Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb--Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the {\it full-time} dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.Comment: Manuscript formatted for submission to SciPost Physics. Revised version. New section and two figures added. 26 pages, 10 figure

Early Prediction of Movie Box Office Success based on Wikipedia Activity Big Data

Use of socially generated "big data" to access information about collective states of the minds in human societies has become a new paradigm in the emerging field of computational social science. A natural application of this would be the prediction of the society's reaction to a new product in the sense of popularity and adoption rate. However, bridging the gap between "real time monitoring" and "early predicting" remains a big challenge. Here we report on an endeavor to build a minimalistic predictive model for the financial success of movies based on collective activity data of online users. We show that the popularity of a movie can be predicted much before its release by measuring and analyzing the activity level of editors and viewers of the corresponding entry to the movie in Wikipedia, the well-known online encyclopedia.Comment: 13 pages, Including Supporting Information, 7 Figures, Download the dataset from: http://wwm.phy.bme.hu/SupplementaryDataS1.zi

R\ue9nyi entropies of generic thermodynamic macrostates in integrable systems

We study the behaviour of R\ue9nyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\ue9nyi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary R\ue9nyi entropies after the quench from the dimer and the tilted N\ue9el state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full detail the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies

Histograms of different variables for our sample of movies from 2010.

<p>A: Time of creation of the corresponding article in Wikipedia, shown in days of <i>movie time</i> ( is the release time), B: Release weekend box office revenue in the U. S., in USD C: <i>number of theaters</i> that screened the movie on the first weekend, D: Accumulated <i>number of views</i>, and E: <i>users</i>, F: <i>edits</i>, G: <i>rigor</i> for the Wikipedia page up to days after release.</p

Temporal evolution of , the Pearson correlation of the box office revenue with different predictors.

<p>The shorthands , , , , and denote the <i>number of views</i>, the <i>number of users</i>, the <i>rigor</i>, the <i>number of edits</i>, and the <i>number of theaters</i>, respectively. Time is measured in movie time. <i>Inset</i>: magnified detail of the main panel, showing the Pearson correlation around the day of release. Dashed horizontal line shows the correlation for <i>the number of theaters</i>.</p

Comparison of the results with the Twitter-based prediction in Asur and Huberman work [27].

<p>Same sample of 24 movies is considered as both training and test set. The coefficient of determination obtained with the Twitter-based method is 0.98 at the night of the release (day 0 in movie time).</p

Illustration of different variables characterizing the activity of Wikipedia editors on an article.

<p>Each tick on the axis represents a modification of the page. Different tick styles refer to different users.</p