Integrable Circular Brane Model and Coulomb Charging at Large Conduction

TL;DR

This paper investigates an integrable 2D quantum field theory model with boundary conditions, connecting it to Coulomb charging in quantum dots and providing exact solutions at specific topological angles.

Contribution

It introduces an integrable boundary QFT model at specific angles and proposes an exact partition function, linking it to quantum Brownian motion in Coulomb charging.

Findings

Model is integrable at $ heta=0$ and $ heta=\pi$

Exact partition function at $ heta=0$ expressed via differential equations

Connection established between the boundary QFT and Coulomb charging in quantum dots

Abstract

We study a model of 2D QFT with boundary interaction, in which two-component massless Bose field is constrained to a circle at the boundary. We argue that this model is integrable at two values of the topological angle, $\theta =0$ and $\theta=\pi$. For $\theta=0$ we propose exact partition function in terms of solutions of ordinary linear differential equation. The circular brane model is equivalent to the model of quantum Brownian dynamics commonly used in describing the Coulomb charging in quantum dots, in the limit of small dimensionless resistance $g_0$ of the tunneling contact. Our proposal translates to partition function of this model at integer charge.