Decay estimates for unitary representations with applications to continuous- and discrete-time models

2021/08/31 by S. Richard, Richard, S., Rafael Tiedra de Aldecoa +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2109.00108

openalex publication_date 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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