The Quantum Steeplechase

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 nonchiral 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 noninvariant single particle wave functions. 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.