628 research outputs found
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 , 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 and of the dynamic exponent
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 , number-preserving states and
Glauber-like trial states are compared to evidence the specific
properties of such schemes. After deriving the Hamiltonian picture relevant to
from that based on , the latter is shown to exhibit a Poisson
algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the
-based picture. Then states are shown to be a superposition of -boson states and the similarities/differences of the -based and
-based pictures are discussed. Finally, after proving that the simple,
symmetric state indeed corresponds to a SU(M) coherent state, a dual
version of states and 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%
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