An introduction to real-time renormalization group

TL;DR

This tutorial introduces a real-time renormalization group method for analyzing nonequilibrium properties of quantum systems coupled to environments, demonstrated through an exactly solvable quantum dot model.

Contribution

It provides a clear, accessible introduction to a new real-time RG technique for nonequilibrium quantum systems, with practical illustration.

Findings

Demonstrates the method on a quantum dot model

Provides exact solutions for the model

Serves as an educational resource for advanced students

Abstract

This article presents a tutorial introduction to a recently developed real-time renormalization group method. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We illustrate the technique by a simple and exactly solvable model: A quantum dot consisting of a single non-degenerate level coupled to two reservoirs. The article is intended for advanced students. Besides elementary quantum mechanics and statistical mechanics, it requires only knowledge of second quantization and Wick's theorem.