Active matter refers to a distinct class of nonequilibrium materials composed of units that are individually powered or self-driven. A large collection of such interacting active units can display striking collective behaviour emergent on large-scales. While largely motivated by the endeavour to bring biological living matter into the inclusive ambit of condensed matter, active matter poses fundamental challenges to the physics of nonequilibrium systems. There are by now many examples of active matter spanning diverse scales, ranging from bird flocks spanning several meters to micron sized cells in tissues and even cytoskeletal processes on sub-micron scales. In addition, there are plenty of synthetic realizations of active matter as well, such as vibrated granular beads and auto-phoretic colloids to name a few.
I briefly summarize my contributions to this field below.
Topological aspects of active matter
A major paradigm in modern condensed matter is the use of topology to characterize phases and phase transitions beyond the usual Landau-Ginzburg framework of symmetry breaking. My work has extended two canonical topological phenomena to the active realm.
The physics of two dimensional equilibrium matter is well known to be dominated by topological excitations. The entropic unbinding of these point defects (vortices in superfluids, superconductors and XY magnets, disclinations in liquid crystals, and dislocations in crystals) leads to the famous Berezinskii-Kosterlitz-Thouless (BKT) transition, which is now a canonical example of a defect mediated phase transition. In apolar active nematics, the nonequilibrium drive causes topological defects to be spontaneously motile and we have developed a detailed theoretical framework to address the dynamics, unbinding and proliferation of defects in active nematics. In doing so we uncovered a novel nonequilibrium universality class of motility driven defect unbinding and new phases of defect order arising from spatio-temporal chaos.
In polar fluids, activity allows for flocking or collective motion. When on a curved surface, such collective motion realizes a different topological phenomena akin to the quantum Hall effect or topological insulators. We showed that propagating sound modes present in a flock moving on a sphere get localized to the equator and are topologically protected from backscattering by obstacles and disorder. Crucial to this phenomenon is the breakdown of time-reversal symmetry, which is an immediate consequence of the nonequilibrium nature of flocking. It also offers a natural non-structured realization of topological acoustic modes in a classical setting, complementing the growing number of examples of mechanical and photonic topological metamaterials.
Apart from these, I’ve also worked on giant particle number fluctuations, viscoelasticity, rheology and the impact of noise in active liquid crystals.
Thermodynamics of active matter
By virtue of violating detailed balance on the microscopic scale, active systems sustain a continuous intake and dissipation of free energy, consequently leading to a non-vanishing entropy production rate even in steady state. Quantifying this irreversibility is crucial to developing a thermodynamic framework for active matter.
Using common models of self-propelled particles and different implementations of time reversal, we demonstrate that active particles are thermodynamically irreversible only when all appropriate actively driven variables are retained. This is so even if some of these variables are fast degrees of freedom, such as the momentum of the particle. In addition to pointing out such “hidden” contributions to entropy production, we also address the role of fluctuations in thermodynamic quantities in relation to recently obtained current-dissipation bounds.