On Classical Time Delay

Evgeni E. Kolomeitsev, D N Voskresensky

This article reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics and classical electrodynamics. Then we quantify durations of various quantum mechanical processes. The duration of the quantum tunneling is studied, and an interpretation of the Hartmann paradox is suggested. Time delays and advances appearing in the three-dimensional scattering problem on a central potential are considered. We then discuss delays and advances appearing in quantum field theory and after that we focus on the issue of time delays and advancements in quantum kinetics. We discuss problems of the application of generalized kinetic equations in simulations of the system relaxation toward equilibrium and analyze the kinetic entropy flow. Possible measurements of time delays and advancements in experiments similar to the recent OPERA neutrino experiment are also discussed.

G. Morpurgo, B. F. Touschek, Luigi A. Radicati

Benjamin Schwager, Lars Meschede, Jamal Berakdar

Elastic scattering of a wave can be quantified by a shift in the phase with respect to the phase of the incoming wave. A qualitative measure of the time during which the effect occurs is given by the Wigner time delay. The tunneling time is known to saturate with increasing tunneling barrier width (Hartman effect). Here, we analyze the elastic quantum mechanical scattering in a deformed one-dimensional Riemannian manifold, particularly with respect to the Wigner time delay and conclude on the Hartman effect. It is shown that scattering due to local curvature variations results in imperfect conduction and leads to a Wigner time delay that at low energies, is in variance with the classical time delay that is inferred from the arc length. At moderate and high energies, however, classical and quantum time delays coincide.

Josh Izaac, Jingbo Wang

Slobodan Danko Bosanac

Sen Kuang, Xiujuan Lu, Daoyi Dong

The bounded stability problem of linear mixed quantum-classical feedback control systems with time delays is investigated in this paper. The whole feedback system is composed of a quantum plant, a classical controller, and some interconnection devices. Two classes of feedback delays in the feedback loop are considered: constant delays and time-varying delays. The stability of the closed-loop systems under these two classes of time delays is analyzed by constructing different Lyapunov-Krasovskii functions and the corresponding stability criteria are derived, respectively. In particular, a weighting matrix is introduced into stability analysis and the obtained stability results are less conservative than relevant results for this class of quantum systems.