State Orthogonalization by Building a Hilbert Space: A New Approach to Electronic Quantum Transport in Molecular Wires

TL;DR

This paper introduces a novel Hilbert space embedding technique to orthogonalize non-orthogonal states, enabling exact solutions for quantum transport in molecular wires and predicting unique conductance antiresonances.

Contribution

It presents a new method for handling non-orthogonal quantum states by embedding them in an orthogonal Hilbert space, applied to molecular wire transport problems.

Findings

Predicted conductance antiresonances due to non-orthogonality

Provided an exact solution framework for non-orthogonal quantum models

Demonstrated the method's effectiveness in molecular electronics

Abstract

Quantum descriptions of many complex systems are formulated most naturally in bases of states that are not mutually orthogonal. We introduce a general and powerful yet simple approach that facilitates solving such models exactly by embedding the non-orthogonal states in a new Hilbert space in which they are by definition mutually orthogonal. This novel approach is applied to electronic transport in molecular quantum wires and is used to predict conductance antiresonances of a new type that arise solely out of the non-orthogonality of the local orbitals on different sites of the wire.