Representation of complex probabilities and complex Gibbs sampling
Departamento de Física Atómica Molecular y Nuclear, Universidad de Granada, E-18071, Spain
2 Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Spain
* Acknowledges financial support by Spanish Ministerio de Economía y Competitividad (Grant No. FIS2014-59386-P), and Agencia de Innovación y Desarrollo de Andalucía (Grant No. FQM225), and Centro de Servicios de Informática y Redes de Comunicaciones (CSIRC), Universidad de Granada, for providing computing time, e-mail: email@example.com
Published online: 26 March 2018
Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the wellknown sign problem. The complex Langevin approach amounts to effectively construct a positive 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 representations 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.
© The Authors, published by EDP Sciences, 2018
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