3,929 research outputs found
Self-consistent Keldysh approach to quenches in weakly interacting Bose-Hubbard model
We present a non-equilibrium Green's functional approach to study the
dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The
technique is based on the self-consistent solution of a set of equations which
represents a particular case of the most general set of Hedin's equations for
the interacting single-particle Green's function. We use the ladder
approximation as a skeleton diagram for the two-particle scattering amplitude
useful, through the self-energy in the Dyson equation, for finding the
interacting single-particle Green's function. This scheme is then implemented
numerically by a parallelized code. We exploit this approach to study the
correlation propagation after a quench in the interaction parameter, for one
(1D) and two (2D) dimensions. In particular, we show how our approach is able
to recover the crossover from ballistic to diffusive regime by increasing the
boson-boson interaction. Finally we also discuss the role of a thermal initial
state on the dynamics both for 1D and 2D Bose Hubbard models, finding that
surprisingly at high temperature a ballistic evolution is restored.Comment: 13 figure
Spreading of correlations and Loschmidt echo after quantum quenches of a Bose gas in the Aubry-Andr\'e potential
We study the spreading of density-density correlations and the Loschmidt
echo, after different sudden quenches in an interacting one dimensional Bose
gas on a lattice, also in the presence of a superimposed aperiodic potential.
We use a time dependent Bogoliubov approach to calculate the evolution of the
correlation functions and employ the linked cluster expansion to derive the
Loschmidt echo.Comment: 10 pages, 14 figures, a section on momentum distribution function is
include
Conditional Reliability in Uncertain Graphs
Network reliability is a well-studied problem that requires to measure the
probability that a target node is reachable from a source node in a
probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned
a probability of existence. Many approaches and problem variants have been
considered in the literature, all assuming that edge-existence probabilities
are fixed. Nevertheless, in real-world graphs, edge probabilities typically
depend on external conditions. In metabolic networks a protein can be converted
into another protein with some probability depending on the presence of certain
enzymes. In social influence networks the probability that a tweet of some user
will be re-tweeted by her followers depends on whether the tweet contains
specific hashtags. In transportation networks the probability that a network
segment will work properly or not might depend on external conditions such as
weather or time of the day. In this paper we overcome this limitation and focus
on conditional reliability, that is assessing reliability when edge-existence
probabilities depend on a set of conditions. In particular, we study the
problem of determining the k conditions that maximize the reliability between
two nodes. We deeply characterize our problem and show that, even employing
polynomial-time reliability-estimation methods, it is NP-hard, does not admit
any PTAS, and the underlying objective function is non-submodular. We then
devise a practical method that targets both accuracy and efficiency. We also
study natural generalizations of the problem with multiple source and target
nodes. An extensive empirical evaluation on several large, real-life graphs
demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
Criticality, factorization and long-range correlations in the anisotropic XY-model
We study the long-range quantum correlations in the anisotropic XY-model. By
first examining the thermodynamic limit we show that employing the quantum
discord as a figure of merit allows one to capture the main features of the
model at zero temperature. Further, by considering suitably large site
separations we find that these correlations obey a simple scaling behavior for
finite temperatures, allowing for efficient estimation of the critical point.
We also address ground-state factorization of this model by explicitly
considering finite size systems, showing its relation to the energy spectrum
and explaining the persistence of the phenomenon at finite temperatures.
Finally, we compute the fidelity between finite and infinite systems in order
to show that remarkably small system sizes can closely approximate the
thermodynamic limit.Comment: 8 pages, 8 figures. Close to published versio
Autoriciclaggio
L'introduzione del delitto di autoriciclaggio ha indubbiamente rappresentato un momento di rottura rispetto alla nostra tradizione di non punire l'autore o il concorrente nel delitto presupposto. La formulazione normativa dell'art. 648-ter.1. c.p. ha subito sollevato numerose e delicate questioni interpretative: dalla definizione del perimetro della fattispecie; al ruolo della clausola di non punibilit\ue0 di cui al quarto comma della disposizione; ai rapporti tra riciclaggio e autoriciclaggio, per citarne solo alcuni. L'obiettivo del presente lavoro \ue8 quello di affrontare, muovendo da un'analisi degli elementi costitutivi del delitto in esame, tali nodi interpretativi, cercando di prospettare delle soluzioni in linea con il nuovo assetto di disciplina prefigurato dal legislatore
The determination of velocity fluctuations in shear flows by means of PTV
The present study considers the effects of some parameters in image acquisition and analysis procedures in connection with the use of the Particle Tracking Velocimetry (PTV) technique. The interest is focused towards flow fields with large velocity gradients as shear flows; in the paper, velocity measurements by PTV are performed in a turbulent channel flow upstream and downstream of a backward facing step at low Reynolds numbers. This is a flow field largely investigated in the past with available numerical and experimental to make comparison with. Among the possible parameters to be chosen in particle image acquisition and analysis, the following are considered
- the concentration of seeding particles in the imaged region;
- the spatial resolution of the image acquisition system;
- the parameters used in the image analysis algorithm
- …