Light with Tunable Non-Markovian Phase Imprint.

We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and by recording its diffraction pattern after a double slit: In both cases we observe, instead of a central intensity maximum, a line- or cross-shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Because these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serving as a test bed to study and gain a deeper understanding of non-Markovian processes.

Nonequilibrium stationary states of 3D self-gravitating systems.

Three-dimensional self-gravitating systems do not evolve to thermodynamic equilibrium but become trapped in nonequilibrium quasistationary states. In this Letter, we present a theory which allows us to a priori predict the particle distribution in a final quasistationary state to which a self-gravitating system will evolve from an initial condition which is isotropic in particle velocities and satisfies a virial constraint 2K=-U, where K is the total kinetic energy, and U is the potential energy of the system.

Topological hypothesis on phase transitions: the simplest case.

We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like, e.g., the topology of potential energy submanifolds (PES's). This topological hypothesis has been successfully tested in a few statistical models but up to now there has been no rigorous proof of its general validity. We make a new test of it analyzing the, probably, simplest example of a nontrivial system undergoing a continuous phase transition: the completely connected version of the spherical model. Going through the topological properties of its PES it is shown that, as expected, the phase transition is correlated with a change in their topology. Nevertheless, this change, as reflected in the behavior of a particular topological invariant, the Euler characteristic, is small, at variance with the strong singularity observed in other systems. Furthermore, it is shown that in the presence of an external field, when the phase transition is destroyed, a similar topology change in the submanifolds is still observed at the maximum value of the potential energy manifold, a level which nevertheless is thermodynamically inaccessible. This suggests that static properties of the PES's are not enough in order to decide whether a phase transition will take place; some input from dynamics seems necessary.

Ergodicity breaking and quasistationary states in systems with long-range interactions.

In the thermodynamic limit, systems with long-range interactions do not relax to equilibrium, but become trapped in quasistationary states (qSS), the life time of which diverges with the number of particles. In this paper we will explore the relaxation of the Hamiltonian Mean-Field model to qSS for a class of initial conditions of the multilevel water-bag form. We will show that if the initial distribution satisfies the virial condition, thereby reducing mean field changes, the final distribution in the qSS can be predicted very accurately using a reduced exactly integrable model. The calculated distribution functions obtained using this approach are found to be more accurate than the ones predicted by the Lynden-Bell theory.

Glassy behavior of two-dimensional stripe-forming systems.

We study two-dimensional frustrated but nondisordered systems applying a replica approach to a stripe-forming model with competing interactions. The phenomenology of the model is representative of several well-known systems, like high-Tc superconductors and ultrathin ferromagnetic films, which have been the subject of intense research. We establish the existence of a glass transition to a nonergodic regime accompanied by an exponential number of long-lived metastable states, responsible for slow dynamics and nonequilibrium effects.

Topology, phase transitions, and the spherical model.

The topological hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the configuration space of the short range Berlin-Kac spherical model, for spins lying in hypercubic lattices of dimension d. We find a continuum of changes in the topology and also a finite number of discontinuities in some topological functions. We show, however, that these discontinuities do not coincide with the phase transitions which happen for d > or = 3, and conversely, that no topological discontinuity can be associated with them. This is the first short range, confining potential for which the existence of special topological changes are shown not to be sufficient to infer the occurrence of a phase transition.