Exponential decay, recurrences, and quantum-mechanical spreading in a quasicontinuum model

Abstract

We consider a single quantum state coupled equally to each of a set of evenly spaced quasicontinuum (QC) states. We obtain a delay differential equation for the initial-state probability amplitude, and this equation is solved analytically. When the QC-level spacing goes to zero, the initial-state probability decays exactly exponentially.For finite QC-level spacings, however, there are recurrences of initial-state probability. We discuss Tolman's "quantum-mechanical spreading" of probability and also a classical analog of our model.

Theory of ultrafast photoinduced heterogeneous electron transfer: Decay of vibrational coherence into a finite electronic–vibrational quasicontinuum

“…͑19͔͒, which can be calculated analytically for the present case of a regular as well as an infinite QC that has a constant transfer coupling. The solution for A e (t) is given as [25][26][27] A e ͑ t ͒ϭe Ϫt ͩ 1Ϫ ͚ nϭ1 ϱ ͑tϪn r ͒exp͑͑i e ϩ ͒n r ͒…”

The Leggett–Garg inequalities and the relative entropy of coherence in the Bixon–Jortner model

“…These background states are not directly coupled to each other. The time evolution of the population of the single state and a superposition of the quasi-continuum levels were examined in References [4,5,6,7]. We can observe discontinuities of the step functions, or kicks, in the time evolution of the occupation probability of the single state.…”

Photoexcitation to a Periodic Continuum

“…The e citation of a single discrete state to a quasicontinuum of levels has been the subject of much study [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . In the Bi on-Jortner [1] model, the groundstate population dynamics e hibits an initial Weisskopf-Wigner e ponential decay followed by a complicated evolution which includes periodic disruptions or `kicks' .…”