论文标题
费米黄金法则的发作时间
The onset time of Fermi's golden rule
论文作者
论文摘要
费米（Fermi）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，并预测了时间性衰减。尽管它是在相对较短的时间出现的，但在量子动力学的最早阶段，费米制度并未占据。费米制度发作时间的文献中的标准标准为$ t_f \ sim1/δΩ$，$ΔΩ$围绕系统的共振频率$ω_0$的频率间隔，在该频率上，耦合到储存器上的耦合并不能使储存量变化。在这项工作中，该标准通常不适合宽带储层，在该储层中，储层耦合频谱采用$ r \ weft（ω\右）\proptoΩ^η$的形式，并为$η> 1 $提供了fermi rentime的时间， $ t_f \ propto \ left（ω_ {\ mathrm {x}}/ω__0\ right）^{η-1} \ times1/ω_0$其中$ω_ {\ mathrm {x}} $是储层的高频截止。因此，费米制度的开始时有时会比标准标准预测的数量级大。这种现象被证明与短时间储层的异频频率的激发有关。对于具有$η\ leq1 $的宽带水库，对于窄带储层，可以证明标准标准是正确的。我们的发现重新审视了费米黄金法则的适用条件，并提高了我们对不稳定量子系统动态的理解。
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 $t_F\sim1/Δω$, with $Δω$ the frequency interval around the resonant transition frequency $ω_0$ 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 $R\left(ω\right)\proptoω^η$, and for which it is found that for $η>1$, the onset time of the Fermi regime is given by $t_F\propto\left(ω_{\mathrm{X}}/ω_0\right)^{η-1}\times1/ω_0$ where $ω_{\mathrm{X}}$ 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 $η\leq1$, and for narrowband reservoirs, it is shown that the standard criterion is correct. Our findings revisit the conditions of applicability of Fermi's golden rule and improve our understanding of the dynamics of unstable quantum systems.
