Second-order corrections to mean field evolution for weakly interacting Bosons. I

Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \epsilon \chi(x) |x|^{-1}$, where $\epsilon$ is sufficiently small and $\chi \in C_0^{\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper

Constraints on coupling constant between dark energy and dark matter

We have investigated constraints on the coupling between dark matter and the interacting Chaplygin gas. Our results indicate that the coupling constant $c$ between these two entities can take arbitrary values, which can be either positive or negative, thus giving arbitrary freedom to the inter-conversion between Chaplygin gas and dark matter. Thus our results indicate that the restriction $0<c<1$ on the coupling constant occurs as a very special case. Our analysis also supports the existence of phantom energy under certain conditions on the coupling constant.Comment: 16 Pages, 3 figure

Cumulative Response of Ecosystem Carbon and Nitrogen Stocks to Chronic CO2 Exposure in a Subtropical Oak Woodland

·Rising atmospheric carbon dioxide (CO2) could alter the carbon (C) and nitrogen (N) content of ecosystems, yet the magnitude of these effects are not well known. We examined C and N budgets of a subtropical woodland after 11 yr of exposure to elevated CO2. ·We used open-top chambers to manipulate CO2 during regrowth after fire, and measured C, N and tracer 15N in ecosystem components throughout the experiment. ·Elevated CO2 increased plant C and tended to increase plant N but did not significantly increase whole-system C or N. Elevated CO2 increased soil microbial activity and labile soil C, but more slowly cycling soil C pools tended to decline. Recovery of a long-term 15N tracer indicated that CO2 exposure increased N losses and altered N distribution, with no effect on N inputs. · Increased plant C accrual was accompanied by higher soil microbial activity and increased C losses from soil, yielding no statistically detectable effect of elevated CO2 on net ecosystem C uptake. These findings challenge the treatment of terrestrial ecosystems responses to elevated CO2 in current biogeochemical models, where the effect of elevated CO2 on ecosystem C balance is described as enhanced photosynthesis and plant growth with decomposition as a first-order response

A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model

A recently proposed molecular model is discussed as a non-trivial extension of the Ising model. For d=2 the two models are shown to be equivalent, while for d>2 the molecular model describes a peculiar second order transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. The general mean field analysis is compared with the results achieved by a variational Migdal-Kadanoff real space renormalization group method and by standard Monte Carlo sampling for d=3. By finite size scaling the critical exponent has been found to be 0.44\pm 0.02 thus establishing that the molecular model does not belong to the universality class of the Ising model for d>2.Comment: 25 pages, 5 figure

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order $n^{-1/2}$ and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present an empirical application.Comment: Paper submitted for publication, with 13 pages and 1 figur

Vision based referee sign language recognition system for the RoboCup MSL league

In RoboCup Middle Size league (MSL) the main referee uses assisting technology, controlled by a second referee, to support him, in particular for conveying referee decisions for robot players with the help of a wireless communication system. In this paper a vision-based system is introduced, able to interpret dynamic and static gestures of the referee, thus eliminating the need for a second one. The referee's gestures are interpreted by the system and sent directly to the Referee Box, which sends the proper commands to the robots. The system is divided into four modules: a real time hand tracking and feature extraction, a SVM (Support Vector Machine) for static hand posture identification, an HMM (Hidden Markov Model) for dynamic unistroke hand gesture recognition, and a FSM (Finite State Machine) to control the various system states transitions. The experimental results showed that the system works very reliably, being able to recognize the combination of gestures and hand postures in real-time. For the hand posture recognition, with the SVM model trained with the selected features, an accuracy of 98,2% was achieved. Also, the system has many advantages over the current implemented one, like avoiding the necessity of a second referee, working on noisy environments, working on wireless jammed situations. This system is easy to implement and train and may be an inexpensive solution

Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.Comment: 10 pages, 3 figure

Pair excitations and the mean field approximation of interacting Bosons, I

In our previous work \cite{GMM1},\cite{GMM2} we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve on a background formed by the condensate. In \cite{GMM2} we carried out the analysis assuming that the interactions are independent of the number of particles $N$. Here we consider the case of stronger interactions. We offer a new transparent derivation for the evolution of pair excitations. Indeed, we obtain a pair of linear equations describing their evolution. Furthermore, we obtain apriory estimates independent of the number of particles and use these to compare the exact with the approximate dynamics

Nonergodic Behavior of Interacting Bosons in Harmonic Traps

We study the time evolution of a system of interacting bosons in a harmonic trap. In the low-energy regime, the quantum system is not ergodic and displays rather large fluctuations of the ground state occupation number. In the high energy regime of classical physics we find nonergodic behavior for modest numbers of trapped particles. We give two conditions that assure the ergodic behavior of the quantum system even below the condensation temperature.Comment: 11 pages, 3 PS-figures, uses psfig.st