Adiabatic-Markovian bath dynamics at avoided crossings

We investigate the dissipative influence of environmental fluctuations on the dynamics of driven quantum systems at an avoided crossing. We derive two simple approximative equations valid for weak system-bath coupling and compare results for the dissipative Landau-Zener problem with numerically exact results. Very good agreement is found for slow, i.e., adiabatic, driving. Specifically, the minimum in the Landau-Zener probability resulting from the competition of driving and dissipation is well described. For system-bath couplings and temperatures, where this minimum is observed in the adiabatic driving regime, good agreement is also observed for fast driving when the dynamics tends toward nonadiabatic behavior. Otherwise, however, for large temperatures and fast driving our approximation fails even for weak system-bath couplings, for which an undriven system is still accurately described by weak-coupling approximations.

Figure 1

Landau-Zener probability vs sweep speed $v$ for various temperatures. Symbols are numerically exact results from [14]. Full black lines are results from Eq. (8) and dashed blue lines are results from Eq. (9).

Figure 2

Excitation survival probability vs sweep speed $v$ for various temperatures. Symbols are numerically exact results from [15]. Full black lines are results from Eq. (8) and dashed blue lines are results from Eq. (9).

Figure 3

Excitation survival probability vs sweep speed $v$ for various temperatures. Symbols are numerically exact results from [15]. Full black lines are results from Eq. (8) and dashed blue lines are results from Eq. (9).

Figure 4

Excitation survival probability vs sweep speed $v$ for various temperatures. Symbols are numerically exact results from [15]. Full black lines are results from Eq. (8) and dashed blue lines are results from Eq. (9).