Nonequilibrium Dynamics of Relativistic Quantum Fields
نویسندگان
چکیده
The understanding of quantal many-body systems is a challenging task for far-from-equilibrium conditions as appearing in high energy heavy-ion collisions or cosmological problems. It is of relevance to describe ab-initio thermalization by taking into account all quantum aspects of the particles rather than invoking semi-classical approximation schemes from the beginning [1, 2]. We here consider the equilibration of the scalar φtheory in 2+1 space-time dimensions. The evolution equations for the Green function iG(x, y) =< φ(y)φ(x) > are derived self-consistently by a loop expansion of the 2PI action. When considering contributions up to the three loop order one obtains the Kadanoff-Baym equation that incorporates 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). Equilibration requires the inclusion of collisions as inherent in the sunset diagram [2]. Due to the numerical expense we concentrate on homogeneous systems in space. It is of general interest to check approximate schemes with respect to the Kadanoff-Baym theory which contains the full spectral information of the system. We investigate here in particular the widely used Boltzmann approximation which consists of a time local (Markovian) evolution equation for on-shell quasi-particles. For the comparison we concentrate on the time scale on which the initially nonisotropic distribution proceeds to a polar symmetric equilibrium form. This is described quantitatively by the quadrupole momentQ(t) of the actual particle distribution which shows a nearly exponential decrease in time with relaxation rate ΓQ. This quantity is displayed (scaled by the coupling constant λ) in Fig.1 for two different initial distributions consisting of two particle accummulations separated on the px-axis. We find that thermalization in the
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تاریخ انتشار 2003