Time Evolution of a Harmonic Chain with Fixed Boundary Conditions

  • Received Date: January 16, 2011
  • Published Date: March 31, 2011
  • We investigate the time evolution of a coupled harmonic-oscillator chain under two boundary conditions: two ends fixed and one end fixed. The dynamics of the coupled chain and the steady variances of the coordinates are explicitly analyzed by the entire Hamiltonian using a diagonalization approach. Our result shows the desirable symmetry for the case with two ends fixed. In particular, a Langevin simulation technique is proposed to sample the harmonic chain across the entire equilibrium distribution.
  • Article Text

  • [1] Smith S T and Onofrio R 2008 Eur. Phys. J. B 61 271
    [2] Chaudhuri J R, Chaudhury P and Chattopadhyay S 2009 J. Chem. Phys. 130 234109
    [3] Wei Q, Smith S T and Onofrio R 2009 Phys. Rev. E 79 031128
    [4] Rosa J and Beims M W 2008 Phys. Rev. E 78 031126
    [5] Plyukhin A V and Schofield J 2002 Phys. Rev. E 65 026603
    [6] Roy D and Dhar A 2007 Phys. Rev. B 75 195110
    [7] Zwanzig R W 1960 J. Chem. Phys. 32 1173
    [8] Adelman S A and Doll J D 1974 J. Chem. Phys. 61 4242
    [9] Zeiri Y 1987 J. Chem. Phys. 86 7181
    [10] Kim J and Sawada I 2000 Phys. Rev. E 61 R2172
    [11] Barrio R A, Galeener F L and Martinez E 1984 Phys. Rev. Lett. 52 1786
    [12] Dhar A and Roy D 2006 J. Stat. Phys. 125 805
    [13] Segal D 2009 Phys. Rev. E 79 012103
    [14] Florencio J and Lee M H 1985 Phys. Rev. A 31 3231
    [15] Plyukhin A V and Schofield J 2001 Phys. Rev. E 64 041103
    [16] Cai W, de Koning M, Bulatov V V and Yip S 2000 Phys. Rev. Lett. 85 3213
    [17] Weiss U 1999 Quantum Dissipative Systems 2nd edn (Singapore: World Scientific)
    [18] Wagner G J, Karpov E G and Liu W K 2004 Comput. Methods Appl. Mech. Engrg. 193 1579
    [19] Lievens S, Stoilova N I and Van der Jeugt J 2008 J. Math. Phys. 49 073502
    [20] Bao J D 2009 The Stochastic Simulation Methods in Calssical and Quantum Dissipation Systems (Beijing: Science)(in Chinese)

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