1,451 research outputs found
Ultracoherence and Canonical Transformations
The (in)finite dimensional symplectic group of homogeneous canonical
transformations is represented on the bosonic Fock space by the action of the
group on the ultracoherent vectors, which are generalizations of the coherent
states.Comment: 24 page
Driven Brownian transport through arrays of symmetric obstacles
We numerically investigate the transport of a suspended overdamped Brownian
particle which is driven through a two-dimensional rectangular array of
circular obstacles with finite radius. Two limiting cases are considered in
detail, namely, when the constant drive is parallel to the principal or the
diagonal array axes. This corresponds to studying the Brownian transport in
periodic channels with reflecting walls of different topologies. The mobility
and diffusivity of the transported particles in such channels are determined as
functions of the drive and the array geometric parameters. Prominent transport
features, like negative differential mobilities, excess diffusion peaks, and
unconventional asymptotic behaviors, are explained in terms of two distinct
lengths, the size of single obstacles (trapping length) and the lattice
constant of the array (local correlation length). Local correlation effects are
further analyzed by continuously rotating the drive between the two limiting
orientations.Comment: 10 pages 13 figure
Some Remarks on Effective Range Formula in Potential Scattering
In this paper, we present different proofs of very recent results on the
necessary as well as sufficient conditions on the decrease of the potential at
infinity for the validity of effective range formulas in 3-D in low energy
potential scattering (Andr\'e Martin, private communication, to appear. See
Theorem 1 below). Our proofs are based on compact formulas for the
phase-shifts. The sufficiency conditions are well-known since long. But the
necessity of the same conditions for potentials keeping a constant sign at
large distances are new. All these conditions are established here for
dimension 3 and for all angular momenta
Piecewise constant potentials and discrete ambiguities
This work is devoted to the study of discrete ambiguities. For parametrized
potentials, they arise when the parameters are fitted to a finite number of
phase-shifts. It generates phase equivalent potentials. Such equivalence was
suggested to be due to the modulo uncertainty inherent to phase
determinations. We show that a different class of phase-equivalent potentials
exists. To this aim, use is made of piecewise constant potentials, the
intervals of which are defined by the zeros of their regular solutions of the
Schr\"odinger equation. We give a classification of the ambiguities in terms of
indices which include the difference between exact phase modulo and the
numbering of the wave function zeros.Comment: 26 pages Subject: Mathematical Physics math-p
Brownian transport in corrugated channels with inertia
The transport of suspended Brownian particles dc-driven along corrugated
narrow channels is numerically investigated in the regime of finite damping. We
show that inertial corrections cannot be neglected as long as the width of the
channel bottlenecks is smaller than an appropriate particle diffusion length,
which depends on the the channel corrugation and the drive intensity. Being
such a diffusion length inversely proportional to the damping constant,
transport through sufficiently narrow obstructions turns out to be always
sensitive to the viscosity of the suspension fluid. The inertia corrections to
the transport quantifiers, mobility and diffusivity, markedly differ for
smoothly and sharply corrugated channels.Comment: 9 pages including figures. arXiv admin note: substantial text overlap
with arXiv:1202.436
Extending bioacoustic monitoring of birds aloft through flight call localization with a three-dimensional microphone array
Bioacoustic localization of bird vocalizations provides unattended observations of the location of calling individuals in many field applications. While this technique has been successful in monitoring terrestrial distributions of calling birds, no published study has applied these methods to migrating birds in flight. The value of nocturnal flight call recordings can increase with the addition of three-dimensional position retrievals, which can be achieved with adjustments to existing localization techniques. Using the time difference of arrival method, we have developed a proof-of-concept acoustic microphone array that allows the three-dimensional positioning of calls within the airspace. Our array consists of six microphones, mounted in pairs at the top and bottom of three 10-m poles, arranged in an equilateral triangle with sides of 20 m. The microphone array was designed using readily available components and costs less than $2,000 USD to build and deploy. We validate this technique using a kite-lofted GPS and speaker package, and obtain 60.1% of vertical retrievals within the accuracy of the GPS measurements (+/- 5 m) and 80.4% of vertical retrievals within +/- 10 m. The mean Euclidian distance between the acoustic retrievals of flight calls and the GPS truth was 9.6 m. Identification and localization of nocturnal flight calls have the potential to provide species-specific spatial characterizations of bird migration within the airspace. Even with the inexpensive equipment used in this trial, low-altitude applications such as surveillance around wind farms or oil platforms can benefit from the three-dimensional retrievals provided by this technique
The Classical Schrodinger's Equation
A non perturbative numerical method for determining the discrete spectra is
deduced from the classical analogue of the Schrodinger's equation. The energy
eigenvalues coincide with the bifurcation parameters for the classical orbits.Comment: UUEncoded Postscript, 18 pages, 4 figures inserted in tex
The Schwarzian derivative and the Wiman-Valiron property
Consider a transcendental meromorphic function in the plane with finitely many critical values, such that the multiple points have bounded multiplicities and the inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that if the Schwarzian derivative is transcendental then the function has infinitely many multiple points, the inverse function does not have a direct transcendental singularity over infinity, and infinity is not a Borel exceptional value. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method
Brownian Simulations and Uni-Directional Flux in Diffusion
Brownian dynamics simulations require the connection of a small discrete
simulation volume to large baths that are maintained at fixed concentrations
and voltages. The continuum baths are connected to the simulation through
interfaces, located in the baths sufficiently far from the channel. Average
boundary concentrations have to be maintained at their values in the baths by
injecting and removing particles at the interfaces. The particles injected into
the simulation volume represent a unidirectional diffusion flux, while the
outgoing particles represent the unidirectional flux in the opposite direction.
The classical diffusion equation defines net diffusion flux, but not
unidirectional fluxes. The stochastic formulation of classical diffusion in
terms of the Wiener process leads to a Wiener path integral, which can split
the net flux into unidirectional fluxes. These unidirectional fluxes are
infinite, though the net flux is finite and agrees with classical theory. We
find that the infinite unidirectional flux is an artifact caused by replacing
the Langevin dynamics with its Smoluchowski approximation, which is classical
diffusion. The Smoluchowski approximation fails on time scales shorter than the
relaxation time of the Langevin equation. We find the unidirectional
flux (source strength) needed to maintain average boundary concentrations in a
manner consistent with the physics of Brownian particles. This unidirectional
flux is proportional to the concentration and inversely proportional to
to leading order. We develop a BD simulation that maintains
fixed average boundary concentrations in a manner consistent with the actual
physics of the interface and without creating spurious boundary layers
Autonomous Bursting in a Homoclinic System
A continuous train of irregularly spaced spikes, peculiar of homoclinic
chaos, transforms into clusters of regularly spaced spikes, with quiescent
periods in between (bursting regime), by feeding back a low frequency portion
of the dynamical output. Such autonomous bursting results to be extremely
robust against noise; we provide experimental evidence of it in a CO2 laser
with feedback. The phenomen here presented display qualitative analogies with
bursting phenomena in neurons.Comment: Submitted to Phys. Rev. Lett., 14 pages, 5 figure
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