This award supports theoretical research and education on a suite of inter-related topics in the statistical physics of classical and quantal soft matter. Its two major portions focus on (i) the structure and elasticity of soft random solid media formed via vulcanization, especially in settings in which the constituents are prone to liquid crystallinity; and (ii) non-equilibrium atom-light co-crystallization and its consequences for laser-driven ultracold atoms confined to multimode optical cavities - a topic the PI terms "soft quantum matter." Related elements of the project address (iii) systems of fibrous, strongly interacting polymers and their fluctuations, made tractable via the use of concepts and techniques from quantum many-body physics; (iv) the physics of the pericellular coat, a polymer-rich zone that covers many biological cells and, under the control of the cell, seems to play central roles in important cell functions, including motility and division; and (v) the liquid, crystal, and glassy behavior of deformable colloidal particle systems, which appears to be governed by an interplay between the external configurations of the particles and their internal deformability. In large measure these topics are inspired by experiments, either ongoing or anticipated.
Random solids, the focus of topic (i), are materials made via the permanent chemical bonding of randomly selected constituents, as exemplified by vulcanized rubber. This bonding creates a new state of matter, which has shear elasticity and spatial localization of its constituents - but with no long-range crystallinity. The PI aims to develop an understanding of the qualitatively new features that arise when the parent liquids exhibit long- or short-range liquid crystallinity in one of its many forms. This order influences and is influenced by the random solid structure. To accomplish these goals, statistical-mechanical tools will be applied to properly account for the many levels of randomness that such materials present.
Topic (ii) concerns laser-driven atomic gases, trapped in high-finesse optical cavities. These systems are expected to undergo fascinating non-equilibrium phase transitions to states of spontaneous organization among the atoms, which self-consistently populate either the even or the odd anti-nodes of certain modes of the cavity radiation. For suitably designed cavities, these transitions are expected to be accompanied by strong fluctuations in the atomic organization, which will imprint themselves on the spatial and temporal correlations of the light leaking from the cavity. The PI aims to develop a thorough picture of the ordering, its steady-state fluctuations, and the rich kinetics through which this non-equilibrium steady state is achieved.
Their multiple levels of randomness, thermal, quenched, and emergent, make understanding vulcanized media deeply challenging. Progress in understanding them, especially when they also feature liquid crystallinity, continues to demand the creation of refined concepts and powerful techniques. Ultracold atom/laser systems have enabled stimulating new realizations of the dynamics of quantum particles normally associated with hard condensed matter. The multimode cavity-based setting is opening up new vistas - of quantal soft matter and quantum non-equilibrium phase transitions - in which the optical lattice is now an emergent entity, capable, for example, of crystallization/melting, and supporting excitations and defects.
This research on random solids and soft quantal matter may have impact on other areas of science beyond its intended domain and immediate goals.
NONTECHNICAL SUMMARY
This award supports theoretical research and education in the area of soft materials and matter. The PI aims to identify and understand emergent behavior in soft materials and soft matter. Emergent behavior arises from the collective organization or action of the constituent atoms or molecules. Examples include the elasticity of crystals, magnetism, and liquid crystallinity. Liquid crystals are a fascinating class of soft materials that have a rich variety of internal structures with molecules in spatial arrangements less organized than solid crystals but with directional patterns formed by the orientation of the constituent molecules. So, they can exhibit a range of phases intermediate between liquid and crystalline.
Central to this project are two specific themes involving emergent behavior. The first addresses soft random solids, such as those formed via Goodyear's vulcanization process, in which long, flexible macromolecules are bonded together, at random, to form a disordered, quivering, giant structure. The PI asks: What properties do such media have? How can they be understood and modeled, despite their evident complexity? Are they truly solid and, if so, how can this be so, since their internal organization is so different from that of familiar solids, say copper or quartz? Media created via vulcanization, such as rubber, have been manufactured for more than 170 years. However, only relatively recently has it been appreciated that the mingling of vulcanization with liquid crystallinity can produce remarkable, qualitatively new materials - liquid crystalline elastomers - which the PI aims to understand and which have surprising, rich, and valuable properties.
The second theme also involves qualitatively new collective behavior, triggered by changes in organization and motion resulting from strong interactions. The constituents are atoms, held at astonishingly low temperatures between highly polished mirrors, and irradiated with laser light. It has recently been realized that such systems can undergo a new kind of crystallization process, in which the atoms partner with the light, assisting one another to organize in space. The PI aims to answer: What kinds of atom-light crystals are thus created, how are they related to conventional crystalline media, and what can they teach us about other phenomena - familiar ones such as crystallinity and glassiness?
