIA manifold was
constructed but this used a colorimetric detector. The methodology
was based on the coupling of 1-naphthol with phenylhydrazine
hydrochloride to produce a red complex which
has maximum absorbance at 495 nm. The response was
linear from 1.0×10–5 to 1.5×10–3 mol L–1 with a detection
limit of 1.0×10–6 mol L–1. Sample-throughput was about
60 samples h–1. Validation of the results provided by the
two FIA methodologies was performed by comparing
them with results from a standard HPLC–UV technique.
The relative deviation was <5%. Recovery trials were also
carried out and the values obtained ranged from 97.0 to
102.0% for both methods. The repeatability (RSD, %) of
12 consecutive injections of one sample was 0.8% and
1.6% for the amperometric and colorimetric systems, respectively
Capture into Rydberg states and momentum distributions of ionized electrons
The yield of neutral excited atoms and low-energy photoelectrons generated by
the electron dynamics in the combined Coulomb and laser field after tunneling
is investigated. We present results of Monte-Carlo simulations built on the
two-step semiclassical model, as well as analytic estimates and scaling
relations for the population trapping into the Rydberg states. It is shown that
mainly those electrons are captured into bound states of the neutral atom that
due to their initial conditions (i) have moderate drift momentum imparted by
the laser field and (ii) avoid strong interaction ("hard" collision) with the
ion. In addition, it is demonstrated that the channel of capture, when
accounted for in semiclassical calculations, has a pronounced effect on the
momentum distribution of electrons with small positive energy. For the
parameters that we investigated its presence leads to a dip at zero momentum in
the longitudinal momentum distribution of the ionized electrons.Comment: 9 pages, 8 figures in one zip-archiv
Temperature Variation of Ultra Slow Light in a Cold Gas
A model is developed to explain the temperature dependence of the group
velocity as observed in the experiments of Hau et al (Nature {\bf397}, 594
(1999)). The group velocity is quite sensitive to the change in the spatial
density. The inhomogeneity in the density and its temperature dependence are
primarily responsible for the observed behavior.Comment: 12 pages, 4 figure
Multiphoton Ionization as Time-Dependent Tunneling
A new semiclassical approach to ionization by an oscillating field is
presented. For a delta-function atom, an asymptotic analysis is performed with
respect to a quantity h, defined as the ratio of photon energy to ponderomotive
energy. This h appears formally equivalent to Planck's constant in a suitably
transformed Schroedinger equation and allows semiclassical methods to be
applicable. Systematically, a picture of tunneling wave packets in complex time
is developped, which by interference account for the typical ponderomotive
features of ionization curves. These analytical results are then compared to
numerical simulations and are shown to be in good agreement.Comment: 36 pages (also printable half size), uuencoded compressed tarred
Latex file with 9 Postscript figures included automaticall
Stochastic ionization through noble tori: Renormalization results
We find that chaos in the stochastic ionization problem develops through the
break-up of a sequence of noble tori. In addition to being very accurate, our
method of choice, the renormalization map, is ideally suited for analyzing
properties at criticality. Our computations of chaos thresholds agree closely
with the widely used empirical Chirikov criterion
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