摘要:

AbstractA recent paper using the Riemann ζ‐function to regularize the (divergent) coefficients occurring in the high‐temperature expansions of one‐loop thermodynamic potentials is extended. This method proves to be a powerful tool for converting Dirichlet‐type seriesΣmam(xi)/msinto powerseries in the dimensionless parametersxi. The coefficients occurring in the power series are (proportional to) ζ‐functions evaluated away from their poles ‐ this is where the regularization occurs. High‐temperature expansions are just one example of this highly‐nontrivial rearrangement of Dirichlet series into power series form. We discuss in considerable detail series in whicham(xi) is a product of trigonometrie, algebraic and Bessel function factors. The ζ‐function method is carefully explained, and a large number of new formulae are provided. The means to generalize these formulae are also provided. Previous results on thermodynamic potentials are generalized to include a nonzero constant term in the gauge potential (time component) which can be used to probe the electric sector of tempe

ISSN:0015-8208    

DOI:10.1002/prop.2190351202

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY

摘要:

AbstractThe various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation forS‐matrix. The following problems are discussed: continuous stochastic evolution equations for probaibility distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes. stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion ‐ controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and nonequilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reactionX+X→A(Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also consi

ISSN:0015-8208    

DOI:10.1002/prop.2190351203

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.2190351201

出版商:WILEY‐VCH Verlag    

年代:1987

数据来源: WILEY