Comment on "Nonexponential Decay Via Tunneling in Tight-Binding Lattices and the Optical Zeno Effect"

TL;DR

This paper critiques and extends previous work on nonexponential decay in tight-binding lattices, clarifying conditions for the Zeno and anti-Zeno effects using spectral analysis and interference effects.

Contribution

It removes the restriction on site energy placement and clarifies the conditions for Zeno and anti-Zeno effects through spectral and interference analysis.

Findings

Spectral formulation removes the site energy restriction.

Anti-Zeno effect requires destructive interference, not just strong coupling.

Analytical expressions for the critical times t* and t** are provided.

Abstract

S. Longhi [1] studied the survival probability P(t) of an unstable state coupled to a tight-binding lattice finding an exact analytical solution that describes the nonexponential decay. When the first coupling is smaller than the others, he shows that P(t) has a natural decomposition into two terms; one is the exponential decay, consistent with the Gamow's approach, and the other is the correction to this decay. The first purpose of this Comment is to show that the condition imposed on the system; the site energy of the first site is set in the center of the band, limits the generality of the results. A decomposition based on the spectral properties of the system removes this restriction [2]. Other point of this Comment is that, for the weak coupling limit, the author stated that a Zeno effect occurs for t less than t*, where t* is the smallest root of the equation g_eff(t*)=g_0, and for the strong coupling limit an anti-Zeno effect occurs for t close to t**, where t** is the first peak of g_eff. By using a spectral formulation we show that, the anti-Zeno effect not only requires a strong coupling limit, also is necessary to choose the resonance energy and width such that a destructive interference can occur. We present this interference and give an analytical expression and physically interpretation for t* and t**.