Thermostats

    Molecular dynamics is the simulation of Newton's equations for atoms and molecules on a computer. It is used in systems of a few hundred to a few million atoms, being much less intensive than quantum approaches, and giving more detailed information on dynamical properties such as time correlation functions than competing stochastic Monte-Carlo methods. Thermostats are additional terms in the equations of motion to simulate the effects of the environment ("heat bath") in molecular dynamics simulations; the main alternative is the stochastic (Langevin) approach. Examples include the Gaussian thermostat, which fixes the energy to remain constant, for example in a nonequilibrium driven system, and the Nose-Hoover thermostat which is a feedback mechanism that can be shown to reproduce the canonical distribution of statistical mechanics.

    My work demonstrates dynamical effects such as Lyapunov exponent pairing and local Hamiltonian structure for thermostatted systems. Notice that these systems were not expected to be Hamiltonian since in the usual formulation they are dissipative and lead to fractal attractors. The Hamiltonian structure of the equations is very important, as it allows the use of the much stabler sympletic integration algorithms; the "Nose-Poincare" approach comes from this work. The theory is general; specific numerical simulations are carried out for the Lorentz gas. Recently I have proposed some new approaches, a "Smoluchowski" thermostat, in which all (presumed rapidly varying) momentum degrees of freedom are averaged out, and in the same paper, a Nose-Hoover-Langevin thermostat that combines the best features of the deterministic Nose-Hoover approach and the stochastic Langevin equation.

  1. Conjugate Pairing in the three dimensional periodic Lorentz gas C. P. Dettmann, G. P. Morriss and L. Rondoni, Phys. Rev. E 52, R5746-R5748 (1995) pdf
  2. Proof of Lyapunov exponent pairing for systems at constant kinetic energy. C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 53, R5545-R5548 (1996) pdf ps["Dettmann-Morriss theorem"; mis-cited 15 times at last count!]
  3. Hamiltonian formulation of the Gaussian isokinetic thermostat. C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 54, 2495-2500 (1996) pdf ps
  4. The field dependence of Lyapunov exponents for nonequilibrium systems G. P. Morriss, C. P. Dettmann and D. J. Isbister, Phys. Rev. E, 54 4748-4654 (1996) pdf
  5. Crisis in the periodic Lorentz gas. C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54, 4782-4790 (1996) pdf (4.9M)
  6. Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics C. P. Dettmann and G. P. Morriss, Phys. Rev. E, 55, 3693-3696 (1997) pdf ps arxiv [Origin of the "Nose-Poincare" symplectic integrator]
  7. Stability ordering of cycle expansions C. P. Dettmann and G. P. Morriss, Phys. Rev. Lett. 78, 4201-4204 (1997) pdf ps arxiv
  8. Irreversibility, diffusion and multifractal measures in thermostatted systems, C. P. Dettmann, G. P. Morriss, and L. Rondoni, Chaos, Solitons and Fractals 8, 783-792 (1997)
  9. Recent results for the thermostatted Lorentz gas, G. P. Morriss, C. P. Dettmann and L. Rondoni, Physica A 240, 84-95 (1997)
  10. Thermostats: Analysis and application G. P. Morriss and C. P. Dettmann, Chaos 8,321-336 (1998) ps pdf
  11. Hamiltonian for a restricted isoenergetic thermostat C. P. Dettmann, Phys. Rev. E 60,7576-7577 (1999) pdf ps arxiv
  12. Thermostats for "slow" configurational modes A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Stat. Phys. 128 1321-1336 (2007) [Origin of the "Nose-Hoover-Langevin" thermostat] pdf arxiv
  13. Notes on configurational thermostat schemes, A. A. Samoletov, C. P. Dettmann and M. A. J. Chaplain, J. Chem. Phys. 132 246101 (2010) pdf arxiv
  14. Book chapter: The Lorentz gas as a paradigm for nonequilibrium stationary states, C. P. Dettmann, pp 315-365 in Hard ball systems and the Lorentz gas (edited by D. Szasz), Encyclopaedia of Mathematical Sciences Vol 101 (Springer, 2000). Full size version, 50 pages pdf. Environmental microscopic version, 25 pages pdf.

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