Random-walk statistics in moment-based O(N) tight binding and applications in carbon nanotubes

Adam D. Schuyler, G. S. Chirikjian, Jun Qiang Lu, H. T. Johnson

Research output: Contribution to journalArticle

Abstract

A computational framework for a moment-based O(N) tight-binding atomistic method is presented, analyzed, and applied to the problem of electronic properties of deformed carbon nanotubes, where N is the number of atoms in the system. The moment-based approach is based on the maximum entropy and kernel polynomial methods for constructing the electronic density of states from local statistical information about the environment around individual atoms. Random-walk statistics are formally presented as the basis for several methods to collect the moments of the density of states in a computationally efficient manner. The computational complexity and accuracy of these methods are systematically analyzed. Using these methods for the problem of deformed carbon nanotubes, it is shown that the computational cost for some cases, per atom, scales as efficiently as O(M log M), where M is the desired number of moments in the expansion of the density of states. These methods are compared to other methods such as direct diagonalization and a Green's function approach.

Original languageEnglish (US)
Article number046701
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume71
Issue number4
DOIs
StatePublished - Apr 1 2005

Fingerprint

Tight-binding
Nanotubes
random walk
Random walk
Carbon
carbon nanotubes
statistics
Moment
Statistics
moments
Density of States
atoms
electronics
Polynomial Methods
polynomials
Green's functions
Kernel Methods
Electronic Properties
Diagonalization
Maximum Entropy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Random-walk statistics in moment-based O(N) tight binding and applications in carbon nanotubes. / Schuyler, Adam D.; Chirikjian, G. S.; Lu, Jun Qiang; Johnson, H. T.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 71, No. 4, 046701, 01.04.2005.

Research output: Contribution to journalArticle

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