Nonequilibrium Dynamics and Off-Shell Transport of Relativistic Quantum Fields
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摘要
The dynamics of quantum many-body systems are a challenging task for far-from-equilibrium conditions as ap- pearing in high energy heavy-ion collisions or cosmological problems. It is of fundamental importance to describe ab- initio thermalization by taking into account all quantum aspects of the particles (or fields) rather than invoking semi-classical approximation schemes -as inherent in the Boltzmann limit -from the beginning (1, 2) and to develop tractable approximation schemes that retain the essential quantum dynamics. We here consider the equilibration of the scalar φ4- theory in 2+1 space-time dimensions. The evolution equa- tions for the Green function iG<(x, y )= <φ (y) φ(x) > are derived self-consistently by a loop expansion of the two-particle irreducible (2PI) action (3). When consider- ing contributions up to the three-loop order one obtains a Kadanoff-Baym equation incorporating two types of self- energies: a) the tadpole diagram that produces a mean field while b) the sunset diagram contains the influence of scattering processes and leads to a non-locality in time (memory integrals). We recall that equilibration requires the inclusion of collisions as inherent in the sunset diagram (2). Due to the numerical expense we here restrict to ho- mogeneous systems in space and solve the Kadanoff-Baym (KB) equations in momentum space. As an example for the quantum equilibration in 2+1 space-time dimensions we show in the upper part of Fig. 1 the time evolution of the occupation numbers for sev- eral momentum modes within the full KB-theory (3). For the initial distribution D1 we have adopted two particle accummulations separated on the px-axis. The thermal-
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