Dr. Shamik Gupta

---

Systems with long-range interactions have interaction
potentials that decay slower than 1/r^d at large distances r in
d dimensions. Common examples are self-gravitating systems,
non-neutral plasmas, dipolar ferroelectrics and ferromagnets, etc.
Long-range interacting systems are non-additive. This leads to unusual
properties, both thermodynamic (e.g., negative microcanonical specific
heat, ensemble inequivalence) and dynamic (e.g., slow relaxation,
breaking of ergodicity). After a brief review, I will discuss a
paradigmatic example, the Hamiltonian Mean-Field model, involving XY
spins with mean-field interactions. For this model, relaxation of some
initial states towards equilibrium proceeds through intermediate
quasistationary states characterized by a slow variation of
macroscopic observables over time. The life time of these states
diverges with the system size. These states are observed in
deterministic microcanonical evolution within a certain energy
interval. Our recent study suggests that in presence of noise,
quasistationary states occur only as a crossover phenomenon depending
on the relative magnitudes of two timescales set by the system size
and the level of noise in the evolution. Our proposed scaling form for
the relaxation time to equilibrium is verified in simulations by a
scheme of piecewise deterministic evolution for the model.

---

ENS Lyon
Konferenzraum Theoretische Physik
Contact: not specified