# Long range interactions

## Overview

Long-range interactions are such that the two-body interaction potential decays at large distances with a power-law exponent which is smaller than the space dimension. The thermodynamics and dynamical properties of physical systems subject to long--range couplings were poorly understood until a few years ago, and their study essentially restricted to astrophysics (e.g. self-gravitating systems). Later, it was recognised that long-range systems display universal out-of-equilibrium features, for which conventional equilibrium statistical mechanics is inadequate. In particular, it has been shown that long range interacting systems generally exhibit a whole set of new qualitative properties and behaviours: ensemble inequivalence (negative specific heat, temperature jumps), long-time relaxation (quasi-stationary states), violations of ergodicity and disconnection of the energy surface, subtleties in the relation of the fluid (i.e. continuum) picture and the particle (granular) picture, new macroscopic quantum effects, etc. While progress has been made in understanding such phenomena, an overall thermodynamic and statistical framework is, however, still lacking. Our work aims at contributing to the development of such a comprehensive picture.

## People involved

## Recent publications

Federico Corberi, Eugenio Lippiello, **Paolo Politi**:

Phys. Rev. E 102, 020102(R) (2020) [PDF]

We study condensation phenomena which are accompanied by a process of localization in the real space: a finite fraction of the energy of the whole system is concentrated on a few sites. The correct order parameter of this transition is the participation ratio Y_2, basically the second moment of the energy distribution divided by the system size N. Localization corresponds to a nonvanishing Y_2 for diverging N. The figure shows that in some models Y_2(N) is not monotonous and displays a minimum, which is due to a maximum in the number K of sites hosting the condensate. This behavior has striking consequences in terms of real condensates and in terms of negative temperatures.