Complex Langevin equations and their applications to quantum statistical and lattice field models

Journal Article · Sun Jun 15 00:00:00 EDT 1986 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.33.3678· OSTI ID:5796429

Gausterer, H; Klauder, J R

We discuss the calculation of statistical averages of variables lying on S/sub 1/ or S/sub 2/ using (complex) Langevin equations. Assuming that the drift term is proportional to the gradient of a possibly complex function S()x/sub i/)), x/sub i/element ofS/sub 1/ or S/sub 2/ we give the general form of such Langevin equations. These variables cause unphysical singularities and computational problems; thus we transform them to those of the embedding Euclidean space. We show in several examples that these modified (complex) Langevin equations have good convergence properties using an improved two-stage Runge-Kutta algorithm.

• Research Organization: Institut fuer Theoretische Physik, Universitat Graz, A-8010 Graz, Austria
• OSTI ID: 5796429
• Journal Information: Phys. Rev. D; (United States), Vol. 33:12
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
LATTICE FIELD THEORY
LANGEVIN EQUATION
STATISTICAL MODELS
ALGORITHMS
DIFFERENTIAL EQUATIONS
EUCLIDEAN SPACE
MANY-DIMENSIONAL CALCULATIONS
MONTE CARLO METHOD
PARTITION FUNCTIONS
STOCHASTIC PROCESSES
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICAL SPACE
QUANTUM FIELD THEORY
RIEMANN SPACE
SPACE
645400* - High Energy Physics- Field Theory
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