Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

TL;DR

This paper connects one-dimensional Fermi fluid density fluctuations to vicinal surface dynamics and develops a hydrodynamic fluctuation theory for long-range interacting particles, revealing fundamental relations and nonperturbative results.

Contribution

It establishes a link between Fermi fluid fluctuations, surface models, and stochastic particle dynamics, providing new theoretical insights and nonperturbative proofs.

Findings

Derivation of the Haldane relation from surface models

Identification of scaling exponents for Luttinger liquids

Proof of Gaussian fluctuations in certain stochastic models

Abstract

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse distance decay. In the surface picture one easily obtains the Haldane relation and identifies the scaling exponents governing the low energy, Luttinger liquid behavior. For the stochastic particle model we develop a hydrodynamic fluctuation theory, through which in some cases the large distance Gaussian fluctuations are proved nonperturbatively.