Universal long-wavelength nonlinear optical response of noble gases

We demonstrate numerically that the long-wavelength nonlinear dipole moment and ionization rate versus electric field strength $F$ for different noble gases can be scaled onto each other, revealing universal functions that characterize the form of the nonlinear response. We elucidate the physical origin of the universality by using a metastable state analysis of the light-atom interaction in combination with a scaling analysis. Our results also provide a powerful new means of characterizing the nonlinear response in the mid-infrared and long-wave infrared for optical filamentation studies.Comment: 8 pages, 6 figure

Antibunching in an optomechanical oscillator

We theoretically analyze antibunching of the phonon field in an optomechanical oscillator employ- ing the membrane-in-the-middle geometry. More specifically, a single-mode mechanical oscillator is quadratically coupled to a single-mode cavity field in the regime in which the cavity dissipation is a dominant source of damping, and adiabatic elimination of the cavity field leads to an effective cubic nonlinearity for the mechanics. We show analytically in the weak coupling regime that the mechan- ics displays a chaotic phonon field for small optomechanical cooperativity, whereas an antibunched single-phonon field appears for large optomechanical cooperativity. This opens the door to control of the second-order correlation function of a mechanical oscillator in the weak coupling regime

Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases

We investigate some exact static and dynamic properties of one-dimensional fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive p-wave interactions induced by a Feshbach resonance. A closed form solution for the one-body density matrix for harmonic trapping is analyzed in terms of its natural orbitals, with the surprising result that for odd, but not for even, numbers of fermions the maximally occupied natural orbital coincides with the ground harmonic oscillator orbital and has the maximally allowed fermionic occupancy of unity. The exact dynamics of the trapped gas following turnoff of the p-wave interactions are explored.Comment: 4 pages, 2 figures, submitted to PR

A Rank Approach to Equity Forecast Construction

The purpose of this paper is to present a rank based approach to cross-sectionallinear factor modelling. The emphasis is on approximating factor exposures in aconsistent manner in order to facilitate the merging of subjective information(from professional investors) with objective information (from accounting dataand/or state of the art quantitative models) in a statistically rigorous way withoutneeding to impose the unrealistic simplifying assumptions typical of more standardtime series models. We deal with the problems of identifying country and sectorreturns by an innovative hierarchical factor structure. This is all discussed fromthe perspective that investment models are not immutable but rather need to bedesigned with characteristics that are fit for their purpose; for example, returningaggregate county and sector forecasts that are consistent by construction

Control of unstable steady states by time-delayed feedback methods

We show that time-delayed feedback methods, which have successfully been used to control unstable periodic ortbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and non-zero latency times associated with the generation and injection of the feedback signal.Comment: 8 pages, 11 figure

Circulating Subbeam Systems and the Physics of Pulsar Emission

The purpose of this paper is to suggest how detailed single-pulse observations of ``slow'' radio pulsars may be utilized to construct an empirical model for their emission. It links the observational synthesis developed in a series of papers by Rankin starting in the 1980s to the more recent empirical feedback model of Wright (2003a) by regarding the entire pulsar magnetosphere as a non-steady, non-linear interactive system with a natural built-in delay. It is argued that the enhanced role of the outer gap in such a system indicates an evolutionary link to younger pulsars, in which this region is thought to be highly active, and that pulsar magnetospheres should no longer be seen as being ``driven'' by events on the neutron star's polar cap, but as having more in common with planetary magnetospheres and auroral phenomena.Comment: 15 pages, 3 figure