The six-functor formalism for rigid analytic motives

We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud's approach to rigid analytic geometry

Transport and Scaling in Quenched 2D and 3D L\'evy Quasicrystals

We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $\alpha$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a {\it single-long jump} approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution, as a function of $\alpha$ and of the dynamic exponent $z$ associated to the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated L\'evy-walks models.Comment: 10 pages, 11 figures; some concepts rephrased to improve on clarity; a few references added; symbols and line styles in some figures changed to improve on visibilit

Propagation of Discrete Solitons in Inhomogeneous Networks

In many physical applications solitons propagate on supports whose topological properties may induce new and interesting effects. In this paper, we investigate the propagation of solitons on chains with a topological inhomogeneity generated by the insertion of a finite discrete network on the chain. For networks connected by a link to a single site of the chain, we derive a general criterion yielding the momenta for perfect reflection and transmission of traveling solitons and we discuss solitonic motion on chains with topological inhomogeneities

Bose-Einstein condensation in inhomogeneous Josephson arrays

We show that spatial Bose-Einstein condensation of non-interacting bosons occurs in dimension d < 2 over discrete structures with inhomogeneous topology and with no need of external confining potentials. Josephson junction arrays provide a physical realization of this mechanism. The topological origin of the phenomenon may open the way to the engineering of quantum devices based on Bose-Einstein condensation. The comb array, which embodies all the relevant features of this effect, is studied in detail.Comment: 4 pages, 5 figure

Topological Filters for Solitons in Coupled Waveguides Networks

We study the propagation of discrete solitons on chains of coupled optical waveguides where finite networks of waveguides are inserted at some points. By properly selecting the topology of these networks, it is possible to control the transmission of traveling solitons: we show here that inhomogeneous waveguide networks may be used as filters for soliton propagation. Our results provide a first step in the understanding of the interplay/competition between topology and nonlinearity for soliton dynamics in optical fibers

Some remarks on the coherent-state variational approach to nonlinear boson models

The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving states $|\xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $\cal N$-boson states $|\xi>$ and the similarities/differences of the $|Z>$-based and $|\xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|\xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and $|\xi>$ in terms of momentum-mode operators is discussed together with some applications.Comment: 16 page

Glassy features of a Bose Glass

We study a two-dimensional Bose-Hubbard model at a zero temperature with random local potentials in the presence of either uniform or binary disorder. Many low-energy metastable configurations are found with virtually the same energy as the ground state. These are characterized by the same blotchy pattern of the, in principle, complex nonzero local order parameter as the ground state. Yet, unlike the ground state, each island exhibits an overall random independent phase. The different phases in different coherent islands could provide a further explanation for the lack of coherence observed in experiments on Bose glasses.Comment: 14 pages, 4 figures

Evidence for the super Tonks-Girardeau gas

We provide evidence in support of a recent proposal by Astrakharchik at al. for the existence of a super Tonks-Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the super T-G gas-like stat

Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result

We give a rigorous proof of the existence of spontaneous magnetization at finite temperature for the Ising spin model defined on the Sierpinski carpet fractal. The theorem is inspired by the classical Peierls argument for the two dimensional lattice. Therefore, this exact result proves the existence of spontaneous magnetization for the Ising model in low dimensional structures, i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure

Temporal Model Adaptation for Person Re-Identification

Person re-identification is an open and challenging problem in computer vision. Majority of the efforts have been spent either to design the best feature representation or to learn the optimal matching metric. Most approaches have neglected the problem of adapting the selected features or the learned model over time. To address such a problem, we propose a temporal model adaptation scheme with human in the loop. We first introduce a similarity-dissimilarity learning method which can be trained in an incremental fashion by means of a stochastic alternating directions methods of multipliers optimization procedure. Then, to achieve temporal adaptation with limited human effort, we exploit a graph-based approach to present the user only the most informative probe-gallery matches that should be used to update the model. Results on three datasets have shown that our approach performs on par or even better than state-of-the-art approaches while reducing the manual pairwise labeling effort by about 80%