29 research outputs found
Effective cavity pumping from weakly coupled quantum dots
We derive the effective cavity pumping and decay rates for the master
equation of a quantum dot-microcavity system in presence of weakly coupled
dots. We show that the in-flow of photons is not linked to the out-flow by
thermal equilibrium relationships.Comment: 6 pages, 1 figure, PLMCN10 conference proceeding
Conformal Mappings and Dispersionless Toda hierarchy
Let be the space consists of pairs , where is a
univalent function on the unit disc with , is a univalent function
on the exterior of the unit disc with and
. In this article, we define the time variables , on which are holomorphic with respect to the natural
complex structure on and can serve as local complex coordinates
for . We show that the evolutions of the pair with
respect to these time coordinates are governed by the dispersionless Toda
hierarchy flows. An explicit tau function is constructed for the dispersionless
Toda hierarchy. By restricting to the subspace consists
of pairs where , we obtain the integrable hierarchy
of conformal mappings considered by Wiegmann and Zabrodin \cite{WZ}. Since
every homeomorphism of the unit circle corresponds uniquely to
an element of under the conformal welding
, the space can be naturally
identified as a subspace of characterized by . We
show that we can naturally define complexified vector fields \pa_n, n\in \Z
on so that the evolutions of on
with respect to \pa_n satisfy the dispersionless Toda
hierarchy. Finally, we show that there is a similar integrable structure for
the Riemann mappings . Moreover, in the latter case, the time
variables are Fourier coefficients of and .Comment: 23 pages. This is to replace the previous preprint arXiv:0808.072
Non-Equilibrium Statistical Physics of Currents in Queuing Networks
We consider a stable open queuing network as a steady non-equilibrium system
of interacting particles. The network is completely specified by its underlying
graphical structure, type of interaction at each node, and the Markovian
transition rates between nodes. For such systems, we ask the question ``What is
the most likely way for large currents to accumulate over time in a network
?'', where time is large compared to the system correlation time scale. We
identify two interesting regimes. In the first regime, in which the
accumulation of currents over time exceeds the expected value by a small to
moderate amount (moderate large deviation), we find that the large-deviation
distribution of currents is universal (independent of the interaction details),
and there is no long-time and averaged over time accumulation of particles
(condensation) at any nodes. In the second regime, in which the accumulation of
currents over time exceeds the expected value by a large amount (severe large
deviation), we find that the large-deviation current distribution is sensitive
to interaction details, and there is a long-time accumulation of particles
(condensation) at some nodes. The transition between the two regimes can be
described as a dynamical second order phase transition. We illustrate these
ideas using the simple, yet non-trivial, example of a single node with
feedback.Comment: 26 pages, 5 figure
Shape Analysis of Planar Objects with Arbitrary Topologies using Conformal Geometry
The study of 2D shapes is a central problem in the field of computer vision. In 2D shape analysis, classification and recognition of objects from their observed silhouette are extremely crucial and yet difficult. It usually involves an efficient representation of 2D shape space with natural metric, so that its mathematical structure can be used for further analysis. Although significant progress has been made for the study of 2D simply-connected shapes, very few works have been done on the study of 2D objects with arbitrary topologies. In this work, we proposed a representation of general 2D domains with arbitrary topologies using conformal geometry. A natural metric can be defined on the proposed representation space, which gives a metric to measure dissimilarities between objects. The main idea is to map the exterior and interior of the domain conformally to unit disks and punctual disks (circle domains), using holomorphic 1-forms. A set of diffeomorphisms from the unit circle S1 to itself can be obtained, which together with the conformal modules are used to define the shape signature. We prove mathematically that our proposed signature uniquely represents shapes with arbitrary topologies. We also introduce a reconstruction algorithm to obtain shapes from their signatures. This completes our framework and allows us to go back and forth between shapes and signatures. Experimental results shows the efficacy of our proposed algorithm as a stable shape representation scheme