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Acta Physica Sinica

THE CLOSED TIME PATH GREEN'S FUNCTIONS AND THE THEORY OF NONLINEAR RESPONSE (Ⅰ)

WANG WAI-TONG, LIN ZHONG-HENG, Zhao-Bin Su, Hao Bai-lin, (1)复旦大学; (2)中国科学院理论物理研究所

Published Jan 1, 1982• 3 citations
Publisher

Abstract

By using the generating functional and the transformations for different forms of the closed time path Green's functions, the general equations on nonlinear response are derived. On the basis of the algebraic identities, KMS condition, time reversal inva-riance and spectral representation, the general considerations for seeking the relations among many-point functions are suggested.

DOI
10.7498/aps.31.1483

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By using the generating functional and the transformations for different forms of the closed time path Green's functions, the general equations on nonlinear response are derived. On the basis of the algebraic identities, KMS condition, time reversal inva-riance and spectral representation, the general considerations for seeking the relations among many-point functions are suggested.
The closed time path Green's function (CTPGF) formalism is applied to the critical dynamics. The related results for the CTPGF approach are briefly reviewed. Three different forms of CTPGF's are defined, transformations from one to another form and other useful computation rules are given. The path integral presentation of the generating functional for CTPGF's is used to derive the Ward-Takahashi identities under both linear and nonlinear transformations of field variables. The generalized Langevin equations for the order parameters and conserved variables are derived from the vertex functional on the closed time path. The proper form of the equations for the conserved variables, including automatically the mode coupling terms, is determined according to the Ward-Takahashi identities and the linear response theory. All existing dynamic models are reobtained by assuming the corresponding symmetry properties for the system. The effective action for the order parameters is deduced by averaging over the random external field. The Lagrangian formulation of the statistical field theory is obtained if the random field one-loop approximation and the second-order approximation of order-parameter fluctuations on different time branches are both taken. The various possibilities of improving the current theory of critical dynamics within the framework of CTPGF's are discussed. The problem of renormalization for the finite-temperature field theory is considered. The whole theoretical framework is also applicable to systems near the stationary states far from equilibrium, whenever there exists an analog of the potential function (free energy).
The closed time path Green's function (CTPGF) formalism is applied to the critical dynamics. The related results for the CTPGF approach are briefly reviewed. Three different forms of CTPGF's are defined, transformations from one to another form and other useful computation rules are given. The path integral presentation of the generating functional for CTPGF's is used to derive the Ward-Takahashi identities under both linear and nonlinear transformations of field variables. The generalized Langevin equations for the order parameters and conserved variables are derived from the vertex functional on the closed time path. The proper form of the equations for the conserved variables, including automatically the mode coupling terms, is determined according to the Ward-Takahashi identities and the linear response theory. All existing dynamic models are reobtained by assuming the corresponding symmetry properties for the system. The effective action for the order parameters is deduced by averaging over the random external field. The Lagrangian formulation of the statistical field theory is obtained if the random field one-loop approximation and the second-order approximation of order-parameter fluctuations on different time branches are both taken. The various possibilities of improving the current theory of critical dynamics within the framework of CTPGF's are discussed. The problem of renormalization for the finite-temperature field theory is considered. The whole theoretical framework is also applicable to systems near the stationary states far from equilibrium, whenever there exists an analog of the potential function ("free energy").
A nonlinear generalization of the fluctuation-dissipation theorem (FDT) for the n-point Green functions and the amputated one particle irreducible vertex functions at finite temperature is derived in the framework of the closed time path formalism. We verify that this generalized FDT coincides with known results for n=2n=2n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.