In the present article we consider some general class of divergent diagrams in Keldysh diagram technique. These divergences arise for nonequilibrium matter and closely related to the divergences in the kinetic theory of gases. We suggest a scheme of renormalization of such divergences and illustrate it on some examples. In the other papers of these series we develop the general theory of renormalization of nonequilibrium diagram technique. The fact that thermal divergences in non-equilibrium diagram technique can be renormalized leads to the following consequence: to prove that the system tends to the thermal equilibrium one should to take into account the behaviour of the system on its boundary. In this paper we illustrate this fact on Bogoliubov derivation of kinetic equations.In the present article we consider some general class of divergent diagrams in Keldysh diagram technique. These divergences arise for nonequilibrium matter and closely related to the divergences in the kinetic theory of gases. We suggest a scheme of renormalization of such divergences and illustrate it on some examples. In the other papers of these series we develop the general theory of renormalization of nonequilibrium diagram technique. The fact that thermal divergences in non-equilibrium diagram technique can be renormalized leads to the following consequence: to prove that the system tends to the thermal equilibrium one should to take into account the behaviour of the system on its boundary. In this paper we illustrate this fact on Bogoliubov derivation of kinetic equations.

arXiv:0707.3949Jul 26, 20070 citations

Exact and scaling approaches to nonequilibrium models

Robin B. Stinchcombe, T. Hanney

Physica D Nonlinear PhenomenaAug 1, 20025 citations

Recent Development in Nonequilibrium Relaxation Method

Nobuyasu Ito, S. Fukushima, H. Watanabe +1 more

Springer proceedings in physicsJan 1, 20027 citations

Feynman rule of a nonequilibrium process

R. Fukuda, Masayoshi Sumino, Kazumasa Nomoto

The complete rule of the Feynman-diagram expansion of a nonequilibrium process is given by using the path-integral technique. At an initial time ${\mathit{t}}_{\mathit{I}}$ , the system is in equilibrium and is brought into the nonequilibrium state by a time-dependent Hamiltonian. All the interactions, including the initial correlation, are taken into account by a diagrammatic expansion. Besides the well-known equilibrium propagators and the conventional 2\ifmmode\times\else\texttimes\fi{}2 nonequilibrium propagator matrix, the propagator becomes a 3\ifmmode\times\else\texttimes\fi{}3 matrix that contains extra elements depending explicitly on ${\mathit{t}}_{\mathit{I}}$ . Both the Feynman rule of the coordinate representation and the coherent-state representation are presented. It is shown that the propagator matrix is expressed compactly by the contour representation. The classical limit is also discussed.The complete rule of the Feynman-diagram expansion of a nonequilibrium process is given by using the path-integral technique. At an initial time ${\mathit{t}}_{\mathit{I}}$, the system is in equilibrium and is brought into the nonequilibrium state by a time-dependent Hamiltonian. All the interactions, including the initial correlation, are taken into account by a diagrammatic expansion. Besides the well-known equilibrium propagators and the conventional 2\ifmmode\times\else\texttimes\fi{}2 nonequilibrium propagator matrix, the propagator becomes a 3\ifmmode\times\else\texttimes\fi{}3 matrix that contains extra elements depending explicitly on ${\mathit{t}}_{\mathit{I}}$. Both the Feynman rule of the coordinate representation and the coherent-state representation are presented. It is shown that the propagator matrix is expressed compactly by the contour representation. The classical limit is also discussed.

Physical Review AMar 1, 199217 citations

The complete rule of the Feynman-diagram expansion of a nonequilibrium process is given by using the path-integral technique. At an initial time

{\mathit{t}}_{\mathit{I}}

, the system is in equilibrium and is brought into the nonequilibrium state by a time-dependent Hamiltonian. All the interactions, including the initial correlation, are taken into account by a diagrammatic expansion. Besides the well-known equilibrium propagators and the conventional 2\ifmmode\times\else\texttimes\fi{}2 nonequilibrium propagator matrix, the propagator becomes a 3\ifmmode\times\else\texttimes\fi{}3 matrix that contains extra elements depending explicitly on

{\mathit{t}}_{\mathit{I}}

. Both the Feynman rule of the coordinate representation and the coherent-state representation are presented. It is shown that the propagator matrix is expressed compactly by the contour representation. The classical limit is also discussed.