Accelerating diffusions

Roughly speaking, L-C is a perturbation of the self-adjoint L-0 by an antisymmetric operator C (.) del, where C is weighted divergence free. We prove that lambda(C) <= (0) and equality holds only in some rare situations. Furthermore, rho(C) <= lambda(C) and equality holds for C = 0. In other words, adding an extra drift, C(x), accelerates convergence. Related problems are also discussed.