39 research outputs found
Emergent information dynamics in many-body interconnected systems
No full textThe information implicitly represented in the state of physical systems
allows one to analyze them with analytical techniques from statistical
mechanics and information theory. In the case of complex networks such
techniques are inspired by quantum statistical physics and have been used to
analyze biophysical systems, from virus-host protein-protein interactions to
whole-brain models of humans in health and disease. Here, instead of node-node
interactions, we focus on the flow of information between network
configurations. Our numerical results unravel fundamental differences between
widely used spin models on networks, such as voter and kinetic dynamics, which
cannot be found from classical node-based analysis. Our model opens the door to
adapting powerful analytical methods from quantum many-body systems to study
the interplay between structure and dynamics in interconnected systems.Comment: 7 pages, 3 figure
Exact solutions of the SI model on networks
No full textThe logistic differential equation of Verhulst is a landmark result in
many areas of science concerning growth, such as population growth or
information spreading processes. We analyze the exact Markovian system
describing logistic growth on a network, otherwise known as the SI
model. Exact solutions can be organized in terms of contributions from
subgraphs of the network of interest and we present here a general code
for computing these contributions systematically. The Python package relies on NetworkX for representing the contributing
diagrams and SymPy for the analytical integration of each diagram. Each
diagram corresponds to a function of time, which can be found by tracing
the spreading process backwards and integrating the sum over all
diagrams which transition into the sought-after diagram. This gives a
graph of parental relations between the different contributing diagrams,
which we construct explicitly for all diagrams with up to 10 edges. Several Jupyter notebooks explain the main code in SI_script.py,
including: - GeneralCode.ipynb: description of the code and the construction of the
graph of diagrams. - Florentine Families.ipynb: example of the computation of expectation
values in a simple network - Compare FF with MC.ipynb: A comparison between the exact result,
mean-field theory and Monte Carlo simulations of SI outbreaks on the
Florentine families graph.
In addition, several datasets are included: - diagrams.csv contains all 80 332 diagrams with up to 10 edges and
their respective contribution as a function of time - diagrams_ff.csv contains all diagrams contributing to the Florentine
families graph. - Several .csv files contain 50 000+ Monte Carlo runs on the Florentine
families graph. requirement.txt is a configuration file of all installed packages.This software package is an accompaniment to the paper 'Logistic growth
on networks" by Wout Merbis and Ivano Lodato and is distributed under
the GNU General Public License, version 3.</div
Operator entanglement growth quantifies complexity of cellular automata
No full textCellular automata (CA) exemplify systems where simple local interaction rules
can lead to intricate and complex emergent phenomena at large scales. The
various types of dynamical behavior of CA are usually categorized empirically
into Wolfram's complexity classes. Here, we propose a quantitative measure,
rooted in quantum information theory, to categorize the complexity of classical
deterministic cellular automata. Specifically, we construct a Matrix Product
Operator (MPO) of the transition matrix on the space of all possible CA
configurations. We find that the growth of entropy of the singular value
spectrum of the MPO reveals the complexity of the CA and can be used to
characterize its dynamical behavior. This measure defines the concept of
operator entanglement entropy for CA, demonstrating that quantum information
measures can be meaningfully applied to classical deterministic systems.Comment: 15 pages, 5 figures, accepted for publication in ICCS 2024
proceeding
Near horizon dynamics of three dimensional black holes
No full textWe perform the Hamiltonian reduction of three dimensional Einstein gravity with negative cosmological constant under constraints imposed by near horizon boundary conditions. The theory reduces to a Floreanini–Jackiw type scalar field theory on the horizon, where the scalar zero modes capture the global black hole charges. The near horizon Hamiltonian is a total derivative term, which explains the softness of all oscillator modes of the scalar field. We find also a (Korteweg–de Vries) hierarchy of modified boundary conditions that we use to lift the degeneracy of the soft hair excitations on the horizon.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Most general flat space boundary conditions in three-dimensional Einstein gravity
No full textWe consider the most general asymptotically flat boundary conditions in three-dimensional Einstein gravity in the sense that we allow for the maximal number of independent free functions in the metric, leading to six towers of boundary charges and six associated chemical potentials. We find as associated asymptotic symmetry algebra an isl(2)κ current algebra. Restricting the charges and chemical potentials in various ways recovers previous cases, such as bms3, Heisenberg or Detournay-Riegler, all of which can be obtained as contractions of corresponding AdS3 constructions. Finally, we show that a flat space contraction can induce an additional Carrollian contraction. As examples we provide two novel sets of boundary conditions for Carroll gravity.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Asymptotic dynamics of AdS3 gravity with two asymptotic regions
No full textinfo:eu-repo/semantics/publishe
Supersymmetric Galilean conformal blocks
No full textAbstract We set up the bootstrap procedure for supersymmetric Galilean Conformal (SGC) field theories in two dimensions by constructing the SGC blocks in the N=1 and two possible N=2 extensions of the Galilean conformal algebra. In all analyzed cases, we present the bootstrap equations by crossing symmetry of the four point function. In addition, we compute the global SGC blocks analytically by solving the differential equations obtained by acting with the Casimirs of the global subalgebras inside the four point function. These global blocks agree with the general SGC blocks in the limit of large central charge. We comment on possible applications to supersymmetric BMS3 invariant field theories and flat holography
Soft hairy warped black hole entropy
No full textAbstract We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u (1) current algebras and recover the surprisingly simple entropy formula S = 2π(J 0+ + J 0−), where J 0± are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality
