Ergodicity of the Stochastic Nosé–Hoover Heat Bath

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概要

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• We numerically study the ergodicity of the stochastic Nosé–Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé–Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker–Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker–Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi–Pasta–Ulam (FPU-$\beta$) and Frenkel–Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

• 2010-07-15

著者

• Li Baowen

  Department Of Physics And Centre For Computational Science And Engineering National University Of Si

• Li Baowen

  Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore

• Lo Wei

  P. O. Box 51, 91007, Tawau, Sabah, East Malaysia, Malaysia

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