Condensed Matter Theory

Abstract:

We consider classical normal modes and non-interacting bosonic excitations in disordered systems. We emphasise generic aspects of such problems and parallels with disordered, non-interacting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of non-interacting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low frequency limit, above a critical dimension $d_c$, which in different circumstances takes the values $d_c=2$ and $d_c=0$. For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\rho(\omega) \propto \omega^4$ is a universal feature in systems with ground states that depend on the disorder realisation. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.

Abstract:

A study was conducted on the growth of a domain of a nematic liquid crystal at the expense of a second domain with a different director orientation. As such, defects form at the walls between domains and their dynamics was vital in controlling the rate of growth. It was found that a spatial anisotropy in domain growth can result from backflow and discuss how the wall speed varies with the material parameters of the liquid crystal the geometry and the surface properties of the confining cell, and an external electric field.

Abstract:

The effective interactions and the second osmotic virial coefficient B2 of protein solutions incorporating the electrostatics within the "primitive" model of electrolytes was calculated. For discrete charge distributions, the interactions and related B2 vary in a nonmonotonic fashion with increasing ionic strength, while for the smeared charge model, a standard workhorse of colloidal physics, this effect was absent. These correlated-induced effects were missed within nonlinear PB theory, and similar coarse-graining techniques taken from the theory of colloids.