Perturbation theory of large quantum systems

Achim Rosch, Johann Kroha, P. Wölfle

We examine the properties of a dc-biased quantum dot in the Coulomb blockade regime. For voltages V that are large compared to the Kondo temperature T(K), the physics is governed by the scales V and gamma, where gamma approximately V/ln(2)(V/T(K)) is the nonequilibrium decoherence rate induced by the voltage-driven current. Based on scaling arguments, self-consistent perturbation theory, and perturbative renormalization group, we argue that due to the large gamma the system can be described by renormalized perturbation theory in 1/ln(V/T(K))<<1. However, in certain variants of the Kondo problem, two-channel Kondo physics is induced by a large voltage V.

Luigi E. Picasso, L. Bracci, Emilio d’Emilio

Quanhui Liu, Z. Li, M.N. Zhang +2 more

The difficulty that the probabilities infinitely increase with time when the time is large enough in time-dependent perturbation theory for quantum systems with finite number of levels is treated by means of simply transforming the straightforward form of the perturbative series into the natural exponential functions, or their combinations, of new perturbative series. Three exactly solvable models are taken to check our new formulation, and excellent agreements with the exact solution are achieved.

Clemens Müller, Thomas M. Stace

Motivated by correlated decay processes driving gain, loss and lasing in driven semiconductor quantum-dots, we develop a theoretical technique using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms terms contribute to the system behaviour at the same order of perturbation theory, and make substantial contributions to the behaviour of the system.