Systems with long-range interactions
Long-range interactions emerge in a wide variety of many-body systems. Since the end of the 90’s, an increasing number of works in the literature has been devoted to the cases where the interaction potential is not screened by collective mechanisms. Significant progresses, to which we contributed, have been made recently in the understanding of the dynamics and thermodynamics of systems with long-range interactions. An interaction is said to be long-range if its energy diverges faster than the volume of the system considered: it is thus non-additive. Among numerous examples, one may quote gravity, unscreened coulombian interactions, dipolar interactions, or wave-particle interactions. Unusual behaviors may be observed in such systems, like negative specific heat, ensemble inequivalence, as well as striking dynamical effects.
The research in this field has been also pursued, in particular for equilibrium properties of self-gravitating systems and for out-of equilibrium features. In general, real self-gravitating systems, like globular clusters, are in out-of-equilibrium quasi-stationary states. Nevertheless, it is instructive to study the corresponding equilibrium states within the micro-canonical ensemble, which is a priori the most appropriate statistical ensemble since the total energy is fixed a priori. The attractive gravitational interaction has to be regularized at short distances for preventing the collapse between point objects. Within the introduced microscopic description, we analyze the validity of the celebrated mean-field hydrostatic approach for computing the mass density profile [1]: the number of objects has to be sufficiently large, so local equilibrium states emerge, and they entirely depend on the short-range part of the pair interactions. These validity conditions are tested in a one-dimensional model of self-gravitating hard rods which is solvable [2]
The long-standing study of quantum Coulomb systems at equilibrium has been also continued. Besides the previous cases where the interactions between the particles or objects are primarily long-ranged, effective long-range interactions can be generated by collective phenomena, for instance at critical points where the divergent correlation length induces Casimir-like forces. Various novel approaches to such phenomena have been established, with important theoretical and experimental consequences for a wide class of physical systems. Eventually, the interplay between primary and effective long-range interactions may also intervene in various phase transitions, as analyzed for the Bose-Einstein condensation [3] and for the liquid-gas transition of classical electrolytes
- M. Champion, A. Alastuey, T. Dauxois, and S. Ruffo. Validity conditions of the hydrostatic approach for self-gravitating systems: a microcanonical analysis. Journal of Physics A-Mathematical and Theoretical, 47(22), JUN 6 2014.
- M. Champion and A. Alastuey. A solvable model of hard rods with gravitational interactions. Journal of Statistical Mechanics-Theory and Experiment 2015
- A. Alastuey, J. Piasecki, and P. Szymczak. Hartree-Fock analysis of the effects of long-range interactions on the Bose-Einstein condensation. Journal of Statistical Mechanics-Theory and Experiment 2019