283 research outputs found
Nonlinear Optical Galton Board: thermalization and continuous limit
The nonlinear optical Galton board (NLOGB), a quantum walk like (but
nonlinear) discrete time quantum automaton, is shown to admit a complex
evolution leading to long time thermalized states. The continuous limit of the
Galton Board is derived and shown to be a nonlinear Dirac equation (NLDE). The
(Galerkin truncated) NLDE evolution is shown to thermalize toward states
qualitatively similar to those of the NLOGB. The NLDE conserved quantities are
derived and used to construct a stochastic differential equation converging to
grand canonical distributions that are shown to reproduce the (micro canonical)
NLDE thermalized statistics. Both the NLOGB and the Galerkin-truncated NLDE are
thus demonstrated to exhibit spontaneous thermalization.Comment: 8 pages, 14 figures, accepted on PRE as Regular Articl
Relativistic graphene ratchet on semidisk Galton board
Using extensive Monte Carlo simulations we study numerically and analytically
a photogalvanic effect, or ratchet, of directed electron transport induced by a
microwave radiation on a semidisk Galton board of antidots in graphene. A
comparison between usual two-dimensional electron gas (2DEG) and electrons in
graphene shows that ratchet currents are comparable at very low temperatures.
However, a large mean free path in graphene should allow to have a strong
ratchet transport at room temperatures. Also in graphene the ratchet transport
emerges even for unpolarized radiation. These properties open promising
possibilities for room temperature graphene based sensitive photogalvanic
detectors of microwave and terahertz radiation.Comment: 4 pages, 4 figures. Research done at Quantware
http://www.quantware.ups-tlse.fr/. More detailed analysis is give
Directing transport by polarized radiation in presence of chaos and dissipation
We study numerically the dynamics of particles on the Galton board of
semi-disk scatters in presence of monochromatic radiation and dissipation. It
is shown that under certain conditions the radiation leads to appearance of
directed transport linked to an underlining strange attractor. The direction of
transport can be efficiently changed by radiation polarization. The
experimental realization of this effect in asymmetric antidot superlattices is
discussed.Comment: revtex, 4 pages, 6 fig
Nonlinear optical Galton board
We generalize the concept of optical Galton board (OGB), first proposed by
Bouwmeester et al. {[}Phys. Rev. A \textbf{61}, 013410 (2000)], by introducing
the possibility of nonlinear self--phase modulation on the wavefunction during
the walker evolution. If the original Galton board illustrates classical
diffusion, the OGB, which can be understood as a grid of Landau--Zener
crossings, illustrates the influence of interference on diffusion, and is
closely connected with the quantum walk. Our nonlinear generalization of the
OGB shows new phenomena, the most striking of which is the formation of
non-dispersive pulses in the field distribution (soliton--like structures).
These exhibit a variety of dynamical behaviors, including ballistic motion,
dynamical localization, non--elastic collisions and chaotic behavior, in the
sense that the dynamics is very sensitive to the nonlinearity strength.Comment: 8 pages, 8 figure
Experiments with a Galton board
Galton boards have been used for over a half-century as a tool to illustrate the formation of Gaussian shaped distributions as well as the Central Limit Theorem. Here, the Galton board was used to study the spontaneous percolation of a particle through an ordered array of rigid scatterers. The apparatus that was designed and fabricated provided a means to release 1/8 diameter spheres one at a time in a controlled and precise manner at any location on the board. The three experimental variables used in these experiments were the particle material, the release height, and the board tilt. angle. The data, consisting of residence time and exit location, were analyzed and the relationship between statistical values and parameter settings was found to be as follows: (1) standard deviation of the radial displacement increased with release height and was unaffected by board angle, (2) average residence time increased with release height and decreased with board angle, (3) standard deviation of the residence time increased with release height, (4) average axial velocity was unaffected by release height and increased with board angle, and (5) standard deviation of the axial velocity increased with a decrease of release height and increased with an increase in board angle. From an analysis of the data, it can be inferred that the motion of particles on the Galton board is governed by a diffusional mechanism
Directed transport born from chaos in asymmetric antidot structures
It is shown that a polarized microwave radiation creates directed transport
in an asymmetric antidot superlattice in a two dimensional electron gas. A
numerical method is developed that allows to establish the dependence of this
ratchet effect on several parameters relevant for real experimental studies. It
is applied to the concrete case of a semidisk Galton board where the electron
dynamics is chaotic in the absence of microwave driving. The obtained results
show that high currents can be reached at a relatively low microwave power.
This effect opens new possibilities for microwave control of transport in
asymmetric superlattices.Comment: 8 pages, 10 figure
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