Landau-Zener transition driven by a slow noise

Abstract

The effect of a slow noise in non-diagonal matrix element, J(t), that describes the diabatic level coupling, on the probability of the Landau-Zener transition is studied. For slow noise, the correlation time, τ_c, of J(t) is much longer than the characteristic time of the transition. Existing theory for this case suggests that the average transition probability is the result of averaging of the conventional Landau-Zener probability, calculated for a given constant J, over the distribution of J. We calculate a finite-τ_c correction to this classical result. Our main finding is that this correction is dominated by sparse realizations of noise for which J(t) passes through zero within a narrow time interval near the level crossing. Two models of noise, random telegraph noise and gaussian noise, are considered. Naturally, in both models the average probability of transition decreases upon decreasing τ_c. For gaussian noise we identify two domains of this fall-off with specific dependencies of average transition probability on τ_c.

arXiv comment8 pages, 5 figures

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• Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise
• Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models
• Landau-Zener transition with energy-dependent decay rate of the excited state