Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mode-locking transitions in nano-structured weakly disordered lasers   We report on a statistical approach to mode-locking transitions of
nano-structured laser cavities characterized by an enhanced density of states.
We show that the equations for the interacting modes can be mapped onto a
statistical model exhibiting a first order thermodynamic transition, with the
average mode-energy playing the role of inverse temperature. The transition
corresponds to a phase-locking of modes. Extended modes lead to a mean-field
like model, while in presence of localized modes, as due to a small disorder,
the model has short range interactions. We show that simple scaling arguments
lead to observable differences between transitions involving extended modes and
those involving localized modes. We also show that the dynamics of the light
modes can be exactly solved, predicting a jump in the relaxation time of the
coherence functions at the transition. Finally, we link the thermodynamic
transition to a topological singularity of the phase space, as previously
reported for similar models.

1
The categories of this paper are: cs
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn