The Quantum Steeplechase

Abstract

Quantum Steeplechase is the study of a Luttinger liquid (LL) in one dimension in the presence of a finite number of barriers and wells clustered around an origin. The powerful non-chiral bosonization technique (NCBT) is introduced to write down closed formulas for the two-point functions in the sense of the random phase approximation (RPA). Unlike g-ology based methods that are tied to the translationally invariant, free particle basis, the NCBT explicitly makes use of the translationally non-invariant single particle wavefunctions. The present method that provides the most singular part of the asymptotically exact Green function in a closed form, is in contrast to competing methods that require a combination of renormalization group and/or numerical methods in addition to the bosonization techniques.