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Due to its versatility and low cost, the use of unmanned aerial vehicles has been rapidly spreading in recent years, in applications ranging form military operations, to land mapping, rescuing of lost people, aiding of natural disaster victims and many others. To properly design and operate such a vehicle, it is necessary to know its flight mechanics in the various stages of the flight. Despite the fact that the physic behind the analysis of an aircraft's flight mechanics is well known and purely based on Classical Mechanics, the large quantity of input and output data involved favors the use of a computational toll. This work presents the development of a toolbox called APT (Aircraft Performance Toolbox), able to make preliminary aircraft flight mechanics calculations regarding its performance. To achieve this goal, a number of Matlab scripts were created to perform the calculations, and a graphical interface was created to unify them and to allow the end-user to perform the analysis in a clear and intuitive way. To illustrate the potential of the toolbox, we use APT to in the analysis of an UAV meant to participate in the SAE Brasil AeroDesign competition of the year of 2014.

We extend the two leading methods for the \emph{ab initio} computational descrip tion of phonon-mediated superconductors, namely Eliashberg theory and density fu nctional theory for superconductors (SCDFT), to include plasmonic effects. Furth ermore, we introduce a hybrid formalism in which the Eliashberg approximation fo r the electron-phonon coupling is combined with the SCDFT treatment of the dynam ically screened Coulomb interaction. The methods have been tested on a set of we ll-known conventional superconductors by studying how the plasmon contribution a ffects the phononic mechanism in determining the critical temperature (\tc). Our simulations show that plasmonic SCDFT leads to a good agreement between predict ed and measured \tc's, whereas Eliashberg theory considerably overestimates the plasmon-mediated pairing and, therefore, \tc. The hybrid approach, on the other hand, gives results close to SCDFT and overall in excellent agreement with exper iments.

In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV/m. Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 meters. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by ~50 nm-rad normalized emittances. These beams, when injected into innovative, short-period (1-10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine which may profit from this new model of performing XFEL science., Comment: 80 pages, 24 figures

Oscillators are at the heart of optical lasers, providing stable transform limited pulses. In contrast, X-ray free electron lasers use self-amplified spontaneous emission (SASE), resulting in large stochastic intensity and spectral fluctuations. Amplified spontaneous emission (ASE) of the $K\alpha_1$ line has been recently observed for Ne gas, Cu compounds and Mn solutions at the LCLS and SACLA X-ray free electron lasers (XFELs), using an X-ray SASE pulse as a pump to create population inversion. Here we describe the physics and realization of an X-ray laser oscillator (XLO) based on periodically pumping a Cu compound gain medium in a tunable Bragg cavity with a SASE pulse train, generating intense ($\sim$ 5 x 10$^{10}$ ph/pulse), fully coherent, transform limited 8 keV pulses with 48 meV spectral resolution. We also discuss extending these results to other elements to operate XLO from about 5 to 12 keV, improving X-ray-based research beyond current capabilities.

In Quantum Non Demolition measurements, the sequence of observations is distributed as a mixture of multinomial random variables. Parameters of the dynamics are naturally encoded into this family of distributions. We show the local asymptotic mixed normality of the underlying statistical model and the consistency of the maximum likelihood estimator. Furthermore, we prove the asymptotic optimality of this estimator as it saturates the usual Cram\'er Rao bound.

We consider a non-interacting bipartite quantum system $\mathcal H_S^A\otimes\mathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independant quantum systems interacting one after the other with the bipartite system. The interactions are made so that the pieces of environment interact first with $\mathcal H_S^A$ and then with $\mathcal H_S^B$. Even though the bipartite systems are not interacting, the interactions with the environment create an entanglement. We show that, in the limit of short interaction times, the environment creates an effective interaction Hamiltonian between the two systems. This interaction Hamiltonian is explicitly computed and we show that it keeps track of the order of the successive interactions with $\mathcal H_S^A$ and $\mathcal H_S^B$. Particular physical models are studied, where the evolution of the entanglement can be explicitly computed. We also show the property of return of equilibrium and thermalization for a family of examples.

We study a particular class of complex-valued random variables and their associated random walks: the complex obtuse random variables. They are the generalization to the complex case of the real-valued obtuse random variables which were introduced in \cite{A-E} in order to understand the structure of normal martingales in $\RR^n$.The extension to the complex case is mainly motivated by considerations from Quantum Statistical Mechanics, in particular for the seek of a characterization of those quantum baths acting as classical noises. The extension of obtuse random variables to the complex case is far from obvious and hides very interesting algebraical structures. We show that complex obtuse random variables are characterized by a 3-tensor which admits certain symmetries which we show to be the exact 3-tensor analogue of the normal character for 2-tensors (i.e. matrices), that is, a necessary and sufficient condition for being diagonalizable in some orthonormal basis. We discuss the passage to the continuous-time limit for these random walks and show that they converge in distribution to normal martingales in $\CC^N$. We show that the 3-tensor associated to these normal martingales encodes their behavior, in particular the diagonalization directions of the 3-tensor indicate the directions of the space where the martingale behaves like a diffusion and those where it behaves like a Poisson process. We finally prove the convergence, in the continuous-time limit, of the corresponding multiplication operators on the canonical Fock space, with an explicit expression in terms of the associated 3-tensor again.

Starting from a generalization of the quantum trajectory theory (based on the stochastic Schr\"odinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in this article is based on the introduction of random coefficients in the usual linear SSE. A major interest is that this allows to develop a consistent theory of quantum measurement in continuous time for these non-Markovian quantum trajectory models. In this context, the notions of instrument, a priori and a posteriori states are rigorously described. The key point is that by starting from a stochastic equation on the Hilbert space of the system, we are able to respect the complete positivity of the mean dynamics for the statistical operator and the requirements of the axioms of quantum measurement theory. The flexibility of the theory is next illustrated by a concrete physical model of a noisy oscillator where non Markovian effects come from random environment, coloured noises, randomness in the stimulating light, delay effects. The statistics of the emitted photons and the heterodyne and homodyne spectra are studied and we show how these quantities are sensible to the non-Markovian features of the system dynamics, so that, in principle, the observation and analysis of the fluorescence light could reveal the presence of non-Markovian effects and allow for a measure of the spectra of the noises affecting the system dynamics., Comment: 21 pages, RevTeX4-1; minor corrections

The "correlated-projection technique" has been successfully applied to derive a large class of highly non Markovian dynamics, the so called non Markovian generalized Lindblad type equations or Lindblad rate equations. In this article, general unravellings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unravelling can be interpreted in terms of measurements continuous in time, but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and we discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory., Comment: 23 pages

By starting from the stochastic Schr\"odinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise quantum trajectories we use an Ornstein-Uhlenbeck coloured noise as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, we show that our non-Markovian stochastic Schr\"odinger equations unravel some master equations with memory kernels., Comment: 18 pages

We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic differential equations of jump-diffusion type. At strictly positive temperature, we show that only pure diffusion type equations are relevant.

We consider the situation of a two-level quantum system undergoing a continuous indirect measurement, giving rise to so-called "quantum trajectories". We first describe these quantum trajectories in a physically realistic discrete-time setup and we then justify, by going to the continuous-time limit, the "stochastic Schr\"odinger equation" attached to this model. We prove return to equilibrium properties for these equations., Comment: 24 pages

Recent initiatives in ultra-short, GeV electron beam generation have focused on achieving sub-fs pulses for driving X-ray free-electron lasers (FELs) in single-spike mode. This scheme employs very low charge beams, which may allow existing FEL injectors to produce few-100 as pulses, with high brightness. Towards this end, recent experiments at SLAC have produced ~2 fs rms, low transverse emittance, 20 pC electron pulses. Here we examine use of such pulses to excite plasma wakefields exceeding 1 TV/m. We present a focusing scheme capable of producing ~200 nm beam sizes, where the surface Coulomb fields are also ~TV/m. These conditions access a new regime for high field atomic physics, allowing frontier experiments, including sub-fs plasma formation for wake excitation., Comment: Preprint, 10 pages, 4 figures, submitted to Physical Review Letters

A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, non-Markovian stochastic Schr\"odinger equations which unravel non-Markovian master equations are derived., Comment: 4pages, revtex

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed., Comment: 22 pages