6,299 research outputs found
On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means
The Jensen-Shannon divergence is a renown bounded symmetrization of the
unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler
divergence to the average mixture distribution. However the Jensen-Shannon
divergence between Gaussian distributions is not available in closed-form. To
bypass this problem, we present a generalization of the Jensen-Shannon (JS)
divergence using abstract means which yields closed-form expressions when the
mean is chosen according to the parametric family of distributions. More
generally, we define the JS-symmetrizations of any distance using generalized
statistical mixtures derived from abstract means. In particular, we first show
that the geometric mean is well-suited for exponential families, and report two
closed-form formula for (i) the geometric Jensen-Shannon divergence between
probability densities of the same exponential family, and (ii) the geometric
JS-symmetrization of the reverse Kullback-Leibler divergence. As a second
illustrating example, we show that the harmonic mean is well-suited for the
scale Cauchy distributions, and report a closed-form formula for the harmonic
Jensen-Shannon divergence between scale Cauchy distributions. We also define
generalized Jensen-Shannon divergences between matrices (e.g., quantum
Jensen-Shannon divergences) and consider clustering with respect to these novel
Jensen-Shannon divergences.Comment: 30 page
Tunable Polarons in Bose-Einstein Condensates
A toolbox for the quantum simulation of polarons in ultracold atoms is
presented. Motivated by the impressive experimental advances in the area of
ultracold atomic mixtures, we theoretically study the problem of ultracold
atomic impurities immersed in a Bose-Einstein condensate mixture (BEC). The
coupling between impurity and BEC gives rise to the formation of polarons whose
mutual interaction can be effectively tuned using an external laser driving a
quasi-resonant Raman transition between the BEC components. Our scheme allows
one to change the effective interactions between polarons in different sites
from attractive to zero. This is achieved by simply changing the intensity and
the frequency of the two lasers. Such arrangement opens new avenues for the
study of strongly correlated condensed matter models in ultracold gases.Comment: Revised version, results changed from last versio
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