Evolution of a vibrational wave packet on a disordered chain

American Journal of Physics

Volumn 66, Issue 6, 1998, Pages 497-506

  Allen, Philip B ^a   Kelner, Jonathan ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b Wheatley School   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032339748     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18890     Document Type: Article

References (21)

1. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996), 7th ed., see especially pp. 99-100.
2. N. F. Mott and W. D. Twose, "The theory of impurity conduction," Adv. Phys. 10, 107-163 (1961); see especially pp. 137-139.
3. The original article is P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958); Anderson's Nobel address is reprinted in "Local moments and localized states," Rev. Mod. Phys. 50, 191-201 (1978).
4. The original article is P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958); Anderson's Nobel address is reprinted in "Local moments and localized states," Rev. Mod. Phys. 50, 191-201 (1978).
5. Mott's Nobel address is reprinted in "Electrons in glass," Rev. Mod. Phys. 50, 203-208 (1978).
6. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, 1995).
7. D. J. Thouless, "Electrons in disordered systems and the theory of localization," Phys. Rep. 13C, 93-142 (1974).
8. M. Silva Santos, E. Soares Rodrigues, and P. M. Castro de Oliveira, "Spring-mass chains: Theoretical and experimental studies," Am. J. Phys. 58, 923-928 (1990).
9. S. Parmley, T. Zobrist, T. Clough, A. Perez-Miller, M. Makely, and R. Yu. "Vibrational properties of a loaded string," Am. J. Phys. 63, 547-553 (1995).
10. J. Hori, Spectral Properties of Disordered Chains and Lattices (Pergamon, New York, 1968).
11. S. Alexander, J. Bernasconi, R. Orbach, and W. R. Schneider, "Excitation dynamics in random one-dimensional systems," Rev. Mod. Phys. 53, 175-198 (1981).
12. J. Fabian, "Decay of localized vibrational states in glasses: A one-dimensional example," Phys. Rev. B 55, 3328-3331 (1997).
13. R. J. Bell and P. Dean, "Atomic vibrations in vitreous silica," Discuss. Faraday Soc. 50, 55-61 (1970).
14. M. Ya. Azbel, "One dimension. Thermodynamics, kinetics, eigenstates, and universality," Phys. Rev. B 27, 3901-3904 (1983); "Eigenstates and properties of random systems in one dimension at temperature zero," 28, 4106-4125 (1983).
15. M. Ya. Azbel, "One dimension. Thermodynamics, kinetics, eigenstates, and universality," Phys. Rev. B 27, 3901-3904 (1983); "Eigenstates and properties of random systems in one dimension at temperature zero," 28, 4106-4125 (1983).
16. (ω-ω0)2/2δω2-1]p(ω).
17. P. A. Lee and T. V. Ramakrishnan, "Disordered electronic systems," Rev. Mod. Phys. 57, 287-337 (1985).
18. S. Chakravarty and A. Schmid, "Weak localization: The quasiclassical theory of electrons in a random potential," Phys. Rep. 140, 194 (1986).
19. See Ref. 1, pp. 119-120, and problem 1, p. 139.
20. D. Quinney, An Introduction to the Numerical Solution of Differential Equations (Research Studies Press, Letchworth, or Wiley, New York, 1985), p. 114ff.
21. L. Verlet, "Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules," Phys. Rev. 159, 98-103 (1967).