Dynamical properties of quantum many-body systems with long-range interactions

Many-body physics in long-range interacting quantum systems

Long-range many-body polyelectrolyte bridging interactions.

We investigate polyelectrolyte bridging interactions mediated by charged, flexible, polyelectrolyte chains between fixed cylindrical macroions of opposite charge in a two-dimensional hexagonal crystalline array. We show that in the asymptotic regime of small macroion density, the polyelectrolyte-mediated attraction is long range, falling off approximately linearly with the macroion array densit...

Many-body theory of synchronization by long-range interactions.

Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r) = g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ϵ = α/d-1. For α ≤ d, the system exhibits a sharp synchronization transition as described by the conventio...

Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions.

Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are investigated by means of the Green’s function method. The model Hamiltonian is given by H = −(J0/2) ∑ i6=j r −p ij Si · Sj − H ∑ j S z j . It is shown that there exists a finite-temperature phase transition in the region d < p < 2d for the d-dimensional case and that no transitions at any finite temperature exist...

Equilibrium and nonequilibrium properties of systems with long-range interactions

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, like negative specific heat in the microcanonical ensemble, temperature jumps at first order phase transitions, broken ergodicity. Here, we mainly restrict ou...