Zusammenfassung
The electromagnetic field in nonlinear disordered active media, i.e. random lasers, can be described by coupled-mode equations for the complex field amplitudes introducing an Hamiltonian with many-body interaction terms among overlapping modes. Within the quenched-amplitudes approximation, the relevant variables are the mode-phases which interact through quenched disordered couplings $J$:
equation
H = - \sum_spqr J_spqr
( \varphi_s+\varphi_p-\varphi_q-\varphi_r)
\nonumber
equation
Statistical mechanics methods can be applied to study the thermodynamics of the model. In the weakly disordered case (couplings fluctuation negligible with respect to their mean values) a paramagnetic-ferromagnetic phase transition is predicted, corresponding to phase-mode locking transition in multimode lasers. In the opposite regime (strongly disordered case) a glassy behaviour emerges: a one-step replica symmetry breaking glass transition is present at a given temperature (or pumping rate, i.e. stored energy in the modes), corresponding to a random mode-locking transition in random lasers. In the intermediate regime (couplings fluctuation comparable with mean values) a reach phase diagram is expected to hold, with the presence of paramagnetic, ferromagnetic and glassy phases. Implications on numerical and real experiments will be discussed.\\
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References:
1. L.~Angelani, C.~Conti, G.~Ruocco, and F.~Zamponi,
Phys. Rev. Lett. 96, 065702 (2006),
Phys. Rev. B 74, 104207 (2006).
2. L.~Angelani, C.~Conti, L.~Prignano, G.~Ruocco, and F.~Zamponi,
Phys. Rev. B (submitted);
cond-mat/0612024.
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