Quantum classical correspondence for the statistical moments of eigenfunctions in closed systems with chaotic dynamics

Abstract

Abstract Quantum classical correspondence, QCC, is a wide subject of interest from the historical approaches to current studies in simple and complex systems, including time dependent Hamiltonians. Quantum eigenfunctions, or wave-functions, are part of the quantities analysed in recent years, including the implementation due to M V Berry and A Voros in 1977 of a suitable quantity to be considered as the classical eigenfunction counterpart. Here we present the calculation of the statistical moments of eigenfunctions in energy representation for anharmonic oscillators. The classical counter part of the system is fully chaotic. The comparison of the quantum version in order to test for quantum classical correspondence is analysed using a slightly modified formula of the proposed by Berry and Voros. The agreement is good with the corresponding classical counterpart being at the bottom of the quantum version for all the energy range considered.