A monatomic chain with an impurity in mass and Hooke constant. (English) Zbl 1516.82027
Summary: A classical monatomic chain with an impurity in both mass and Hooke constant is studied by means of the recurrence relations method. The momentum autocorrelation function of the impurity is contributed by resonant poles and a branch cut. Though the model has two pairs of poles but only one pair is physical and contributes a cosine to the momentum autocorrelation function, whose frequency and amplitude are derived. The cut contribution is given by a convolution product of a sine and a sum of two Bessel functions of zeroth and second order. The memory function of the model is also derived which is contributed by a pair of poles and a branch cut. The former gives a cosine and the latter a convolution of a sine and a sum of two Bessel functions. The ergodicity of the momentum of the impurity is also discussed.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
Keywords:
statistical and nonlinear physicsReferences:
| [1] | Montroll, E. W.; Potts, R. B., Phys. Rev., 100, 525 (1955) · doi:10.1103/PhysRev.100.525 |
| [2] | Mazur, P.; Montroll, E. W.; Potts, R. P., J. Wash. Acad. Sci., 46, 2 (1956) |
| [3] | A.A. Maradudin, E.W. Montroll, G.H. Weiss, inTheory of Lattice Dynamics in the Harmonic Approximation (Academic, New York, 1963), p. 179 |
| [4] | Dean, P., J. Inst. Math. Appl., 3, 98 (1967) · doi:10.1093/imamat/3.1.98 |
| [5] | Fox, R. F., Phys. Rev. A, 27, 3216 (1983) · doi:10.1103/PhysRevA.27.3216 |
| [6] | Baker, A. S. Jr.; Sievers, A. J., Rev. Mod. Phys., 47, S1 (1975) · doi:10.1103/RevModPhys.47.S1.2 |
| [7] | Lee, M. H., Phys. Rev. Lett., 49, 1072 (1982) · doi:10.1103/PhysRevLett.49.1072 |
| [8] | Lee, M. H., J. Math. Phys., 24, 2512 (1983) · doi:10.1063/1.525628 |
| [9] | Lee, M. H.; Hong, J.; Florencio, J. Jr., Phys. Scr., T19, 498 (1987) · doi:10.1088/0031-8949/1987/T19B/029 |
| [10] | Balucani, U.; Lee, M. H.; Tognetti, V., Phys. Rep., 373, 409 (2003) · Zbl 1005.82018 · doi:10.1016/S0370-1573(02)00430-1 |
| [11] | Lee, M. H.; Hong, J., Phys. Rev. Lett., 48, 634 (1982) · doi:10.1103/PhysRevLett.48.634 |
| [12] | Lee, M. H.; Hong, J., Phys. Rev. B, 32, 7734 (1985) · doi:10.1103/PhysRevB.32.7734 |
| [13] | Silva, E. M., Phys. Rev. E, 92, 042146 (2015) · doi:10.1103/PhysRevE.92.042146 |
| [14] | Sen, S.; Long, M., Phys. Rev. B, 46, 14617 (1992) · doi:10.1103/PhysRevB.46.14617 |
| [15] | Sen, S., Physica A, 360, 304 (2006) · doi:10.1016/j.physa.2005.06.047 |
| [16] | Mokshin, A. V.; Yulmetyev, R. M.; Hanggi, P., Phys. Rev. Lett., 95, 200601 (2005) · doi:10.1103/PhysRevLett.95.200601 |
| [17] | Chen, S. X.; Shen, Y. Y.; Kong, X. M., Phys. Rev. B, 82, 174404 (2010) · doi:10.1103/PhysRevB.82.174404 |
| [18] | de Alcantara Bonfim, O. F.; Florencio, J., Phys. Rev. E, 92, 042115 (2015) |
| [19] | Nunes, M. E.S.; Silva, E. M.; Martins, P. H.I.; Plascak, J. A.; Florencio, J., Phys. Rev. E, 98, 042124 (2018) · doi:10.1103/PhysRevE.98.042124 |
| [20] | Florencio, J. Jr.; Lee, M. H., Phys. Rev. A, 31, 3231 (1985) · doi:10.1103/PhysRevA.31.3231 |
| [21] | Wierling, A., Eur. Phys. J. B, 85, 20 (2012) · doi:10.1140/epjb/e2011-20571-5 |
| [22] | Lee, M. H.; Florencio, J. Jr.; Hong, J., J. Phys. A, 22, L331 (1989) · doi:10.1088/0305-4470/22/8/005 |
| [23] | Yu, M. B., Eur. Phys. J. B, 86, 57 (2013) · Zbl 1515.70031 · doi:10.1140/epjb/e2012-30844-0 |
| [24] | Yu, M. B., Phys. Lett. A, 380, 3583 (2016) · Zbl 1366.62180 · doi:10.1016/j.physleta.2016.08.042 |
| [25] | Yu, M. B., Eur. Phys. J. B, 90, 87 (2017) · doi:10.1140/epjb/e2017-70752-1 |
| [26] | Yu, M. B., Physica A, 398, 252 (2014) · Zbl 1395.82065 · doi:10.1016/j.physa.2013.11.023 |
| [27] | Yu, M. B., Eur. Phys. J. B, 91, 25 (2018) · doi:10.1140/epjb/e2017-80402-3 |
| [28] | G.E. Roberts, H. Kaufman, inTable of Laplace Transforms (Saunders, Philadelphia, 1966), p. 196 · Zbl 0137.08901 |
| [29] | I.S. Gradsgteyn, I.N. Ryzhik, inTable of Integrals, Series and Products, 7th edn. (A&P 2007), p. 1111 · Zbl 1208.65001 |
| [30] | I.S. Gradsgteyn, I.N. Ryzhik, inTable of Integrals, Series and Products, 7th edn. (A&P 2007), p. 398 · Zbl 1208.65001 |
| [31] | Ullersma, P., Physica, 32, 27 (1966) · doi:10.1016/0031-8914(66)90102-9 |
| [32] | Ullersma, P., Physica, 32, 56 (1966) · doi:10.1016/0031-8914(66)90103-0 |
| [33] | Ullersma, P., Physica, 32, 74 (1966) · doi:10.1016/0031-8914(66)90104-2 |
| [34] | Sen, S.; Cai, Z. X.; Mahanti, S. D., Phys. Rev. Lett., 72, 3287 (1994) · doi:10.1103/PhysRevLett.72.3287 |
| [35] | Lee, M. H., Phys. Rev. Lett., 87, 250061 (2001) |
| [36] | Lee, M. H., Phys. Rev. Lett., 98, 190601 (2007) · Zbl 1228.82054 · doi:10.1103/PhysRevLett.98.190601 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
