Related papers: Beyond Complex Langevin Equations: a Progress Repo…
Recently found positive representation for an arbitrary complex, gaussian weight is used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by…
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to…
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct…
Many research programs aiming to deal with the sign problem were proposed since the advent of lattice field theory. Several of these try to achieve this by exploiting properties of analytic functions. This is also the case for our study.…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
In this review we present the current state-of-the-art on complex Langevin simulations and their implications for the QCD phase diagram. After a short summary of the complex Langevin method, we present and discuss recent developments. Here…
Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a non-thermal initial state, the real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic process in an additional…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue…
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened…
It is hypothesized that the Langevin time of stochastic quantum quantization is a physical time over which quantum fields at all values of space and coordinate time fluctuate. The average over paths becomes a time average as opposed to an…
This review explores the Complex Langevin Method (CLM), a stochastic quantization technique designed to address the sign problem in quantum field theories with complex actions. Beginning with foundational principles, the review examines the…
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the…
This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite step-size…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems.…