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The onset time of Fermis golden rule
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences ( IF 2.741 ) Pub Date : 2021-04-07 , DOI: 10.1098/rspa.2020.0777
V. Debierre, E. Lassalle

Fermi’s golden rule describes the decay dynamics of unstable quantum systems coupled to a reservoir, and predicts a linear decay in time. Although it arises at relatively short times, the Fermi regime does not take hold in the earliest stages of the quantum dynamics. The standard criterion in the literature for the onset time of the Fermi regime is tF ∼ 1/Δω, with Δω the frequency interval around the resonant transition frequency ω0 of the system, over which the coupling to the reservoir does not vary appreciably. In this work, this criterion is shown to be inappropriate in general for broadband reservoirs, where the reservoir coupling spectrum takes the form R (ω) ∝ ωη, and for which it is found that for η > 1, the onset time of the Fermi regime is given by tF ∝ (ωX/ω0)η−1 × 1/ω0 where ωX is the high-frequency cutoff of the reservoir. Therefore, the onset of the Fermi regime can take place at times orders of magnitude larger than those predicted by the standard criterion. This phenomenon is shown to be related to the excitation of the off-resonant frequencies of the reservoir at short times. For broadband reservoirs with η ≤ 1, and for narrowband reservoirs, it is shown that the standard criterion is correct.



中文翻译:

费米斯黄金法则的发作时间

费米的黄金法则描述了耦合到储层的不稳定量子系统的衰减动力学,并预测了时间的线性衰减。尽管费米制度是在相对较短的时间内出现的,但它并没有在量子动力学的最早阶段得到应用。在文献中的费米制度的起效时间的标准准则是˚F  〜1 /Δ ω,用Δ ω围绕谐振过渡频率的频率间隔ω 0的系统中,在其上耦合到储做的不变化相当地。在这项工作中,该准则通常不适用于宽带水库,因为水库耦合谱的形式为Rω)α  ω η,以及用于其被发现对于η  > 1,费米制度的开始时间由下式给出˚F  α(ω X / ω 0η -1  ×1 / ω 0,其中ω X是水库的高频截止。因此,费米政权的发作时间可能比标准判据所预测的时间大几个数量级。事实表明,这种现象与在短时间内激发储层的非共振频率有关。对于η的宽带水库 ≤1,并且对于窄带水库,表明标准准则是正确的。

更新日期:2021-04-08
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