Quantum Zeno and anti-Zeno effects in surface diffusion of interacting adsorbates

Abstract

Abstract. Surface diffusion of interacting adsorbates is here analyzed within the context of two fundamental phenomena of quantum dynamics, namely the quantum Zeno effect and the anti-Zeno effect. The physical implications of these effects are introduced here in a rather simple and general manner within the framework of non-selective measurements and for two (surface) temperature regimes: high and very low (including zero temperature).The quantum intermediate scattering function describing the adsorbate diffusion process is then evaluated for flat surfaces, since it is fully analytical in this case. Finally, a generalization to corrugated surfaces is also discussed. In this regard, it is found that, considering a Markovian framework and high surface temperatures, the antiZeno effect has already been observed, though not recognized as such.

Zeno and anti-Zeno effects in a dissipative quantum Brownian oscillator model

“…This is again a manifestation of the anti-Zeno like behaviour. This observation is similar to that of Rodriguez et al in the context of surface diffusion of an adsorbate for a corrugated surface [24].…”

A temperature behavior of the frustrated translational mode of adsorbate and the nature of the “adsorbate–substrate” interaction

“…Unlike the impulsive collision approximation [5], a "driving term" (2.2) of the Hamiltonian is treated on equal footing with other interaction mechanisms and defines a time evolution of the system. Since there is a lack of data about the T-mode behavior for the case, when the diffusion is mediated by tunnelling, and the non-Markovian effects play an important role [30] (or, what is almost the same, when different regimes of the ohmicity manifest themselves), we believe that our investigations have a good perspective from a viewpoint of the study of transition regimes of the adsorbate.…”

“…The influence of non-selective measurements (e.g. collisions) on the evolution of quantum system was considered more precisely in [30], where the short-and long-time dynamics of the adsorbate has been studied in the context of quantum Zeno and anti-Zeno effects, however, without taking into account the tunnelling-mediated surface diffusion and memory effects.…”

Surface diffusion within the Caldeira–Leggett formalism

“…For one particle, the general properties of G or G s given eqn (2) are fulfilled. As known, [37][38][39] the variance of a Gaussian wave packet in general is given by…”

“…For one particle, the general properties of G or G s given eqn (2) are fulfilled. As known, 37–39 the variance of a Gaussian wave packet in general is given byIn correspondence with eqn (17), the time dependent width given by eqn (16) has three contributions: (i) the initial width, (ii) the commutator through −[ x (0), x ( t )] 2 /4 σ 0 2 and (iii) the mean square displacement (MSD). The expression for G ( x , t ) provides an analytical solution for the probability of finding the particle at position x at time t given that it was at x 0 at t = 0.…”