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.

References in corpus (28)

• Luttinger Liquid Behavior in Carbon Nanotubes
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
• Exact Conductance through Point Contacts in the $\nu =1/3$ Fractional Quantum Hall Effect
• Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices
• Experimental Evidence for Resonant-Tunneling in a Luttinger-Liquid
• Time-dependent density-matrix renormalization group: A systematic method for the study of quantum many-body systems out-of-equilibrium
• Friedel oscillations for interacting fermions in one dimension
• Nonequilibrium functional renormalization group for interacting quantum systems
• Functional renormalization group for non-equilibrium quantum many-body problems
• Impurity and correlation effects on transport in one-dimensional quantum wires
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• Properties of a Luttinger Liquid with Boundaries at Finite Temperature and Size
• Functional renormalization group for Luttinger liquids with impurities
• Density-matrix renormalisation group approach to quantum impurity problems
• Functional Integral Bosonization for Impurity in Luttinger Liquid
• Phase Coherence in a Random One-Dimensional System of Interacting Fermions: A Density Matrix Renormalization Group Study
• Scaling of the conductance in a quantum wire
• Numerical study of transport through a single impurity in a spinful Tomonaga-Luttinger liquid
• Exact Green's function for rectangular potentials and its application to quasi-bound states
• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• Friedel oscillations in a Luttinger liquid with long-range interactions
• Ponderous impurities in a Luttinger liquid
• The one step fermionic ladder
• Tomonaga-Luttinger model with an impurity for a weak two-body interaction
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• Sea-Boson Theory of Landau Fermi Liquids, Luttinger Liquids and Wigner Crystals
• A General Approach to Bosonization

Cited by in corpus (7)

• The one step fermionic ladder
• Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid
• Transport properties of a Luttinger liquid with a cluster of impurities
• Conductance of inhomogeneous Luttinger liquids with a finite bandwidth
• Density-density Correlation Function of Strongly Inhomogeneous Luttinger Liquids
• Non-Markovian transients in transport across chiral quantum wires using space-time non-equilibrium Green functions
• Density-density correlation functions of chiral Luttinger liquids with a point-contact impurity