576 research outputs found
The statistical mechanics of networks
We study the family of network models derived by requiring the expected
properties of a graph ensemble to match a given set of measurements of a
real-world network, while maximizing the entropy of the ensemble. Models of
this type play the same role in the study of networks as is played by the
Boltzmann distribution in classical statistical mechanics; they offer the best
prediction of network properties subject to the constraints imposed by a given
set of observations. We give exact solutions of models within this class that
incorporate arbitrary degree distributions and arbitrary but independent edge
probabilities. We also discuss some more complex examples with correlated edges
that can be solved approximately or exactly by adapting various familiar
methods, including mean-field theory, perturbation theory, and saddle-point
expansions.Comment: 15 pages, 4 figure
Variational dynamics of open quantum systems in phase space
We present a method to simulate the dynamics of large driven-dissipative
many-body open quantum systems using a variational encoding of the Wigner or
Husimi-Q quasi-probability distributions. The method relies on Monte-Carlo
sampling to maintain a polynomial computational complexity while allowing for
several quantities to be estimated efficiently. As a first application, we
present a proof of principle investigation into the physics of the
driven-dissipative Bose-Hubbard model with weak nonlinearity, providing
evidence for the high efficiency of the phase space variational approach.Comment: 7 pages, 5 figure
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