Correspondence between the classical and quantum dynamics of simple systems

Heekyung Han

Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.

D. C. Hutcgings

H. Hernández-Saldaña

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.

Fabio Bagarello

Maciej Zworski

Jiangbin Gong, Paul W. Brumer

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer deeper insights into decoherence, dynamics of quantum entanglement, and quantum chaos.