Decay Estimates for Unitary Representations with Applications to Continuous- and Discrete-Time Models

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies nets operators, representations topological groups, and operators given by evolution group self-adjoint operator or powers operator. results are illustrated with wide range examples in quantum mechanics dynamical systems, as instance Schrödinger Dirac waveguides, horocycle flows, adjacency matrices, Jacobi walks skew products.