The Evolution of Perturbation Theory

Asim Gangopadhyaya, Constantin Rasinariu

In time-independent perturbation theory, we were interested in finding the eigenvalues and eigenstates of a system whose Hamiltonian could be written as the sum of a known Hamiltonian and another “small” term describing the perturbation. In time-dependent perturbation theory, the goal is different. We determine the time evolution operator of the perturbed system and use it to estimate the transition probabilities between two states of the unperturbed system.

Jochen Pade

Andreas Hackl, Stefan K. Kehrein

We develop an analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its nonequilibrium spin dynamics.

Jan-Markus Schwindt

Peter Millington, Apostolos Pilaftsis A

We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. The resulting time-dependent diagrammatic perturbation series are free of pinch singularities without the need for quasi-particle approximation or effective resummation of finite widths. After arriving at a physically meaningful definition of particle number densities, we derive master time evolution equations for statistical distribution functions, which are valid to all orders in perturbation theory and to all orders in a gradient expansion. For a scalar model, we perform a perturbative loopwise truncation of these evolution equations, whilst still capturing fast transient behaviour, which is found to be dominated by energy-violating processes, leading to the non-Markovian evolution of memory effects.

Michele Cini