419 research outputs found
Statistics of the polariton condensate
The influence of polariton-polariton scattering on the statistics of the
polariton condensate in a non-resonantly excited semiconductor quantum well
embedded in a CdTe semiconductor microcavity is discussed. Taking advantage of
the existence of a bottleneck in the polariton dispersion curve, the polariton
states are separated into two domains: reservoir polaritons inside the
bottleneck and active polaritons with wave vector q whose energy lies below the
bottleneck. In the framework of the master equation formalism, the
non-equilibrium stationary reduced density matrix is calculated and the
statistics of polaritons in the condensate at q=0 is determined. The anomalous
correlations between the polaritons in the condensate and those with wave
vectors q, -q leads to an enhancement of the noise in the condensate. As a
consequence, the second order correlation function of the condensate does not
show the full coherence that is characteristic of laser emission.Comment: 35 pages, 5 figure
Mixing of the Averaging process and its discrete dual on finite-dimensional geometries
We analyze the -mixing of a generalization of the Averaging process
introduced by Aldous. The process takes place on a growing sequence of graphs
which we assume to be finite-dimensional, in the sense that the random walk on
those geometries satisfies a family of Nash inequalities. As a byproduct of our
analysis, we provide a complete picture of the total variation mixing of a
discrete dual of the Averaging process, which we call Binomial Splitting
process. A single particle of this process is essentially the random walk on
the underlying graph. When several particles evolve together, they interact by
synchronizing their jumps when placed on neighboring sites. We show that, given
the number of particles and the (growing) size of the underlying graph,
the system exhibits cutoff in total variation if and .
Finally, we exploit the duality between the two processes to show that the
Binomial Splitting satisfies a version of Aldous' spectral gap identity,
namely, the relaxation time of the process is independent of the number of
particles.Comment: 30 pages. Typos fixe
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