Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

Abstract

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 new insights into decoherence, dynamics of quantum entanglement, and quantum chaos.

Dynamics of Loschmidt echoes and fidelity decay

“…This is just the time when the integrated correlation function of R(t) becomes dominated by quantum fluctuation. Comparing the two factors in (106,107), i.e. the fluctuations of two terms in (24), we obtain a semiclassical estimate of t 2…”

“…The classical analog of decoherence has been considered in Refs. [273,108,107,106]. Using a perturbative approach the influence of the type of the perturbation and of the dynamics on the quantum-classical correspondence were explored, see also Ref.…”

Decoherence in regular systems

“…Note that the above integral is essentially a classical average (see [14] for some results) over two densities corresponding to two states |ψ 1,2 (0) and is therefore a sort of crosscorrelation function. We expand the phase around the position j * e of the environmental state, Φ ≈ [v ′ e (j c )− v′ e ( jc )](j e −j * e )−[v ′ e (j c )− v′ e ( jc )]( je −j * e ), where v′ e (j c ) = ∂v(j c , j * e )/∂j e is a vector of partial derivatives with respect to the environment, evaluated at the position of the environmental packet j * e .…”

Entanglement in the classical limit: Quantum correlations from classical probabilities

“…Somewhat more modestly, several recent works [4][5][6][7][8][9][10] have studied in semiclassical systems the link between the generation of entanglement and the dynamics of the corresponding classical system, including in experimental realizations [11]. The numerical and analytical results obtained so far indicate that the entanglement dynamics in quantum systems having a classically chaotic counterpart sharply differs from those whose classical counterpart is regular, though this difference is dependent on the specificities of the considered systems (types and strengths of the coupling, choice of initial states, etc.).…”