The world of long-range interactions: A bird's eye view

Abstract

In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In this invited contribution, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. We also discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers, atoms trapped in optical cavities.

Invited contribution to a special issue on the occasion of Abdus Salam's 90th birthday; v2: Refs. added

References in corpus (5)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Prethermalization of atoms due to photon-mediated long-range interactions
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling
• Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings
• Equilibrium and nonequilibrium properties of systems with long-range interactions

Cited by in corpus (28)

• Metastability and discrete spectrum of long-range systems
• Validity and Failure of the Boltzmann Weight
• Energy transport in the presence of long-range interactions
• Long-range interaction induced collective dynamical behaviors
• Non equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model
• The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential
• Stochastic thermodynamics of a probe in a fluctuating correlated field
• Spontaneous synchronization and nonequilibrium statistical mechanics of coupled phase oscillators
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Out of equilibrium dynamics of repulsive ranked diffusions: the expanding crystal
• Energetics of critical oscillators in active bacterial baths
• Stochastic thermodynamics of inertial-like Stuart-Landau dimer
• Simulating long-range hopping with periodically-driven superconducting qubits
• Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions
• Fractional Klein-Gordon Equation on AdS${}_{2+1}$
• Importance-sampling computation of statistical properties of coupled oscillators
• Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions
• Finite-size Nagle-Kardar model: Casimir force
• Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces
• Irreversibility from staircases in symplectic embeddings
• Critical exponents in mean-field classical spin systems
• Universality of critical dynamics on a complex network
• Relaxation to equilibrium in models of classical spins with long-range interactions
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness
• Relaxation dynamics in a long-range system with mixed Hamiltonian and non-Hamiltonian interactions
• Apparent bistability from weak long-range interactions