The role of a kernel in complex langevin systems

Stability of complex Langevin dynamics in effective models

“…This simple device has been shown to improve the situation in certain cases with quadratic action in refs. [26,27]; the stabilization occurring there is actually equivalent to the one discussed in Section 4.…”

“…[13,14] as the essential prerequisite for a correct CLE process. Some of those modifications, like kernels, were known already in the 1980s [25][26][27], others such as variable transformations, were encountered just recently. In fact the reduction to the Cartan subgroup discussed in the previous section falls into this general category.…”

“…A way of modifying the CL process that was discussed already in the 1980s is the introduction of a so-called kernel [25][26][27]. It is nonneutral in the sense that it does not preserve the Langevin evolution of holomorphic observables (but is supposed to preserve the long-time averages of holomorphic observables).…”

“…The CLE with a kernel can be written aṡ 17) with z = x + iy and a holomorphic function H (see refs. [25][26][27], where H 2 is called the kernel). Separating real and imaginary parts, Eq.…”

Stochastic quantization of scalar fields in Einstein and Rindler spacetime

“…[74] [75]. Finally we would like to mention the approach developed by Okamoto et al [76], where the role of the kernel in the complex Langevin equation was studied.…”