Introduction to the nonequilibrium functional renormalization group

Details Introduction to the nonequilibrium functional renormalization group Introduction to the nonequilibrium functional renormalization group

2012-04-06

arxiv.org/abs/1204.1489v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

Lectures given at the 49th Schladming Winter School `Physics at all scales: The Renormalization Group' (to appear in the proce

Scientific paper

In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.

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