Efficient simulations of epidemic models with tensor networks: Application to the one-dimensional susceptible-infected-susceptible model.

The contact process is an emblematic model of a nonequilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible model, and it is widely used to describe contagious spreading. In this work, we demonstrate how accurate and efficient representations of the full probability distribution over all configurations of the contact process on a one-dimensional chain can be obtained by means of matrix product states (MPSs).

Emergent information dynamics in many-body interconnected systems.

The information implicitly represented in the state of physical systems allows for their analysis using analytical techniques from statistical mechanics and information theory. This approach has been successfully applied to complex networks, including biophysical systems such as virus-host protein-protein interactions and whole-brain models in health and disease, drawing inspiration from quantum statistical physics. Here we propose a general mathematical framework for modeling information dynamics on complex networks, where the internal node states are vector valued, allowing each node to carry multiple types of information.

Logistic growth on networks: Exact solutions for the susceptible-infected model.

The susceptible-infected (SI) model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here using a novel formulation inspired by the mathematical treatment of many-body quantum systems.

Zwei-dreibein gravity: a two-frame-field model of 3D massive gravity.

We present a generally covariant and parity-invariant two-frame field ("zwei-dreibein") action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models and extends them, in the context of the AdS/CFT correspondence, to allow for a positive central charge consistent with bulk unitarity.