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Complex Langevin and boundary terms
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As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, we analyze the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. We also show how some simple modification stabilizes the CL process in such a way that it can produce results agreeing with direct integration. Besides explicitly demonstrating the connection between boundary terms and correct convergence our analysis also suggests a correctness criterion which could be applied in realistic lattice simulations.
Forward citations
Cited by 5 Pith papers
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A regularization inspired by Lefschetz thimbles stabilizes complex Langevin simulations in toy models, with a bias-correction step that restores the original expectation values.
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Complex Langevin results in one- and two-dimensional toy models match a linear combination of integration cycles when boundary terms vanish, and the kernel choice controls which cycles contribute.
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Diffusion models learn distributions generated by complex Langevin dynamics
Diffusion models reproduce the distributions sampled by complex Langevin dynamics in a Gaussian and a quartic toy model with complex mass.
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Energy-based diffusion models trained on complex Langevin data produce an explicit energy function for the sampled distribution, enabling MCMC without re-simulation.
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Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature
Configurational temperature from action gradients and Hessians offers a sensitive new correctness diagnostic for complex Langevin simulations, reproducing input temperature to 0.2-3% in 1D PT-symmetric models.
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