Statistical Mechanics of Thermalized Odd Elastic Membranes

We are interested in studying the mechanical properties of thermalized 'odd' elastic membranes using statistical mechanics. Recently, generalizations of isotropic elastic structures to include active forces, specifically the 'odd' elastic forces were introduced by Colin Scheibner et al. Odd elastic 2-d membranes don't possess conservation of angular momentum and thus conservation of energy, thus rendering them to be systems without a Hamiltonian but possessing chiral forces. It was previously shown that for thermalized elastic membranes described by a Hamiltonian, fluctuations renormalize elastic constants, which become scale-dependent beyond a characteristic thermal length scale (a few nanometers for a real life example such as graphene at room temperature), beyond which the bending rigidity increases, while the in-plane elastic constants reduce with universal power law exponents. However, the fact that odd elastic membranes cannot be described by a Hamiltonian requires us to study this problem by means of the Langevin equation. Thus, dynamical effects will be accounted to better understand the role of these new chiral forces in thermalized thin elastic sheets. Both simulations and theory will be shown.