Necessary conditions for the emergence of homochirality via autocatalytic self-replication

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the auto-catalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.

Slow passage through thresholds in quantum dot lasers

A turn on of a quantum dot (QD) semiconductor laser simultaneously operating at the ground state (GS) and excited state (ES) is investigated both experimentally and theoretically. We find experimentally that the slow passage through the two successive laser thresholds may lead to significant delays in the GS and ES turn ons. The difference between the turn-on times is measured as a function of the pump rate of change and reveals no clear power law. This has motivated a detailed analysis of rate equations appropriate for two-state lasing QD lasers. We find that the effective time of the GS turn on follows an -1/2 power law provided that the rate of change is not too small. The effective time of the ES transition follows an -1 power law, but its first order correction in ln is numerically significant. The two turn ons result from different physical mechanisms. The delay of the GS transition strongly depends on the slow growth of the dot population, whereas the ES transition only depends on the time needed to leave a repellent steady state.