We introduce microscopic polarization and magnetization fields at each site of an extended system, as well as free charge and current density fields associated with charge movement from site to site, by employing a lattice gauge approach based on a set of orthogonal orbitals associated with each site. These microscopic fields are defined using a single-particle electron Green function, and the equations governing its evolution under excitation by an electromagnetic field at arbitrary frequency involve the electric and magnetic fields rather than the scalar and vector potentials. If the sites are taken to be far from each other, we recover the limit of isolated atoms. For an infinite crystal we choose the orbitals to be maximally-localized Wannier functions, and in the long-wavelength limit we recover the expected linear response of an insulator, including the zero frequency transverse conductivity of a topologically nontrivial insulator. For a topologically trivial insulator we recover the expected expressions for the macroscopic polarization and magnetization in the ground state, and find that the linear response to excitation at arbitrary frequency is described solely by the microscopic polarization and magnetization fields. For very general optical response calculations the microscopic fields necessarily satisfy charge conservation, even under basis truncation, and do not suffer from the false divergences at zero frequency that can plague response calculations using other approaches.

Phytoglycogen is a naturally occurring polysaccharide nanoparticle made up of extensively branched glucose monomers. It has a number of unusual and advantageous properties, such as high water retention, low viscosity, and high stability in water, which make this biomaterial a promising candidate for a wide variety of applications. In this study, we have characterized the structure and hydration of aqueous dispersions of phytoglycogen nanoparticles using neutron scattering. Small angle neutron scattering results suggest that the phytoglycogen nanoparticles behave similar to hard sphere colloids and are hydrated by a large number of water molecules (each nanoparticle contains between 250% and 285% of its mass in water). This suggests that phytoglycogen is an ideal sample in which to study the dynamics of hydration water. To this end, we used quasielastic neutron scattering (QENS) to provide an independent and consistent measure of the hydration number, and to estimate the retardation factor (or degree of water slow-down) for hydration water translational motions. These data demonstrate a length-scale dependence in the measured retardation factors that clarifies the origin of discrepancies between retardation factor values reported for hydration water using different experimental techniques. The present approach can be generalized to other systems containing nanoconfined water.

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We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature and consider the orbital electronic contribution of the linear response to spatially varying, time-dependent electromagnetic fields. The charge and current density expectation values generally depend on both the microscopic polarization and magnetization fields, and on the microscopic free charge and current densities. But contributions from the latter vanish in linear response for the class of insulators we consider. Thus we need only consider the former, which can be decomposed into "site" polarization and magnetization fields, from which "site multipole moments" can be constructed. Macroscopic polarization and magnetization fields follow, and we identify the relevant contributions to them; for electromagnetic fields varying little over a lattice constant these are the electric and magnetic dipole moments per unit volume, and the electric quadrupole moment per unit volume. A description of optical activity and related magneto-optical phenomena follows from the response of these macroscopic quantities to the electromagnetic field and, while in this paper we work within the independent particle and frozen-ion approximations, both optical rotary dispersion and circular dichroism can be described with this strategy. Earlier expressions describing the magnetoelectric effect are recovered as the zero frequency limit of our more general equations. Since our site quantities are introduced with the use of Wannier functions, the site multipole moments and their macroscopic analogs are generally gauge dependent. However, the resulting macroscopic charge and current densities, together with the optical effects to which they lead, are gauge invariant, as would be physically expected.

Violent relaxation is a process that occurs in systems with long-range interactions. It has the peculiar feature of dramatically amplifying small perturbations, and rather than driving the system to equilibrium, it instead leads to slowly evolving configurations known as quasistationary states that fall outside the standard paradigm of statistical mechanics. Violent relaxation was originally identified in gravity-driven stellar dynamics; here, we extend the theory into the quantum regime by developing a quantum version of the Hamiltonian mean field (HMF) model which exemplifies many of the generic properties of long-range interacting systems. The HMF model can either be viewed as describing particles interacting via a cosine potential, or equivalently as the kinetic XY model with infinite-range interactions, and its quantum fluid dynamics can be obtained from a generalized Gross-Pitaevskii equation. We show that singular caustics that form during violent relaxation are regulated by interference effects in a universal way described by Thom's catastrophe theory applied to waves and this leads to emergent length scales and timescales not present in the classical problem. In the deep quantum regime we find that violent relaxation is suppressed altogether by quantum zero-point motion. Our results are relevant to laboratory studies of self-organization in cold atomic gases with long-range interactions.