No abstract

Evolution in time of an arbitrary initial state for a parametrically driven quantum oscillator is an interesting problem since there exist regions in parameter space (defined by the amplitude and frequency of the driving) where the moments of the probability distribution can diverge in time. While the first moment satisfies a Mathieu equation, the higher-order moments follow Mathieu like equations of order greater than two. It is not very often that a physical problem gives rise to higher-order Mathieu equations. Hence, we give a detailed study of the different stability zones associated with the parametric quantum oscillator, using perturbative techniques traditionally associated with the Mathieu equation. We verify our results by numerical analysis, thus demonstrating that for the higher-order Mathieu equations, the traditional perturbation theory methods give a consistent account of the stability zones.

We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface...

No abstract

We study the thermodynamics of binary mixtures wherein the volume fraction of the minority component is less than the amount required to form a flat interface. Based on an explicit microscopic mean field theory, we show that the surface tension dominated equilibrium phase of a polymer mixture forms a single macroscopic droplet. A combination of elastic interactions that renormalize the surface tension, and arrests phase separation for a gel-polymer mixture, stabilize a micro-droplet phase. We compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the importance of the rheological properties of the solvent in dictating the thermodynamic phase behavior of biopolymers undergoing liquid-liquid phase separation.