Quantum kinetic equation in the closed-time-path formalism

Critical behavior of the particle mass spectra in a family of gelling systems

The critical and post-critical behavior of coagulating systems, where the coagulation efficiency grows with the masses of colliding particles g and l as K(g,l)=0.5(g(alpha)(l)(beta)+g(beta)(l)(alpha), lambda=alpha+beta>1, mu=/alpha - beta/ <1 is studied. The instantaneous sink that removes the particles with masses exceeding G is introduced which allows one to describe the coagulation kinetics by a finite set of equations and define the gel as the deposit of particles with masses between G+1 and 2G . This system displays the critical behavior (the sol-gel transition) in the limit G-->infinity if lambda=alpha+beta>1. The exact post-critical particle mass spectrum is shown to be an algebraic function of g times a growing exponent. All critical parameters of the systems are determined as the functions of alpha and beta .

Perturbative method for the derivation of quantum kinetic theory based on closed-time-path formalism

Within the closed-time-path formalism, a perturbative method is presented, which reduces the microscopic field theory to the quantum kinetic theory. In order to make this reduction, the expectation value of a physical quantity must be calculated under the condition that the Wigner distribution function is fixed, because it is the independent dynamical variable in the quantum kinetic theory. It is shown that when a nonequilibrium Green function in the form of the generalized Kadanoff-Baym ansatz is utilized, this condition appears as a cancellation of a certain part of contributions in the diagrammatic expression of the expectation value. Together with the quantum kinetic equation, which can be derived in the closed-time-path formalism, this method provides a basis for the kinetic-theoretical description.