9 research outputs found
Non-linear spectroscopy of rubidium: An undergraduate experiment
In this paper, we describe two complementary non-linear spectroscopy methods
which both allow to achieve Doppler-free spectra of atomic gases. First,
saturated absorption spectroscopy is used to investigate the structure of the
transition in rubidium. Using a slightly
modified experimental setup, Doppler-free two-photon absorption spectroscopy is
then performed on the transition in
rubidium, leading to accurate measurements of the hyperfine structure of the
energy level. In addition, electric dipole selection rules of
the two-photon transition are investigated, first by modifying the polarization
of the excitation laser, and then by measuring two-photon absorption spectra
when a magnetic field is applied close to the rubidium vapor. All experiments
are performed with the same grating-feedback laser diode, providing an
opportunity to compare different high resolution spectroscopy methods using a
single experimental setup. Such experiments may acquaint students with quantum
mechanics selection rules, atomic spectra and Zeeman effect.Comment: 16 pages, 8 figure
Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents
We introduce a stochastic heterogeneous interacting-agent model for the
short-time non-equilibrium evolution of excess demand and price in a stylized
asset market. We consider a combination of social interaction within peer
groups and individually heterogeneous fundamentalist trading decisions which
take into account the market price and the perceived fundamental value of the
asset. The resulting excess demand is coupled to the market price. Rigorous
analysis reveals that this feedback may lead to price oscillations, a single
bounce, or monotonic price behaviour. The model is a rare example of an
analytically tractable interacting-agent model which allows us to deduce in
detail the origin of these different collective patterns. For a natural choice
of initial distribution the results are independent of the graph structure that
models the peer network of agents whose decisions influence each other.Comment: 26 pages, 3 figures. v2: minor alterations, to appear in Physica A
(http://www.elsevier.com/wps/find/journaldescription.cws_home/505702/description#description
Loss of erdodicity in the transition from quenched to annealed disorder in a finite kinetic Ising model
We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing "jumpy" transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e. g. high level of corruption) to a desirable one (low level of corruption)
Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents
We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows us to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution the results are independent of the graph structure that models the peer network of agents whose decisions influence each other.