Related papers: Existence of ground states for aggregation-diffusi…
We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled…
We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…
We seek to clarify the concept of active inference by disentangling it from the Free Energy Principle. We show how the optimizations that need to be carried out in order to implement active inference in discrete state spaces can be…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…
We show how to define and calculate the ground state energy of a system of quantum particles with delta attractive interactions when the number of particles n$is non-integer. The question is relevant to obtain the probability distribution…
The present paper is devoted to the study of a simple model of interacting electrons in a random background. In a large interval $\Lambda$, we consider $n$ one dimensional particles whose evolution is driven by the Luttinger-Sy model, i.e.,…
We discuss the behavior of the entanglement entropy of the ground state in various collective systems. Results for general quadratic two-mode boson models are given, yielding the relation between quantum phase transitions of the system…
We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…
We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
We consider a nonlocal aggregation equation with degenerate diffusion, which describes the mean-field limit of interacting particles driven by nonlocal interactions and localized repulsion. When the interaction potential is attractive, it…
Diffusive operations, which mix the populations of different elements of phase space, can irreversibly transform a given initial state into any of a spectrum of different states from which no further energy can be extracted through…
Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from simulations. In this paper I…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We consider the repulsive Hubbard model on a class of lattices or graphs for which there is a large degeneracy of the single particle ground states and where the projector onto the space of single particle ground states is highly reducible.…
We study the scaling of ground state entanglement entropy of various free fermionic models on one dimensional lattices, where the hopping and pairing terms decay as a power law. We seek to understand the scaling of entanglement entropy in…
We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the…
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness…
Motivated by our earlier work, we show in this paper rigorously that the ground state energy and degeneracy of an infinitely extended system of interacting electrons in the background of a homogeneous magnetic field and two separated…
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…