Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

Experimental evidence of antiproton reflection by a solid surface

We report here experimental evidence of the reflection of a large fraction of a beam of low energy antiprotons by an aluminum wall. This derives from the analysis of a set of annihilations of antiprotons that come to rest in rarefied helium gas after hitting the end wall of the apparatus. A Monte Carlo simulation of the antiproton path in aluminum indicates that the observed reflection occurs primarily via a multiple Rutherford-style scattering on Al nuclei, at least in the energy range 1-10 keV where the phenomenon is most visible in the analyzed data. These results contradict the common belief according to which the interactions between matter and antimatter are dominated by the reciprocally destructive phenomenon of annihilation.Comment: 5 pages with 5 figure

Limits on the low energy antinucleon-nucleus annihilations from the Heisenberg principle

We show that the quantum uncertainty principle puts some limits on the effectiveness of the antinucleon-nucleus annihilation at very low energies. This is caused by the fact that the realization a very effective short-distance reaction process implies information on the relative distance of the reacting particles. Some quantitative predictions are possible on this ground, including the approximate A-independence of antinucleon-nucleus annihilation rates.Comment: 10 pages, no figure

Coulomb corrections to low energy antiproton annihilation cross sections on protons and nuclei

We calculate, in a systematic way, the enhancement effect on antiproton-proton and antiproton-nucleus annihilation cross sections at low energy due to the initial state electrostatic interaction between the projectile and the target nucleus. This calculation is aimed at future comparisons between antineutron and antiproton annihilation rates on different targets, for the extraction of pure isospin channels.Comment: 18 pages, 4 figures (latex format

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer

Edge channel mixing induced by potential steps in an integer quantum Hall system

We investigate the coherent mixing of co-propagating edge channels in a quantum Hall bar produced by step potentials. In the case of two edge channels it is found that, although a single step induces only a few percent mixing, a series of steps could yield 50% mixing. In addition, a strong mixing is found when the potential height of a single step allows a different number of edge channels on the two sides of the step. Charge density probability has been also calculated even for the case where the step is smoothened.Comment: final version: 7 pages, 6 figure

Respiratory muscle training in patients recovering recent open cardio-thoracic surgery: a randomized-controlled trial.

Objectives- To evaluate the clinical efficacy and feasibility of an expiratory muscle training (EMT) device (Respilift™) applied to patients recovering from recent open cardio-thoracic surgery (CTS). Design- Prospective, double-blind, 14-day randomised-controlled trial. Participants and setting- 60 inpatients recovering from recent CTS and early admitted to a pulmonary rehabilitation program. Interventions- Chest physiotherapy plus EMT with a resistive load of 30 cm H2O for active group and chest physiotherapy plus EMT with a sham load for control group. Measures- Changes in maximal expiratory pressure (MEP) was considered as primary outcome, while maximal inspiratory pressures (MIP), dynamic and static lung volumes, oxygenation, perceived symptoms of dyspnoea, thoracic pain and well being (evaluated by visual analogic scale-VAS) and general health status were considered secondary outcomes. Results- All outcomes recorded showed significant improvements in both groups; however, the change of MEP (+34.2 mmHg, p<0.001 and +26.1%, p<0.001 for absolute and % of predicted, respectively) was significantly higher in Active group. Also VAS-dyspnoea improved faster and more significantly (p<0.05) at day 12 and 14 in Active group when compared with Control. The drop out rate was 6%, without differences between groups. Conclusions- In patients recovering from recent CTS specific EMT by Respilift™ is feasible and effective