35,394 research outputs found
First-principles quantum dynamics for fermions: Application to molecular dissociation
We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can
be simulated using a Gaussian phase-space representation method. In particular,
we consider the application of the mixed fermion-boson model to ultracold
quantum gases and simulate the dynamics of dissociation of a Bose-Einstein
condensate of bosonic dimers into pairs of fermionic atoms. We quantify
deviations of atom-atom pair correlations from Wick's factorization scheme, and
show that atom-molecule and molecule-molecule correlations grow with time, in
clear departures from pairing mean-field theories. As a first-principles
approach, the method provides benchmarking of approximate approaches and can be
used to validate dynamical probes for characterizing strongly correlated phases
of fermionic systems.Comment: Final published versio
Bayesian optimisation for likelihood-free cosmological inference
Many cosmological models have only a finite number of parameters of interest,
but a very expensive data-generating process and an intractable likelihood
function. We address the problem of performing likelihood-free Bayesian
inference from such black-box simulation-based models, under the constraint of
a very limited simulation budget (typically a few thousand). To do so, we adopt
an approach based on the likelihood of an alternative parametric model.
Conventional approaches to approximate Bayesian computation such as
likelihood-free rejection sampling are impractical for the considered problem,
due to the lack of knowledge about how the parameters affect the discrepancy
between observed and simulated data. As a response, we make use of a strategy
previously developed in the machine learning literature (Bayesian optimisation
for likelihood-free inference, BOLFI), which combines Gaussian process
regression of the discrepancy to build a surrogate surface with Bayesian
optimisation to actively acquire training data. We extend the method by
deriving an acquisition function tailored for the purpose of minimising the
expected uncertainty in the approximate posterior density, in the parametric
approach. The resulting algorithm is applied to the problems of summarising
Gaussian signals and inferring cosmological parameters from the Joint
Lightcurve Analysis supernovae data. We show that the number of required
simulations is reduced by several orders of magnitude, and that the proposed
acquisition function produces more accurate posterior approximations, as
compared to common strategies.Comment: 16+9 pages, 12 figures. Matches PRD published version after minor
modification
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