Quantum walk of a Bose-Einstein condensate in the Brillouin zone

We propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow a robust implementation of quantum walks with several tens of steps at least. In addition, onsite atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone.Comment: 9 pages, 4 figures; in the new version, added a discussion about decoherence in the appendi

Perturbative corrections to power suppressed effects in semileptonic B decays

We compute the $O(\alpha_s)$ corrections to the Wilson coefficient of the chromomagnetic operator in inclusive semileptonic B decays. The results are employed to evaluate the complete $O(\alpha_s \Lambda^2/m_b^2)$ correction to the semileptonic width and to the first moments of the lepton energy distribution.Comment: 15 pages, 2 figure

Higher order corrections to inclusive semileptonic B decays

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Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic instead of diffusive expansion in position space is not a good indicator for the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short and long time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.Comment: 32 pages, 10 figures, 1 table, replaced fig. 10 in the new versio

Numerical evaluation of the IXV Reaction Control System in-flight priming

The RCS is one of the major IXV functional subsystems and its main function is to perform attitude control for the vehicle during the orbital arc and to support the flap control during the autonomous re-entry. Due to the stringent ground safety requirements, three barriers are necessary before the flight to avoid unintended firing of the thrusters during pre-launch operations and ascent flight, with potential catastrophic consequences. For this reason, after the IXV separation from the VEGA AVUM, the IXV RCS has to be prepared for operation through a priming sequence in orbit. This operation may turn out to be critical if the corresponding overpressures are not correctly taken into consideration; moreover, with the utilization of hydrazine, the priming sequence may be even more critical in relation with the phenomenon of adiabatic compression and the low threshold of the propellant thermal decomposition. The objective of this work is to numerically investigate the priming sequences (Nominal and Off-Nominal) through the realisation of suitable models with the software EcosimPro. The analysis has been performed both for a Mock-Up (for which experimental evidences are available) and for the Flight-Hardware. Once the procedure has been validated through the comparison between the Mock-Up EcosimPro-Results and the results of the experimental campaign, the analysis has been extended to the Flight-Hardware. Both the Nominal Priming Sequence and the Off-Nominal Priming Sequence (i.e. priming via LV in case of By-Pass Line failure) have been investigated at different initial conditions (initial tank pressure and initial non-condensable gas pressure) and the criticality has been assessed

Ideal negative measurements in quantum walks disprove theories based on classical trajectories

We report on a stringent test of the non-classicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a $6\sigma$ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e. falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements -- an essential requisite for any genuine Leggett-Garg test -- to acquire information about the atom's position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. We here employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.Comment: 10 pages, 4 figure

On the differentiability of Lipschitz functions with respect to measures in the Euclidean space

For every finite measure μ on R^n we define a decomposability bundle V(μ, ·) related to the decompositions of μ in terms of rectifiable one-dimensional measures. We then show that every Lipschitz function on R^n is differentiable at μ-a.e. x with respect to the subspace V(μ, x), and prove that this differentiability result is optimal, in the sense that, following [4], we can construct Lipschitz functions which are not differentiable at μ-a.e. x in any direction which is not in V(μ,x). As a consequence we obtain a differentiability result for Lipschitz functions with respect to (measures associated to) k-dimensional normal currents, which we use to extend certain basic formulas involving normal currents and maps of class C^1 to Lipschitz maps

On the structure of flat chains with finite mass

We prove that every flat chain with finite mass in $\mathbb{R}^d$ with coefficients in a normed abelian group $G$ is the restriction of a normal $G$-current to a Borel set. We deduce a characterization of real flat chains with finite mass in terms of a pointwise relation between the associated measure and vector field. We also deduce that any codimension-one real flat chain with finite mass can be written as an integral of multiplicity-one rectifiable currents, without loss of mass. Given a Lipschitz homomorphism $\phi:\tilde G\to G$ between two groups, we then study the associated map $\pi$ between flat chains in $\mathbb{R}^d$ with coefficients in $\tilde G$ and $G$ respectively. In the case $\tilde G=\mathbb{R}$ and $G=\mathbb{S}^1$, we prove that if $\phi$ is surjective, so is the restriction of $\pi$ to the set of flat chains with finite mass of dimension $0$, $1$, $d-1$, $d$