A NOTE ON THE DYNAMICS OF A DISORDERED LINEAR CHAIN

Abstract

By a disordered linear chain, we mean a chain of onedimensional harmonic linear oscillators, each coupled to its nearest neighbors by harmonic forces, with the mass of each oscillator and the coupling parameters taken to be random variables with known distributions. The problem of calculating the distribution function of the frequencies of the normal modes of vibration of the chain in the limit as the chain becomes infinitely long was resolved by F. J. dyson. This paper presents a simple algebraic proof of the essential limit relation in Dyson's paper.

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Document Details

Document Type
Technical Report
Publication Date
Aug 03, 1955
Accession Number
AD0604923

Entities

People

  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Couplings
  • Distribution Functions
  • Dynamics
  • Frequency
  • Frequency Shift
  • Microfiche
  • Oscillators
  • Random Variables
  • Vibration

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.