NSF-BSF: Fluctuation phenomena out of equilibrium

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports basic research and education aimed at characterizing emergence of collective behaviors in large assemblies of interacting entities. While actions of individual components of a system may be difficult to chart (due to chaotic classical motion or inherent quantum uncertainty), the collective behavior of a large number can be easier to predict, for example the dispersion of sound waves despite random movements of gas molecules. This is made possible by the tools of statistical physics that enable systematic averaging over stochastic motions of molecules, to describe effective field theories for evolution of relevant densities. The extensive utility of this approach, averaging from uncertain motions of particles to near deterministic collective behavior, in describing physical systems in equilibrium, suggests its applicability to broader class of entities. Some examples of collective behaviors of complex entities, especially in systems out of equilibrium, are explored in this research. (i) The emerging field of active matter is concerned with collective motions of entities, such as bacteria, artificial self-powered nanobots, of even flocks of birds or school of fish, that individually consume and dissipate energy. Despite stochasticity at the individual level, interactions lead to fascinating coordinated motions of the collective. We have found that such long-range coordination can be disrupted by obstacles within the medium, or even disorder at its edges. The research team will explore the roles of disorder and boundaries on phases of active matter. Phenomena to be studied include the long-reach of disruptions caused by impurities, and the wanderings of passive bystanders caught in the flow of active matter. (ii) At a basic level, a key difference between elements of active matter and atoms in “equilibrium matter,” is that consumption of energy sets up a natural arrow of time. In contrast, one cannot distinguish between movies of equilibrium gas particles running forward or backward. Interestingly, insights gained from behavior of “active matter” can be explored in other domains of physics, such as in the context of photons and radiation, for example, heat transfer. The team is investigating the feasibility of heat engines based on radiation, with similarity to non-equilibrium forces exerted in active matter through the ratchet effect arising from asymmetric boundaries. (iii) Living systems, the epitome of non-equilibrium, consume energy not only to move, but to grow and reproduce, presenting other phenomena to explore. For example, as a bacterial film, or a tumor expands into new space, its composition is dominated by successful ancestors at the expansion front. This sets up a connection between the shape of the front, and the competing bacterial variants. The research team will classify possible shapes of films that may appear during growth and expansion of competing variants. This research activity is closely incorporated in seminars and courses of the PI which through his published textbooks and web-pages reach a broad scientific community. This research crosses disciplinary boundaries and has potential impact in diverse areas from applied mathematics to immunology. TECHNICAL SUMMARY Fluctuations, whether of quantum, thermal, or non-equilibrium origin, are cause or signature of various physical phenomena. Generalizing concepts and mathematical tools characterizing equilibrium fluctuations to the realm of non-equilibrium phenomena has been a long-running endeavor. This research aims at quantifying out of equilibrium fluctuations in diverse contexts. Specific goals include: (i) The emerging field of active matter is concerned with collective behaviors of entities that consume energy to move. The current of energy through the system yields novel collective phases and fluctuations, not always describable with field theories of equilibrium matter. The research projects will explore the roles of disorder and boundaries (static or mobile) on active matter. Phenomena to be explored include long-ranged correlations and force, and anomalous dynamics of inclusions. (ii) Quantum electrodynamic phenomena in setups without time reversal symmetry share common features with active matter. In particular, we shall explore the feasibility of a radiative heat engine that utilizes a ratchet effect to generate force, and forces that violate Newton’s third law in setups that break electromagnetic reciprocity. (iii) Growing populations provide yet another venue for exploration of emergent phenomena. One set of research projects pertain to classifying morphologies of films arising during growth and expansion of competing species. Another set deals with dynamics of populations with time-varying reproduction rate due to mutations or external conditions. The projects in this research will be studied through a combination of numerical and analytical methods. The typical starting point would be a simplified model of elements following simplified but refine-able rules. On the analytic front, the goal would be to coarse-grain the model to the level of a continuum description, and to then apply methods of field theory to characterize phases and fluctuations. The numerical task would be to implement the simplified rules and characterize the emergent behaviors, in contrast or support to the theory. Characterizing probability distributions underlying fluctuations in nonequilibrium settings has been a long-standing quest in statistical physics, with notable recent progress on several fronts. Yet, puzzles of force in active matter, and fixation in growing bacterial fronts are but two examples amongst several projects pointing to complexity of the underlying phenomena, which this research aims to unravel. Education and development of human resources are an essential broader impact: The research activity is closely incorporated in seminars and courses of the PI which through textbooks and web-pages reach a broad scientific community. Past students and postdocs of the group are productive members of academic and research communities. This research crosses disciplinary boundaries and has potential impact in diverse areas from applied mathematics to immunology. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.