Research Projects

Two major outstanding questions in theoretical physics are: how to describe 1. driven or active systems far from equilibrium, and 2. disordered systems characterized by a slow relaxation (e.g. glassy dynamics). A recent development in non-equilibrium systems is offering an intriguing new direction that leads to a wealth of novel states and phenomena. As we know, fundamental interactions, like gravitational or electromagnetic forces, obey action-reaction symmetry. This paradigm can be broken if either the medium or the interacting particles are driven out of equilibrium, resulting in non-reciprocal interactions. A striking observation is that non-reciprocal systems can give rise to exotic time-dependent steady states with stable traveling waves. Odd elasticity (a type of non-reciprocal response between the deformation modes) is yet another facet of non-eq. systems that shows unusual elastic response where stress-strain relationship is not compatible with an elastic potential. Such non-trivial systems can only be explored by deploying a broad set of tools and a strongly interdisciplinary approach as this research plan aims to do. This proposed research attempts to develop a unified theoretical and computational description of dense driven matter, systems that exist at the intersection of non-eq. and disordered matter (such as robotic metamaterial, star-fish embryo assembly or a collection of self-spinning chiral colloids) where non-reciprocity in pairwise interaction or odd response can provide a route to achieving novel functionality. In addition to its conceptual and methodological appeal, the theory of dense non-reciprocal (odd) matter is key to advances in soft robotics, processes like wound healing, cancer metastasis, understanding soft mechanical metamaterials, etc. This project will harness and develop tools from the statistical physics of glasses and disordered systems to provide significant insights into the mechanics of non-reciprocal (odd) matter. We plan to explore not only the transport and dynamical responses (like relaxation process, aging dynamics, etc.) but also would like to develop a comprehensive picture of the rheological responses of such materials by exploring shear start up, steady shear, oscillatory shear, etc. To be more specific, we aim to combine statistical mechanical approaches of disordered systems such as dynamical mean field theory and mesoscopic models, as well as hydrodynamic theory with state of the art non-equilibrium simulation techniques and machine learning tools, to explore the dynamical and rheological responses of dense non-equilibrium materials. Combining available human resources (Ph.D. students, post-docs, PI), computational resources (high-performance computing facility at RRI), existing expertise in non-eq simulation techniques, and with the support of the local academic ecosystem, we envision building a coherent and comprehensive picture of such exotic non equilibrium condensed matter systems.