Quantum Monte Carlo Computation of Static and Time-Dependent Thermodynamic Properties of Lennard-Jones Crystals

  • Arthur R. McGurn
  • Alexei A. Maradudin
  • Richard F. Wallis
Part of the NATO ASI Series book series (NSSB, volume 264)


Recently there has been much interest in the study of the thermodynamics of many-body quantum mechanical systems by means of Quantum Monte Carlo (QMC) computer simulation techniques(1–4). Applications of QMC methods to the study of spin systems, the Hubbard model, and to systems of boson and fermion particles have shown them to be effective in the accurate computation of static thermodynamic properties(1–4). However, in spite of these successful QMC treatments of static thermodynamics, the determination of time-dependent thermodynamic averages (spin correlation functions, atomic displacement correlation functions, etc.), related to the time-dependent response of quantum many-body systems, has been less forthcoming. Aside from the increased bookkeeping difficulties associated with having to determine averages which depend on the new variable of time, one finds that this variable enters time-dependent computed averages in such a way that analytic continuation techniques, commonly employed in Green’s function treatments of such properties, are of little or no value in developing QMC methods for this problem.(3,5)


Harmonic Approximation Continue Fraction Expansion Quantum Monte Carlo Dimensional Chain Spin Correlation Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    NATO Advanced Research Workshop on Monte Carlo Methods in Quantum Problems, ed. Malvin H. Kalos, D. Reidel Pub. Co., Hingham, MA, USA (1984).Google Scholar
  2. 2.
    Quantum Monte Carlo Methods in Equilibrium and Non-Equilibrium Systems, ed. M. Suzuki, Springer-Verlag, Berlin and New York (1987).Google Scholar
  3. 3.
    Journal of Statistical Physics 43, pp. 729–1243 (1986).Google Scholar
  4. 4.
    International Workshop on Quantum Simulations of Condensed Matter Phenomena, eds. J. D. Doll and J. E. Gubernatis, World Scientific, Singapore (1990).Google Scholar
  5. 5.
    E. L. Pollock and D. M. Ceperley, Phys. Rev. B30, 2555–2568 (1984).ADSGoogle Scholar
  6. 6.
    Statistical Physics, L. D. Landau and E. M. Lifshitz, Pergamon Press, Oxford (1980), p. 537.Google Scholar
  7. 7.
    A. R. McGurn, P. Ryan, A. A. Maradudin, and R. F. Wallis, Phys. Rev. B40, 2407–2413 (1989).ADSGoogle Scholar
  8. 8.
    H. Mori, Prog. Theor. Phys. 34, 399–416 (1965).ADSCrossRefGoogle Scholar
  9. 9.
    A. A. Maradudin, R. F. Wallis, A. R. McGurn, M. S. Daw, and A.J.C. Ladd, in Lattice Dynamics and Semiconductor Physics, eds. J. Xia, Z. Gan, R. Han, G. Qin, G. Yang, H. Zheng, Z. Zhong, and B. Zhu, World Scientific, Singapore, (1990), pp. 103–157.Google Scholar
  10. 10.
    F. Gürsey, Proc. Camb. Phil. Soc. 46, 182 (1950).ADSMATHCrossRefGoogle Scholar
  11. 11.
    A. A. Maradudin, in Physics of Phonons, ed. T. Paszkiewicz, Springer-Verlag, Berlin (1987), pp. 1–47.CrossRefGoogle Scholar
  12. 12.
    H. F. Trotter, Proc. Am. Math. Soc. 110, 545 551 (1959)MathSciNetGoogle Scholar
  13. 13.
    M. Suzuki, Prog. Theor Phys. 56, 145–1469 (1976).Google Scholar
  14. 14.
    M. Takahashi and M. Imada, J. Phys. Soc. Jpn 53, 3765–3769 (1984).ADSCrossRefGoogle Scholar
  15. 15.
    Applications of Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer-Verlag, Berlin (1984).Google Scholar
  16. 16.
    S. W. Lovesey, Condensed Matter Physics: Dynamic Correlations, second edition, Benjamin/Cummings Pub. Co., Inc. (1986), Ch. 1.Google Scholar
  17. 17.
    S. W. Lovesey, in Physics in One Dimension, eds. J. Bernasconi and T. Schneider, Springer-Verlag, Berlin (1981) pp. 129–139.CrossRefGoogle Scholar
  18. 18.
    H. Tomita and H. Mashiyama, Prog. Theor. Phys. 48, 1133–1149 (1972).ADSCrossRefGoogle Scholar
  19. 19.
    K. Tomita and H. Tomita, Prog. Theor. Phys. 45, 1407–1436 (1971).ADSCrossRefGoogle Scholar
  20. 20.
    R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path-Integrals, McGraw-Hill, New York (1965), Ch. 7.MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Arthur R. McGurn
    • 1
  • Alexei A. Maradudin
    • 2
  • Richard F. Wallis
    • 2
  1. 1.Department of PhysicsWestern Michigan UniversityKalamazooUSA
  2. 2.Department of PhysicsUniversity of CaliforniaIrvineUSA

Personalised recommendations