New analytic solutions of the collective Bohr hamiltonian for a beta-soft, gamma-soft axial rotor

New analytic solutions of the quadrupole collective Bohr hamiltonian are proposed, exploiting an approximate separation of the beta and gamma variables to describe gamma-soft prolate axial rotors. The model potential is a sum of two terms: a beta-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a gamma-dependent term taken as an harmonic oscillator. In particular it is possible to give a one parameter paradigm for a beta-soft, gamma-soft axial rotor that can be applied, with a considerable agreement, to the spectrum of 234U.Comment: (Dipartimento di Fisica ``G.Galilei'' and INFN, via Marzolo 8, I-35131 Padova, Italy) 10 pages, 3 figure

The Krause-Hegselmann Consensus Model with Discrete Opinions

The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For the case of a society in which everybody can talk to everybody else, we find that the chance to reach consensus is much higher as compared to other models; if the number of possible opinions Q<=7, in fact, consensus is always reached, which might explain the stability of political coalitions with more than three or four parties. For Q>7 the number S of surviving opinions is approximately the same independently of the size N of the population, as long as Q<N. We considered as well the more realistic case of a society structured like a Barabasi-Albert network; here the consensus threshold depends on the outdegree of the nodes and we find a simple scaling law for S, as observed for the discretized Deffuant model.Comment: 12 pages, 6 figure

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review

Universality of the Threshold for Complete Consensus for the Opinion Dynamics of Deffuant et al

In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. The opinions of a randomly chosen pair of compatible agents get closer to each other. We provide strong numerical evidence that the threshold value of \epsilon above which all agents share the same opinion in the final configuration is 1/2, independently of the underlying social topology.Comment: 8 pages, 4 figures, to appear in Int. J. Mod. Phys. C 15, issue

Distributed Graph Clustering using Modularity and Map Equation

We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other clusters. In the context of a social network, a cluster could be a group of friends. Modularity and map equation are established formalizations of this internally-dense-externally-sparse principle. We present two versions of a simple distributed algorithm to optimize both measures. They are based on Thrill, a distributed big data processing framework that implements an extended MapReduce model. The algorithms for the two measures, DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality measures is straight-forward. We conduct an extensive experimental study on real-world graphs and on synthetic benchmark graphs with up to 68 billion edges. Our algorithms are fast while detecting clusterings similar to those detected by other sequential, parallel and distributed clustering algorithms. Compared to the distributed GossipMap algorithm, DSLM-Map needs less memory, is up to an order of magnitude faster and achieves better quality.Comment: 14 pages, 3 figures; v3: Camera ready for Euro-Par 2018, more details, more results; v2: extended experiments to include comparison with competing algorithms, shortened for submission to Euro-Par 201

Study of Giant Pairing Vibrations with neutron-rich nuclei

We investigate the possible signature of the presence of giant pairing states at excitation energy of about 10 MeV via two-particle transfer reactions induced by neutron-rich weakly-bound projectiles. Performing particle-particle RPA calculations on $^{208}$Pb and BCS+RPA calculations on $^{116}$Sn, we obtain the pairing strength distribution for two particles addition and removal modes. Estimates of two-particle transfer cross sections can be obtained in the framework of the 'macroscopic model'. The weak-binding nature of the projectile kinematically favours transitions to high-lying states. In the case of (~^6He, \~^4He) reaction we predict a population of the Giant Pairing Vibration with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.Comment: Talk presented in occasion of the VII School-Semina r on Heavy Ion Physics hosted by the Flerov Laboratory (FLNR/JINR) Dubna, Russia from May 27 to June 2, 200

Soft triaxial roto-vibrational motion in the vicinity of γ=π/6\gamma=\pi/6

A solution of the Bohr collective hamiltonian for the $\beta-$soft, $\gamma-$soft triaxial rotor with $\gamma \sim \pi/6$ is presented making use of a harmonic potential in $\gamma$ and Coulomb-like and Kratzer-like potentials in $\beta$. It is shown that, while the $\gamma-$angular part in the present case gives rise to a straightforward extension of the rigid triaxial rotor energy in which an additive harmonic term appears, the inclusion of the $\beta$ part results instead in a non-trivial expression for the spectrum. The negative anharmonicities of the energy levels with respect to a simple rigid model are in qualitative agreement with general trends in the experimental data.Comment: 4 pages, 2 figures, accepted in Phys.Rev.

Percolation in high dimensions is not understood

The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.Comment: 9-dimensional data and more points for large lattices added; statistics improved, text expanded, table of exponents inserte

Implementation of the Quantum Fourier Transform

The quantum Fourier transform (QFT) has been implemented on a three bit nuclear magnetic resonance (NMR) quantum computer, providing a first step towards the realization of Shor's factoring and other quantum algorithms. Implementation of the QFT is presented with fidelity measures, and state tomography. Experimentally realizing the QFT is a clear demonstration of NMR's ability to control quantum systems.Comment: 6 pages, 2 figure

An NMR Analog of the Quantum Disentanglement Eraser

We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.Comment: Four pages, one figure (RevTeX 2.1), to appear in Physics Review Letter