Anomalous lifetimes of ultracold complexes decaying into a single channel

We investigate the lifetimes of complexes formed in ultracold molecule collisions. Employing both transition-state theory and a non-Hermitian microscopic model, we examine processes that can extend the lifetime of complexes beyond that predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) theory. We focus on complexes that possess only one open channel, and find that the extreme distribution of widths for this case favors low decay rates. Thus, decay from a complex into a single energetically available channel can be anomalously slow, even orders of magnitude slower than the RRKM rate, and moreover the decay may be nonexponential in time.

Figure 1

Simulated spectra for $N_{\mathrm{c}}=1200$ closed channels and $N_{\mathrm{o}}=10$ open channels. The top row shows the spectrum from Eq. (9). This representation presents the real parts of the eigenenergies $E_{\lambda }$, normalized by the mean spacing $d$, on the horizontal axis, and the decay rate $k_{\lambda }={\gamma }_{\lambda }/\hslash$, normalized by the RRKM rate, on the vertical axis. Bottom row: Histograms of the rates $k_{\lambda }$ compared to the chi-squared distribution (red line). The three columns are computed for the dimensionless couplings $x=0.1$, 1, and 10, from left to right.

Figure 2

Same as Fig. 1, but for a single open channel, $N_{\mathrm{o}}=1$.

Figure 3

Effective decay rates $k_{\mathrm{eff}}$ as defined by Eq. (33), normalized by the RRKM rate, vs mean sticking coefficient $\overline{x}$, for various numbers of open channels $N_{\mathrm{o}}=100$ (circles), 10 (squares), and 1 (diamonds). Solid line: Transition state theory rate $k_{\mathrm{TST}}$.