Abstract
We study the deterministic dynamics of rotator chain with purely mechanical driving on the boundary by stability analysis and numerical simulation. Globally synchronous rotation, clustered synchronous rotation, and split synchronous rotation states are identified. In particular, we find that the single-peaked variance distribution of angular momenta is the consequence of the deterministic dynamics. As a result, the operational definition of temperature used in the previous studies on rotator chain should be revisited.
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References
A. Dhar, Heat transport in low-dimensional systems, Adv. Phys., 2008, 57(5): 457
S. Lepri, R. Livi, and A. Politi, Heat conduction in chains of nonlinear oscillators, Phys. Rev. Lett., 1997, 78(10): 1896
G. Casati, J. Ford, F. Vivaldi, and W. M. Visscher, Onedimensional classical many-body system having a normal thermal conductivity, Phys. Rev. Lett., 1984, 52(21): 1861
A. V. Savin and O. V. Gendelman, Heat conduction in onedimensional lattices with on-site potential, Phys. Rev. E, 2003, 67(4): 041205
Y. Zhong, Y. Zhang, J. Wang, and H. Zhao, Normal heat conduction in one-dimensional momentum conserving lattices with asymmetric interactions, Phys. Rev. E, 2012, 85(6): 060102
C. Giardinà, R. Livi, A. Politi, and M. Vassalli, Finite thermal conductivity in 1D lattices, Phys. Rev. Lett., 2000, 84(10): 2144
O. V. Gendelman and A. V. Savin, Normal heat conductivity of the one-dimensional lattice with periodic potential of nearest-neighbor interaction, Phys. Rev. Lett., 2000, 84(11): 2381
A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, Negative thermal conductivity of chains of rotors with mechanical forcing, Phys. Rev. E, 2011, 84(6): 061108
D. R. Nelson and D. S. Fisher, Dynamics of classical XY spins in one and two dimensions, Phys. Rev. B, 1977, 16(11): 4945
C. Anteneodo and C. Tsallis, Breakdown of exponential sensitivity to initial conditions: Role of the range of interactions, Phys. Rev. Lett., 1998, 80(24): 5313
D. Kulkarni, D. Schmidt, and S. K. Tsui, Eigenvalues of tridiagonal pseudo-Toeplitz matrices, Linear Algebra Appl., 1999, 297(1–3): 63
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd Ed., Cambridge: Cambridge University Press, 2012
M. Levi, F. Hoppensteadt, and W. Miranker, Q. Appl. Math., 1978, 37
S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity), 1st Ed., Westview Press, 2001
J. M. Haile, Molecular Dynamics Simulation: Elementary Methods (Wiley Professional), 1st Ed., Wiley-Interscience, 1997
S. Lepri, R. Livi, and A. Politi, Thermal conduction in classical low-dimensional lattices, Phys. Rep., 2003, 377(1): 1
R. Yuan and P. Ao, Beyond Itô versus Stratonovich, J. Stat. Mech., 2012, 07: P07010
R. Yuan, X. Wang, Y. Ma, B. Yuan, and P. Ao, Exploring a noisy van der Pol type oscillator with a stochastic approach, Phys. Rev. E, 2013, 87(6): 062109
Y. Ma, Q. Tan, R. Yuan, B. Yuan, and P. Ao, Potential function in a continuous dissipative chaotic system: decomposition scheme and role of strange attractor, arXiv: 1208.1654, 2012
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Ke, P., Zheng, ZG. Dynamics of rotator chain with dissipative boundary. Front. Phys. 9, 511–518 (2014). https://doi.org/10.1007/s11467-014-0427-z
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DOI: https://doi.org/10.1007/s11467-014-0427-z