The Strength of Arcs and Edges in Interaction Networks: Elements of a Model-Based Approach

When analyzing interaction networks, it is common to interpret the amount of interaction between two nodes as the strength of their relationship. We argue that this interpretation may not be appropriate, since the interaction between a pair of nodes could potentially be explained only by characteristics of the nodes that compose the pair and, however, not by pair-specific features. In interaction networks, where edges or arcs are count-valued, the above scenario corresponds to a model of independence for the expected interaction in the network, and consequently we propose the notions of arc strength, and edge strength to be understood as departures from this model of independence. We discuss how our notion of arc/edge strength can be used as a guidance to study network structure, and in particular we develop a latent arc strength stochastic blockmodel for directed interaction networks. We illustrate our approach studying the interaction between the Kolkata users of the myGamma mobile network.Comment: 23 pages, 5 figures, 4 table

The influence of bond-rigidity and cluster diffusion on the self-diffusion of hard spheres with square-well interaction

Hard spheres interacting through a square-well potential were simulated using two different methods: Brownian Cluster Dynamics (BCD) and Event Driven Brownian Dynamics (EDBD). The structure of the equilibrium states obtained by both methods were compared and found to be almost the identical. Self diffusion coefficients ($D$) were determined as a function of the interaction strength. The same values were found using BCD or EDBD. Contrary the EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible the effect of attraction on $D$ is relatively weak compared to systems with rigid bonds. $D$ increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intra-cluster hydrodynamic interaction weakly increases $D$ for a given interaction strength. Introducing bond rigidity causes a strong decrease of $D$ which no longer shows a maximum as function of the attraction strength

Equilibrium phases of dipolar lattice bosons in the presence of random diagonal disorder

Ultracold gases offer an unprecedented opportunity to engineer disorder and interactions in a controlled manner. In an effort to understand the interplay between disorder, dipolar interaction and quantum degeneracy, we study two-dimensional hard-core dipolar lattice bosons in the presence of on-site bound disorder. Our results are based on large-scale path-integral quantum Monte Carlo simulations by the Worm algorithm. We study the ground state phase diagram at fixed half-integer filling factor for which the clean system is either a superfluid at lower dipolar interaction strength or a checkerboard solid at larger dipolar interaction strength. We find that, even for weak dipolar interaction, superfluidity is destroyed in favor of a Bose glass at relatively low disorder strength. Interestingly, in the presence of disorder, superfluidity persists for values of dipolar interaction strength for which the clean system is a checkerboard solid. At fixed disorder strength, as the dipolar interaction is increased, superfluidity is destroyed in favor of a Bose glass. As the interaction is further increased, the system eventually develops extended checkerboard patterns in the density distribution. Due to the presence of disorder, though, grain boundaries and defects, responsible for a finite residual compressibility, are present in the density distribution. Finally, we study the robustness of the superfluid phase against thermal fluctuations

Exact ground state of finite Bose-Einstein condensates on a ring

The exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations for finite $N$. The ground state energies for repulsive and attractive interaction are shown to be smoothly connected at the point of zero interaction strength, implying that the \emph{Bethe-ansatz} can be used also for attractive interaction for all cases studied. For repulsive interaction the exact energies are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii) the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic limit solution can differ substantially from that of the exact solution for finite $N$ when the interaction is weak or when $N$ is small. A simple relation between the Tonks-Girardeau gas limit and the solution for finite interaction strength is revealed. For attractive interaction we find that the true ground state energy is given to a good approximation by the energy of the system of $N$ attractive bosons on an infinite line, provided the interaction is stronger than the critical interaction strength of mean-field theory.Comment: 28 pages, 11 figure

Comparing contact and dipolar interaction in a Bose-Einstein condensate

We have measured the relative strength $\epsilon_dd$ of the magnetic dipole-dipole interaction compared to the contact interaction in a chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of a dipolar chromium BEC with different orientations of the atomic magnetic dipole moments. By comparing them with numerical solutions of the hydrodynamic equations for dipolar condensates, we are able to determine $\epsilon_dd = 0.159\pm0.034$ with high accuracy. Since the absolute strength of the dipole-dipole interaction is known exactly, the relative strength of the dipoledipole interaction can be used to determine the s-wave scattering length $a = 5.08\pm1.06\cdot10^-9 m = 96\pm20 a0$ of 52Cr. This is fully consistent with our previous measurements on the basis of Feshbach resonances

Interaction induced fractional Bloch and tunneling oscillations

We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single particle Bloch oscillations. For strong interaction the Bloch oscillation regime reemerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength is affecting the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength a particle will tunnel from the interacting cloud to a well defined distant lattice location.Comment: 4 pages, 4 figure