Static NLO susceptibilities: testing approximation schemes against exact results

The reliability of the approximations commonly adopted in the calculation of static optical (hyper)polarizabilities is tested against exact results obtained for an interesting toy-model. The model accounts for the principal features of typical nonlinear organic materials with mobile electrons strongly coupled to molecular vibrations. The approximations introduced in sum over states and finite field schemes are analyzed in detail. Both the Born-Oppenheimer and the clamped nucleus approximations turn out to be safe for molecules, whereas for donor-acceptor charge transfer complexes deviations from adiabaticity are expected. In the regime of low vibrational frequency, static susceptibilities are strongly dominated by the successive derivatives of the potential energy and large vibrational contributions to hyperpolarizabilities are found. In this regime anharmonic corrections to hyperpolarizabilities are very large, and the harmonic approximation, exact for the linear polarizability, turns out totally inadequate for nonlinear responses. With increasing phonon frequency the role of vibrations smoothly decreases, until, in the antiadiabatic (infinite vibrational frequency) regime, vibrations do not contribute anymore to static susceptibilities, and the purely electronic responses are regained.Comment: 9 pages, including 3 figure

A Relativistic Version of the Two-Level Atom in the Rest-Frame Instant Form of Dynamics

We define a relativistic version of the two-level atom, in which an extended atom is replaced by a point particle carrying suitable Grassmann variables for the description of the two-level structure and of the electric dipole. After studying the isolated system "atom plus the electro-magnetic field" in the electric-dipole representation as a parametrized Minkowski theory, we give its restriction to the inertial rest frame and the explicit form of the Poincar\'e generators. After quantization we get a two-level atom with a spin 1/2 electric dipole and the relativistic generalization of the Hamiltonians of the Rabi and Jaynes-Cummings models.Comment: 23 page

Negative mass corrections in a dissipative stochastic environment

We study the dynamics of a macroscopic object interacting with a dissipative stochastic environment using an adiabatic perturbation theory. The perturbation theory reproduces known expressions for the friction coefficient and, surprisingly, gives an additional negative mass correction. The effect of the negative mass correction is illustrated by studying a harmonic oscillator interacting with a dissipative stochastic environment. While it is well known that the friction coefficient causes a reduction of the oscillation frequency, we show that the negative mass correction can lead to its enhancement. By studying an exactly solvable model of a magnet coupled to a spin environment evolving under standard non-conserving dynamics we show that the effect is present even beyond the validity of the adiabatic perturbation theory.We are grateful to M Kolodrubetz for the careful reading of the manuscript and helpful comments. This work was partially supported by BSF 2010318 (YK and AP), NSF DMR-1506340 (LD and AP), AFOSR FA9550-10-1-0110 (LD and AP), ARO W911NF1410540 (LD and AP) and ISF grant (YK). LD acknowledges the office of Naval Research. YK is grateful to the BU visitors program. (2010318 - BSF; DMR-1506340 - NSF; FA9550-10-1-0110 - AFOSR; W911NF1410540 - ARO; ISF grant)Accepted manuscrip

The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics

A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3+1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deperametrization to special relativity and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of Theoretical Physics, "Current Mathematical Topics in Gravitation and Cosmology", Ladek, Poland, 6-11 February 200

Multi-wavelength observations of 3FGL J2039.6-5618: a candidate redback millisecond pulsar

We present multi-wavelength observations of the unassociated gamma-ray source 3FGL J2039.6-5618 detected by the Fermi Large Area Telescope. The source gamma-ray properties suggest that it is a pulsar, most likely a millisecond pulsar, for which neither radio nor $\gamma$-ray pulsations have been detected yet. We observed 3FGL J2039.6-5618 with XMM-Newton and discovered several candidate X-ray counterparts within/close to the gamma-ray error box. The brightest of these X-ray sources is variable with a period of 0.2245$\pm$0.0081 d. Its X-ray spectrum can be described by a power law with photon index $\Gamma_X =1.36\pm0.09$, and hydrogen column density $N_{\rm H} < 4 \times 10^{20}$ cm$^{-2}$, which gives an unabsorbed 0.3--10 keV X-ray flux of $1.02 \times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$. Observations with the Gamma-Ray Burst Optical/Near-Infrared Detector (GROND) discovered an optical counterpart to this X-ray source, with a time-average magnitude $g'\sim 19.5$. The counterpart features a flux modulation with a period of 0.22748$\pm$0.00043 d that coincides, within the errors, with that of the X-ray source, confirming the association based on the positional coincidence. We interpret the observed X-ray/optical periodicity as the orbital period of a close binary system where one of the two members is a neutron star. The light curve profile of the companion star, with two asymmetric peaks, suggests that the optical emission comes from two regions at different temperatures on its tidally-distorted surface. Based upon its X-ray and optical properties, we consider this source as the most likely X-ray counterpart to 3FGL J2039.6-5618, which we propose to be a new redback system.Comment: 35 pages, 8 figures, accepted for publication on Astrophysical Journa

Mild behavioral impairment in Parkinson's disease: Data from the Parkinson's disease cognitive impairment study (PACOS)

Neuropsychiatric symptoms (NPS) have been frequently described in Parkinson's disease (PD), even in the earliest stages of the disease. Recently the construct of mild behavioral impairment (MBI) has been proposed as an at-risk state for incident cognitive decline and dementia. The aim of the present study is to evaluate the prevalence and associated factors of MBI in PD. Cross-sectional data from 429 consecutive PD patients enrolled in the PArkinson's disease COgnitive impairment Study (PACOS) were included in the study. All subjects underwent neuropsychological assessment, according to the MDS Level II criteria. NPS were evaluated with the Neuropsychiatric Inventory. Multivariate logistic regression models were used to evaluate clinical and behavioral characteristics, which are associated with PD-MBI. The latter was ascertained in 361 (84.1%) subjects of whom 155 (36.1%) were newly diagnosed patients (disease duration ≥1 year) and 206 (48.0%) had a disease duration &lt;1 year. Furthermore, 68 (15.9%) out of 429 subjects were PDw (without MBI). Across the MBI domains, Impulse Dyscontrol was significantly more prevalent among PD-MBI with disease duration &lt;1 year than newly diagnosed patients. The frequency of Social Inappropriateness and Abnormal Perception significantly increased throughout the entire PD-MBI sample with increasing Hoehn andYahr (H&amp;Y) stages. PD-MBI in newly diagnosed PDwas significantly associated with H&amp;Y stage (OR 2.35, 95% CI 1.05-5.24) and marginally with antidepressant drug use (OR 2.94, 95% CI 0.91-9.47), while in patients with a disease duration &gt;1 year was associated with UPDRS-ME (OR 3.37, 95% CI 1.41-8.00). The overall MBI frequency in the PACOS sample was 84% and 36% among newly diagnosed patients. The presence of MBI mainly related to motor impairment and disability

Data assimilation for the Martian atmosphere using MGS Thermal Emission Spectrometer observations

From the introduction: Given the quantity of data expected from current and forthcoming spacecraft missions to Mars, it is now possible to use data assimilation as a means of atmospheric analysis for the first time for a planet other than the Earth. Several groups have described plans to develop assimilation schemes for Mars [Banfield et al., 1995; Houben, 1999; Lewis and Read, 1995; Lewis et al., 1996, 1997; Zhang et al., 2001]. Data assimilation is a technique for the analysis of atmospheric observations which combines currently valid information with prior knowledge from previous observations and dynamical and physical constraints, via the use of a numerical model. Despite the number of new missions, observations of the atmosphere of Mars in the near future are still likely to be sparse when compared to those of the Earth, perhaps comprising one orbiter and a few surface stations at best at any one time. Data assimilation is useful as a means to extract the maximum information from such observations, both by a form of interpolation in space and time using model constraints and by the combination of information from different observations, e.g. temperature profiles and surface pressure measurements which may be irregularly distributed. The procedure can produce a dynamically consistent set of meteorological fields and can be used directly to test and to refine an atmospheric model against observations

Effects of noise and confidence thresholds in nominal and metric Axelrod dynamics of social influence

We study the effects of bounded confidence thresholds and of interaction and external noise on Axelrod's model of social influence. Our study is based on a combination of numerical simulations and an integration of the mean-field Master equation describing the system in the thermodynamic limit. We find that interaction thresholds affect the system only quantitatively, but that they do not alter the basic phase structure. The known crossover between an ordered and a disordered state in finite systems subject to external noise persists in models with general confidence threshold. Interaction noise here facilitates the dynamics and reduces relaxation times. We also study Axelrod systems with metric features, and point out similarities and differences compared to models with nominal features. Metric features are used to demonstrate that a small group of extremists can have a significant impact on the opinion dynamics of a population of Axelrod agents.Comment: 15 pages, 12 figure