Quantum many-body systems are difficult to study because the space of possible many-body states is huge: its dimension grows exponentially in the system size. However, in recent years progress in our understanding of quantum entanglement has revealed that only a small region of this huge state space is actually relevant to the study of quantum many-body systems.
Abstract: The exact solution to interacting quantum problems is, in general, an exponentially hard task due to the exponential growth of the Hilbert space with the system size. As a result, despite extensive research during the past several decades we still do not have a good understanding of strongly correlated systems even for the simplest ones such as the Hubbard model. We can only obtain exact results for special and very limited classes of models.
The study of liquid crystals occupies a central place in materials science, serving as a context for encountering and using a variety of exotic structural themes of molecular organization, particularly of soft matter. A key feature of molecular ordering in liquid crystals is fluid hierarchical self-assembly, in which molecular structure provides precise control of fluid self-organization over a wide range of length scales.
Animals are capable of performing an amazing set of actions. In many species, particularly invertebrates (although scarily also humans), a large percentage of the behavioral repertoire is comprised of stereotyped behaviors—actions that are seen again and again across time and individuals. I will discuss our recent work trying to uncover how these behaviors are actuated and controlled in the wiggling nematode worm C. elegans and the dancing fruit fly D. melanogaster.
Liquid crystal elastomers combine the orientational order of liquid crystals with the elasticity of polymers. Remarkably, these materials flex and deform under stimuli such as a change of temperature, and undergo autonomous folding, or "auto-origami," into complex shapes. The material's liquid crystal director field defines the local axis of extension/contraction, and can be patterned, or "blueprinted," to induce a programmed shape transformation. Incorporation of photoactive azobenzene makes these materials move in response to illumination.
Optical tweezers allow us to probe the interactions of proteins with single DNA molecules and apply very small forces. Measurement of force-dependent DNA conformations allows us to quantify interactions that govern cellular function. Here we investigate the DNA interactions of human APOBEC3G, an innate antiviral immunity protein that functions as a cytidine deaminase.