Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

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.

References in corpus (4)

• An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime
• The free energy singularity of the asymmetric 6--vertex model and the excitations of the asymmetric XXZ chain
• Interacting fermions in one dimension: The Tomonaga-Luttinger model
• Reduction formula for fermion loops and density correlations of the 1D Fermi gas

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• KPZ fluctuations in finite volume
• Non-local meta-conformal invariance in diffusion-limited erosion
• KPZ modes in $d$-dimensional directed polymers
• Quest for the golden ratio universality class