Phase transitions, KMS condition and decision making: an introductory model.

We consider a simple model of interacting agents asked to choose between 'yes' and 'no' to some given question. The agents are described in terms of spin variables, and they interact according to a mean field Heisenberg model. We discuss under which conditions the agents can come out with a common choice. This is made using, in a social context, the notion of KMS states and phase transitions. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

Spreading of Information on a Network: A Quantum View.

This paper concerns the modeling of the spread of information through a complex, multi-layered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal mathematical apparatus typical of quantum mechanics. Two different approaches are considered: one based on the (H,ρ)-induced dynamics and one on the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. For each method, numerical results are presented.

Spreading of Competing Information in a Network.

We propose a simple approach to investigate the spreading of news in a network. In more detail, we consider two different versions of a single type of information, one of which is close to the essence of the information (and we call it good news), and another of which is somehow modified from some biased agent of the system (fake news, in our language). Good and fake news move around some agents, getting the original information and returning their own version of it to other agents of the network. Our main interest is to deduce the dynamics for such spreading, and to analyze if and under which conditions good news wins against fake news. The methodology is based on the use of ladder fermionic operators, which are quite efficient in modeling dispersion effects and interactions between the agents of the system.

Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics.

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.

Large-scale effects of migration and conflict in pre-agricultural groups: Insights from a dynamic model.

The debate on the causes of conflict in human societies has deep roots. In particular, the extent of conflict in hunter-gatherer groups remains unclear. Some authors suggest that large-scale violence only arose with the spreading of agriculture and the building of complex societies. To shed light on this issue, we developed a model based on operatorial techniques simulating population-resource dynamics within a two-dimensional lattice, with humans and natural resources interacting in each cell of the lattice. The model outcomes under different conditions were compared with recently available demographic data for prehistoric South America. Only under conditions that include migration among cells and conflict was the model able to consistently reproduce the empirical data at a continental scale. We argue that the interplay between resource competition, migration, and conflict drove the population dynamics of South America after the colonization phase and before the introduction of agriculture. The relation between population and resources indeed emerged as a key factor leading to migration and conflict once the carrying capacity of the environment has been reached.

[Formula: see text]-symmetric graphene under a magnetic field.

We propose a [Formula: see text]-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K' points, both in the [Formula: see text]-symmetric and [Formula: see text]-broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the [Formula: see text]-symmetric and [Formula: see text]-broken regions.