Impurity in a Bose-Einstein condensate in a double well

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.Comment: 19 pages, 17 figures. The second version contains minor corrections and some better figures (thicker lines

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page

Kolmogorov turbulence, Anderson localization and KAM integrability

The conditions for emergence of Kolmogorov turbulence, and related weak wave turbulence, in finite size systems are analyzed by analytical methods and numerical simulations of simple models. The analogy between Kolmogorov energy flow from large to small spacial scales and conductivity in disordered solid state systems is proposed. It is argued that the Anderson localization can stop such an energy flow. The effects of nonlinear wave interactions on such a localization are analyzed. The results obtained for finite size system models show the existence of an effective chaos border between the Kolmogorov-Arnold-Moser (KAM) integrability at weak nonlinearity, when energy does not flow to small scales, and developed chaos regime emerging above this border with the Kolmogorov turbulent energy flow from large to small scales.Comment: 8 pages, 6 figs, EPJB style

Leaders and followers: quantifying consistency in spatio-temporal propagation patterns

Repetitive spatio-temporal propagation patterns are encountered in fields as wide-ranging as climatology, social communication and network science. In neuroscience, perfectly consistent repetitions of the same global propagation pattern are called a synfire pattern. For any recording of sequences of discrete events (in neuroscience terminology: sets of spike trains) the questions arise how closely it resembles such a synfire pattern and which are the spike trains that lead/follow. Here we address these questions and introduce an algorithm built on two new indicators, termed SPIKE-Order and Spike Train Order, that define the Synfire Indicator value, which allows to sort multiple spike trains from leader to follower and to quantify the consistency of the temporal leader-follower relationships for both the original and the optimized sorting. We demonstrate our new approach using artificially generated datasets before we apply it to analyze the consistency of propagation patterns in two real datasets from neuroscience (Giant Depolarized Potentials in mice slices) and climatology (El Ni~no sea surface temperature recordings). The new algorithm is distinguished by conceptual and practical simplicity, low computational cost, as well as flexibility and universality.Comment: 18 pages; 18 figures; revised versio