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Quantum Interference, Graphs, Walks, and Polynomials.

Yuta Tsuji1, Ernesto Estrada2, Ramis Movassagh3

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Summary
This summary is machine-generated.

Quantum interference in molecular conductance is explained by graph theory. Only odd-length walks contribute to conductivity, with cancellations causing interference in electron transport.

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Graph Theory

Background:

  • Quantum interference (QI) significantly impacts molecular conductance.
  • Understanding QI requires analyzing electron transmission through molecular graphs.

Purpose of the Study:

  • To explore quantum interference in molecular conductance using graph theory.
  • To investigate the role of walks on lattices and Green's function expansions.

Main Methods:

  • Applying graph theory and lattice walk analysis.
  • Utilizing the Cayley-Hamilton and Coulson-Rushbrooke pairing theorems.
  • Deriving finite series expansions for the Green's function.

Main Results:

  • Established that only odd-length walks contribute to molecular conductivity.
  • Identified conditions for QI, including cases with only even-length walks or cancellations among odd-length walks.
  • Extended analysis to nonalternant hydrocarbons, noting QI can arise from cancellations of both odd and even-length walk terms.

Conclusions:

  • Graph theory provides a framework for understanding QI in molecular conductance.
  • The study advances the understanding of electron transport phenomena in molecules.
  • Introduced perturbation theory and infinite series expansions for further research.