Time-dependent quantum many-body theory of identical bosons in a double well: Early time ballistic interferences of fragmented and number entangled states

A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states.Comment: 16 pages, 5 figure

Kalman filter physical retrieval of surface emissivity and temperature from geostationary infrared radiances

The high temporal resolution of data acquisition by geostationary satellites and their capability to resolve the diurnal cycle allows for the retrieval of a valuable source of information about geophysical parameters. In this paper, we implement a Kalman filter approach to applying tempo-ral constraints on the retrieval of surface emissivity and temperature from radiance measurements made from geostationary platforms. Although we consider a case study in which we apply a strictly temporal constraint alone, the methodology will be presented in its general four-dimensional, i.e., space-time, setting. The case study we consider is the retrieval of emissivity and surface temperature from SEVIRI (Spinning Enhanced Visible and Infrared Imager) observations over a target area encompassing the Iberian Peninsula and northwestern Africa. The retrievals are then compared with in situ data and other similar satellite products. Our findings show that the Kalman filter strategy can simultaneously retrieve surface emissivity and temperature with an accuracy of ± 0.005 and ±0.2 K, respectively

Spatio-temporal constraints for emissivity and surface temperature retrieval: Preliminary results and comparisons for SEVIRI and IASI observation

Infrared instrumentation on geostationary satellites is now rapidly approaching the spectral quality and accuracy of modern sensors flying on polar platforms. Currently, the core of EUMETSAT geostationary meteorological programme is the Meteosat Second Generation (MSG). However, EUMETSAT is preparing for the Meteosat Third Generation (MTG). The capability of geostationary satellites to resolve the diurnal cycle and hence to provide time-resolved sequences or times series of observations is a source of information which could suitably constrain the derivation of geophysical parameters. Nowadays, also because of lack of time continuity, when dealing with observations from polar platforms, the problem of deriving geophysical parameters is normally solved by considering each single observation as independent of past and future events. For historical reason, the same approach is currently pursued with geostationary observations, which are still being dealt with as they were with polar observations. In this study we show some preliminary results on emissivity and surface temperature retrieval for SEVIRI observations, using the Kalman filter methodology (KF) and compare the retrievals with those obtained using IASI observations co-localized with SEVIRI ones using the times accumulation approach (Optimal Estimation OE). The Sahara desert was chosen as target area, and both SEVIRI and IASI data (infrared radiances and cloud mask) were acquired. The time period considered is that of July 2010 (the whole month). ECMWF analyses for the same date and target area have also been acquired, which comprise Ts, T(p), O(p), Q(p) for the canonical hours 0:00, 6:00, 12:00 and 18:00. Moreover, for the purpose of developing a suitable background for emissivity, the Global Infrared Land Surface Emissivity database developed at CIMSS, University of Wisconsin, derived by MODIS observations was used and was available from the year 2003 till 2011. Concerning the performance of the two methodologies, the retrieval of skin temperature is almost equivalent. The agreement between OE and KF is fairly good if compared with ECMWF analysis for sea surface, while for land surface, OE and KF agree fairly well with ECMWF during the night, but at midday ECMWF shows a cold bias of 10 K and more. For emissivity the comparison with the UW/BFEMIS database for the same date and location is fairly good for both methods

Technical note: Functional sliced inverse regression to infer temperature, water vapour and ozone from IASI data.

A retrieval algorithm that uses a statistical strategy based on dimension reduction is proposed. The methodology and details of the implementation of the new algorithm are presented and discussed. The algorithm has been applied to high resolution spectra measured by the Infrared Atmospheric Sounding Interferometer instrument to retrieve atmospheric profiles of temperature, water vapour and ozone. The performance of the inversion strategy has been assessed by comparing the retrieved profiles to the ones obtained by co-locating in space and time profiles from the European Centre for Medium-Range Weather Forecasts analysi

Effect of two different source of forage on the organic matter digestibility in Mediterranean Italian Buffalo cows

The present study aimed to evaluate the influence of two different source of forage (haysilage and hay) during the lactation on organic matter digestibility (OMD) in buffalo cows. Lactating buffaloes (n = 40) at 29.6 days in milk (DIM) were equally divided as function of previous milk yield into Group 1 (meadow hay, n = 20) and Group 2 [haysilage (Lolium multiflorum), n = 20]. The diets were isoenergetic [0.92 milk unit forage (MUF) on dry matter basis] and isoproteic (16.2 % crude protein on dry matter basis) and administred as total mixed ration (TMR). From all the buffaloes, for each group and in two sampling time (first sampling, DIM = 74.0 and second sampling, DIM = 129.0) the faeces were collected in order to evaluate the in vivo digestibility. Overall the trial, the subjects fed haysilage showed higher OMD than those fed hay (66.1 vs 45.7; P<0.01), moreover the in vivo digestibility was affected by the DIM, in particular in the group fed hay (40.6 vs 53.4; P<0.0001, respectively). This work underlines the importance of the administration of the haysilage (Lolium multiflorum) as source of high quality forage because it gives, overall the lactation, more nutritive principles compared with meadow hay

Finite element approximation of the Hardy constant

We consider finite element approximations to the optimal constant for the Hardy inequality with exponent $p=2$ in bounded domains of dimension $n=1$ or $n \geq 3$. For finite element spaces of piecewise linear and continuous functions on a mesh of size $h$, we prove that the approximate Hardy constant converges to the optimal Hardy constant at a rate proportional to $1/| \log h |^2$. This result holds in dimension $n=1$, in any dimension $n \geq 3$ if the domain is the unit ball and the finite element discretization exploits the rotational symmetry of the problem, and in dimension $n=3$ for general finite element discretizations of the unit ball. In the first two cases, our estimates show excellent quantitative agreement with values of the discrete Hardy constant obtained computationally.Comment: Review: Significantly improved estimates compared to the original version (23 pages, 6 figures

Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates

The evolution of Bose-Einstein condensates is usually described by the famous time-dependent Gross-Pitaevskii equation, which assumes all bosons to reside in a single time-dependent orbital. In the present work we address the evolution of fragmented condensates, for which two (or more) orbitals are occupied, and derive a corresponding time-dependent multi-orbital mean-field theory. We call our theory TDMF($n$), where $n$ stands for the number of evolving fragments. Working equations for a general two-body interaction between the bosons are explicitly presented along with an illustrative numerical example.Comment: 16 pages, 1 figur

Topological classification of black Hole: Generic Maxwell set and crease set of horizon

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

Build-up of coherence between initially-independent subsystems: The case of Bose-Einstein condensates

When initially-independent subsystems are made to contact, {\it coherence} can develop due to interaction between them. We exemplify and demonstrate this paradigm through several scenarios of two initially-independent Bose-Einstein condensates which are allowed to collide. The build-up of coherence depends strongly on time, interaction strength and other parameters of each condensate. Implications are discussed.Comment: 11 pages, 3 figure

Multiconfigurational Hartree-Fock theory for identical bosons in a double well

Multiconfigurational Hartree-Fock theory is presented and implemented in an investigation of the fragmentation of a Bose-Einstein condensate made of identical bosonic atoms in a double well potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized many-body states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and Hylleraas-Undheim theorems to find the optimal ground and excited states of the interacting system. The resulting energy spectrum and associated eigenstates are presented as a function of double well barrier height. Delocalized and localized single configurational states are found in the extreme limits of the simple and fragmented condensate ground states, while multiconfigurational states and macroscopic quantum superposition states are revealed throughout the full extent of barrier heights. Comparison is made to existing theories that either neglect mean field or correlation effects and it is found that contributions from both interactions are essential in order to obtain a robust microscopic understanding of the condensate's atomic structure throughout the fragmentation process.Comment: 21 pages, 13 figure