Unusual transport in odd-diffusive systems

Odd systems, characterised by broken time-reversal or parity symmetry, 
exhibit striking transport phenomena due to transverse responses. In this 
talk, I will introduce the concept of odd diffusion, a generalisation of 
diffusion in two-dimensional systems that incorporates antisymmetric tensor 
components. Focusing on systems of interacting particles, I adapt a 
geometric approach to derive effective transport equations and show how 
interactions give rise to unusual transport in odd systems. I present 
effects like enhanced self-diffusion, reversed Hall drift and even absolute 
negative mobility that solely originate in odd diffusion. These results 
reveal how microscopic symmetry-breaking gives rise to emergent, equilibrium 
and non-equilibrium transport, with implications for soft matter, chiral 
active systems, and topological materials.