Sharp vanishing order of solutions to stationary Schrödinger equations on Carnot groups of arbitrary step

Based on a variant of the frequency function approach of Almgren ([1]), under appropriate assumptions we establish an optimal upper bound on the vanishing order of solutions to stationary Schrödinger equations associated to sub-Laplacian on Carnot groups of arbitrary step. Such a bound provides a quantitative form of strong unique continuation and can be thought of as a subelliptic analogue of the recent results obtained by Bakri ([3]) and Zhu ([27]) for the standard Laplacian.