We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non-necessarily connected.

Consistency between preference under uncertainty modeled by Choquet expected utility theory and preference under imprecise risk (a particular situation of uncertainty characterized by the existence of objective upper and lower probabilities) modeled by linear utility theory is shown to imply that the Choquet capacity must coincide on the imprecisely probabilized events with a fixed linear combination of their upper and lower probabilities. This result is used to derive conditions for the existence of subjective upper and lower probabilities on all the events.

A Markov model of semiconductor nanolaser is constructed in order to describe finely the effects of quantum fluctuations in the dynamics of the laser, in particular by considering the transition to lasing. Nanolasers are expected to contain only a small number of emitters, whose semiconductor bands are simulated using true carrier energy states. The model takes into account carrier-carrier interactions in the conduction and valence bands, but the result is a huge Markov chain that is often too demanding for direct Monte-Carlo simulation. We introduce here a technique to split the whole chain into two subchains, one referring to thermalization events within the bands and the other to laser photonic events of interest. The model is applied to the analysis of laser transition and enlightens the coexistence of a pulse regime triggered by the quantum nature of the photon with the birth of the known coherent cw regime. This conclusion is highlighted by calculated time traces. We show that on the ultrasmall scale of nanolasers, we are unable to define perfectly the threshold.

Monte Carlo markovian models of a dual-mode semiconductor laser with quantum well (QW) or quantum dot (QD) active regions are proposed. Accounting for carriers and photons as particles that may exchange energy in the course of time allows an ab initio description of laser dynamics such as the mode competition and intrinsic laser noise. We used these models to evaluate the stability of the dual-mode regime when laser characteristics are varied: mode gains and losses, non-radiative recombination rates, intraband relaxation time, capture time in QD, transfer of excitation between QD via the wetting layer... As a major result, a possible steady-state dual-mode regime is predicted for specially designed QD semiconductor lasers thereby acting as a CW microwave or terahertz-beating source whereas it does not occur for QW lasers.