Dynamics of rotator chain with dissipative boundary
Pu Ke,Zhi-Gang Zheng()
Department of Physics and the Beijing–Hong Kong–Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China
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.
A. Dhar, Heat transport in low-dimensional systems, Adv. Phys., 2008, 57(5): 457 doi: 10.1080/00018730802538522
2
S. Lepri, R. Livi, and A. Politi, Heat conduction in chains of nonlinear oscillators, Phys. Rev. Lett., 1997, 78(10): 1896 doi: 10.1103/PhysRevLett.78.1896
3
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 doi: 10.1103/PhysRevLett.52.1861
4
A. V. Savin and O. V. Gendelman, Heat conduction in onedimensional lattices with on-site potential, Phys. Rev. E, 2003, 67(4): 041205 doi: 10.1103/PhysRevE.67.041205
5
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 doi: 10.1103/PhysRevE.85.060102
6
C. Giardinà, R. Livi, A. Politi, and M. Vassalli, Finite thermal conductivity in 1D lattices, Phys. Rev. Lett., 2000, 84(10): 2144 doi: 10.1103/PhysRevLett.84.2144
7
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 doi: 10.1103/PhysRevLett.84.2381
8
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 doi: 10.1103/PhysRevE.84.061108
9
D. R. Nelson and D. S. Fisher, Dynamics of classical XY spins in one and two dimensions, Phys. Rev. B, 1977, 16(11): 4945 doi: 10.1103/PhysRevB.16.4945
10
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 doi: 10.1103/PhysRevLett.80.5313
11
D. Kulkarni, D. Schmidt, and S. K. Tsui, Eigenvalues of tridiagonal pseudo-Toeplitz matrices, Linear Algebra Appl., 1999, 297(1-3): 63 doi: 10.1016/S0024-3795(99)00114-7
12
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd Ed., Cambridge: Cambridge University Press, 2012 doi: 10.1017/CBO9781139020411
13
M. Levi, F. Hoppensteadt, and W. Miranker, Q. Appl. Math., 1978, 37
14
S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity), 1st Ed., Westview Press, 2001
15
J. M. Haile, Molecular Dynamics Simulation: Elementary Methods (Wiley Professional), 1st Ed., Wiley-Interscience, 1997
16
S. Lepri, R. Livi, and A. Politi, Thermal conduction in classical low-dimensional lattices, Phys. Rep., 2003, 377(1): 1 doi: 10.1016/S0370-1573(02)00558-6
17
R. Yuan and P. Ao, Beyond It? versus Stratonovich, J. Stat. Mech., 2012, 07: P07010
18
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 doi: 10.1103/PhysRevE.87.062109
19
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
