Marek Grabowski

EMERGENT SPATIAL CORRELATIONS IN STOCHASTICALLY EVOLVING POPULATIONS

We study the spatial pattern formation and emerging long-range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a truncation approximation and supported by computer simulations, reveal emergent strategies of survival for minority agents based on selection of patterns. Minority agents exhibit defensive clustering and cooperative behavior close to phase transitions.

Nonlinear optical transmission through a multiple quantum well system

Abstract We consider a superlattice built of an array of narrow layers of a narrow gap material (quantum wells) sandwiched hy thick layers of a wide gap material (barriers). The electromagnetic wave with frequency below the band gap of the wells results in optical nonlinearities confined to narrow layers. We model this system by an array of equally spaced, infinitesimally thin layers. characterized by Kerr nonlinearity. It is shown that the electromagnetic wave induces intensity dependent gaps in the spectrum giving rise to a multivalued transmission coefficient. The origin of gaps, their connection to chaos, and a possible application for bistable devices are discussed.

SUPERCONDUCTING INSTABILITY IN THE LARGE N-LIMIT OF THE COQBLIN-SCHRIEFFER MODEL

Abstract A possible novel mechanism for superconductivity in heavy fermion systems is proposed. The Coqblin-Schrieffer model for a Kondo-like impurity is studied in the limit of large spin degeneracy. The effective dynamical interaction between conduction electrons mediated by spin fluctuations is calculated and shown to be attractive at finite frequencies.