2,128 research outputs found
Representation of Complex Probabilities
Let a ``complex probability'' be a normalizable complex distribution
defined on . A real and positive probability distribution , defined
on the complex plane \C^D, is said to be a positive representation of
if , where is any
polynomial in and its analytical extension on \C^D. In this
paper it is shown that every complex probability admits a real representation
and a constructive method is given. Among other results, explicit positive
representations, in any number of dimensions, are given for any complex
distribution of the form Gaussian times polynomial, for any complex
distributions with support at one point and for any periodic Gaussian times
polynomial.Comment: REVTeX, 15 pages, no figures, uuencode
Representation of complex probabilities and complex Gibbs sampling
Complex weights appear in Physics which are beyond a straightforward
importance sampling treatment, as required in Monte Carlo calculations. This is
the well-known sign problem. The complex Langevin approach amounts to
effectively construct a posi\-tive distribution on the complexified manifold
reproducing the expectation values of the observables through their analytical
extension. Here we discuss the direct construction of such positive
distributions paying attention to their localization on the complexified
manifold. Explicit localized repre\-sentations are obtained for complex
probabilities defined on Abelian and non Abelian groups. The viability and
performance of a complex version of the heat bath method, based on such
representations, is analyzed.Comment: Proceedings of Lattice 2017 (The 35th International Symposium on
Lattice field Theory). 8 pages, 4 figure
Comment on "Quantum back-reaction through the Bohmian particle"
In this Comment I point out some limitations of the proposal of Prezhdo and
Brooksby for coupling quantum and classical degrees of freedom
(Phys.Rev.Lett.86(2001)3215) if it is pushed too far.Comment: 1 page, REVTEX, no figure
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