Non-equilibrium Quantum Many-Body Dynamics: Functional Integral Approaches

Abstract

We discuss functional-integral approaches to far-from-equilibrium quantum many-body dynamics. Specific techniques considered include the two-particle-irreducible effective action and the real-time flow-equation approach. Different applications, including equilibration after a sudden parameter change and non-equilibrium critical phenomena, illustrate the potential of these methods.

Nonequilibrium steady state in open quantum systems: Influence action, stochastic equation and power balance

“…Similar in spirit is an earlier paper by Chen, Lebowitz and Liverani [47] which use the Keldysh techniques in a path integral formalism to consider the dissipative dynamics of an anharmonic oscillator in a bosonic heat bath, and recent papers of Zoli [48], Aron et al [49] for instance. The main tools in nonequilibrium quantum many-body dynamics such as the closed time path (CTP, in-in, or Schwinger-Keldysh) [50] effective action, the two-particle irreducible (2PI) representation, the large N expansion were introduced for the establishment of quantum kinetic field theory a quarter of centuries ago [51] and perfected along the way [52,53,54]. Applications to problems in atomic-optical [55], condensed matter [56], nuclear-particle [57] and gravitation-cosmology [58] have been on the rise in the last decade.…”