Renormalization of the vacuum angle for a particle on a ring

Abstract

We analyze the vacuum (topological) angle $\theta$ renormalization for the quantum mechanical model of a particle moving around a ring, where $\theta$ is the magnetic flux through the ring. We construct a renormalization group (RG) transformation for this model and derive exact RG equations which lead to the flow diagram similar to that of the Quantum Hall effect. Renormalization of $\theta$ is seen to follow from the loss of information about the initial topological charge in the course of the RG procedure.

arXiv comment4 pages, 1 figure

References in corpus (5)

• Classical Equations for Quantum Systems
• Strong Charge Fluctuations in the Single-Electron Box: A Quantum Monte Carlo Analysis
• Aharonov-Bohm oscillations of a particle coupled to dissipative environments
• Non-equlibrium effects in transport through quantum dots
• General topological features and instanton vacuum in quantum Hall and spin liquids

Cited by in corpus (2)

• Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements
• On the macroscopic quantization in mesoscopic rings and single-electron devices