5/28/2023 0 Comments Monte carlo sampling![]() The respective Markov chain is realized in a new set of visible and hidden variables ( v, w ). This allows us to rederive complex Langevin dynamics from a new perspective and establishes a framework for the explicit construction of new sampling schemes for complex actions.Ĭomparison of different algorithms that all make use of the introduction of additional hidden variables, leading to dynamics in an extended state space. These constraints originate from the detailed-balance equations satisfied by the Monte Carlo scheme. Subject to a set of constraints, this sampling process is the physical one. In this approach we derive an explicit real sampling process for generalized complex Langevin dynamics. In the present work we set up a general approach based on a Markov chain Monte Carlo scheme in an extended state space. Moreover, its unphysical nature is hard to detect due to the implicit nature of the process. The statistical sampling process at such a fixed point is not based on the physical action and hence leads to wrong predictions. One of its key challenges is the potential convergence of the dynamics to unphysical fixed points. Among these, complex Langevin dynamics has the appeal of general applicability. Many computational approaches have been developed for tackling the sign problem emerging for complex actions. ![]() Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromodynamics at finite density to the nonequilibrium evolution of quantum systems.
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