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Repeating head-on collisions in an optical trap and the evaluation of spin-dependent interactions among neutral particles
A dynamic process of repeating collisions of a pair of trapped neutral
particles with weak spin-dependent interaction is designed and studied. Related
theoretical derivation and numerical calculation have been performed to study
the inherent coordinate-spin and momentum-spin correlation. Due to the
repeating collisions the effect of the weak interaction can be accumulated and
enlarged, and therefore can be eventually detected. Numerical results suggest
that the Cr-Cr interaction, which has not yet been completely clear, could be
thereby determined. The design can be in general used to determine various
interactions among neutral atoms and molecules, in particular for the
determination of very weak forces.Comment: 15 pages, 7 figure
A Dynamic Analysis of Moving Average Rules
The use of various moving average rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules also used in practice. In this paper we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long run) moving average. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag lengths used for the moving averages. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different moving average rules. The price dynamics of the moving average rule is also examined and one of our main findings is that an increase of the window length of the moving average rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.
Two-body scattering in a trap and a special periodic phenomenon sensitive to the interaction
Two-body scattering of neutral particles in a trap is studied theoretically.
The control of the initial state is realized by using optical traps. The
collisions inside the trap occur repeatedly; thereby the effect of interaction
can be accumulated. Two periodic phenomena with a shorter and a much longer
period, respectively, are found. The latter is sensitive to the interaction.
Instead of measuring the differential cross section as usually does, the
measurement of the longer period and the details of the periodic behavior might
be a valid source of information on weak interactions among neutral particles.Comment: 5 pages, 5 figure
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