Abstract
We use recurrence relations method to study a classical harmonic diatomic chain. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are given in terms of integrals of real and complex elliptic functions for the acoustic and optical branches, respectively. Double convolution results respectively in integrals of trigonometric and hyperbolic functions for expansion coefficients of acoustic and optical branches.
Similar content being viewed by others
References
E.W. Montroll, R.B. Potts, Phys. Rev. 100, 525 (1955)
P. Mazur, E.W. Montroll, R.B. Potts, J. Wash. Acad. Sci. 46, 2 (1956)
A.A. Maradudin, E.W. Montroll, G.H. Weiss, in Theory of Lattice Dynamics in the Harmonic Approximation (Academic, New York, 1963), p. 179
P. Dean, J. Inst. Math. Appl. 3, 98 (1967)
R.F. Fox, Phys. Rev. A 27, 3216 (1983)
L.S. Garcia-Colin, J. Stat. Phys. 7, 243 (1973)
A.S. Baker Jr., A.J. Sievers, Rev. Mod. Phys. 47, S1 (1975)
M.H. Lee, Phys. Rev. Lett. 49, 1072 (1982)
M.H. Lee, J. Math. Phys. 24, 2512 (1983)
M.H. Lee, J. Hong, J. Florencio Jr., Physica Scripta T19, 498 (1987)
U. Balucani, M.H. Lee, V. Tognetti, Phys. Rep. 373, 409 (2003)
J. Florencio Jr., M.H. Lee, Phys. Rev. A 31, 3231 (1985)
M.H. Lee, J. Florencio Jr., J. Hong, J. Phys. A 22, L331 (1989)
M.B. Yu, J.H. Kim, M.H. Lee, J. Lumin. 45, 144 (1990)
M.B. Yu, Eur. Phys. J. B 86, 57 (2013)
M.B. Yu, Phys. Lett. A 380, 3583 (2016)
M.H. Lee, Symmetry 8, 22 (2016)
M.B. Yu, Eur. Phys. J. B 85, 379 (2012)
M.B. Yu, Physica A 398, 252 (2014)
M.B. Yu, Physica A 438, 469 (2015)
A.V. Mokshin, R.M. Yulmetyev, P. Hänggi, Phys. Rev. Lett. 95, 200601 (2005)
A. Wierling, Eur. Phys. J. B 85, 20 (2012)
S. Sen, M. Long, J. Appl. Phys. 73, 5474 (1993)
S. Sen, T.D. Blersch, Physica A 253, 178 (1998)
A.V. Mokshin, R.M. Yulmetyev, P. Hänggi, Phys. Rev. Lett. 95, 200601 (2005)
E.M. Silva, Phys. Rev. E 92, 042146 (2015)
P.R.C. Guimaraes, J.A. Placak, O.F. de Alcantara Bonfim, J. Florencio, Phys. Rev. E 92, 042115 (2015)
I.S. Gradsgteyn, I.N. Ryzhik, in Table of Integrals, Series and Products, 7th edn. (A&P, 2007), p. 34
I.S. Gradsgteyn, I.N. Ryzhik, in Table of Integrals, Series and Products, 7th edn. (A&P, 2007), p. 625
I.S. Gradsgteyn, I.N. Ryzhik, in Table of Integrals, Series and Products, 7th edn. (A&P, 2007), p. 152
I.S. Gradsgteyn, I.N. Ryzhik, in Table of Integrals, Series and Products, 7th edn. (A&P, 2007), p. 110
I.S. Gradsgteyn, I.N. Ryzhik, in Table of Integrals, Series and Products, 7th edn. (A&P, 2007), p. 29
G.J. Tee, New Zealand J. Math. 41, 83 (2011)
L.M. Milne-Thomson, Jacobian Elliptic Functions and Theta Functions, No. 16, 17, p. 569, in Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, Appl. Math. Ser., edited by M. Abramowitz, I.A. Stegun (National Bureau of Standards, Washington, D.C., 1964), Vol. 55
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, M.B. Analytical expressions for momentum autocorrelation function of a classic diatomic chain. Eur. Phys. J. B 90, 87 (2017). https://doi.org/10.1140/epjb/e2017-70752-1
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2017-70752-1