2023/09/12 by Nina Maria Lampl, Lampl, Nina Maria, Dénes Sexty +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Atomic and Subatomic Physics Research #Classical mechanics #FOS: Physical sciences #Geometry #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Kernel (algebra) #Langevin equation #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Path integral formulation #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Scalar field #Statistical physics #Time evolution
paper · pdf · doi:10.48550/arxiv.2309.06103
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/09/12 · openalex created_date 2023/09/14 · openalex updated_date 2026/08/01
The real time evolution of a scalar field in 0+1 dimensions is investigated on a complex time contour. The path integral formulation of the system has a sign problem, which is circumvented using the Complex Langevin equation. Measurement of the boundary terms allow for the detection of correct results (for contours with small real time extents) or incorrect results (at large real time extents), as confirmed by comparison to exact results calculated using diagonalization of the Hamiltonian. We introduce a constant matrix kernel in the Complex Langevin equation, which is optimized with the requirement that distributions of the fields on the complexified manifold remain close to the real manifold. We observe that reachable real times are roughly twice as large with the optimal kernel. We also investigate field dependent kernels represented by a neural network for a toy model as well as for the scalar field, providing promising first results.