Related papers: Statistical systems with nonintegrable interaction…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
The general approach for describing systems with Bose-Einstein condensate, where atoms interact through nonlocal pair potentials, is presented. A special attention is paid to nonintegrable potentials, such as the dipolar interaction…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
Condensed ionic systems are described in the framework of a combined approach that takes into account both long-range and short-range interactions. Short-range interaction is expressed in terms of mean potentials and long-range interaction…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the…
New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to…
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
We consider d-dimensional systems with nonintegrable, algebraically decaying pairwise interactions. It is shown that, upon introduction of periodic boundary conditions and a long-distance cutoff in the interaction range, the bulk…
Interaction is so ubiquitous that imaging a world free from it is a difficult fantasy exercise. At the same time, in understanding any complex physical system, our ability of accounting for the mutual interaction of its constituents is…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
We consider weakly interacting diffusions on the torus, for multichromatic interaction potentials. We consider interaction potentials that are not H-stable, leading to phase transitions in the mean field limit. We show that the mean field…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a…
Dipolar interactions govern the structure and dynamics of many soft-matter systems, from molecular to colloids assemblies. When dipole moments are induced by an external field, mutual interactions lead to a many-body magnetization response…
We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…
The correlated density appears in many physical systems ranging from dense interacting gases up to Fermi liquids which develop a coherent state at low temperatures, the superconductivity. One consequence of the correlated density is the…