### Abstract

This paper develops the theory of a recently introduced computational method for molecular dynamics. The method in question uses the backward‐Euler method to solve the classical Langevin equations of a molecular system. Parameters are chosen to produce a cutoff frequency ω_{c}, which may be set equal to kT/h to simulate quantum‐mechanical effects. In the present paper, an ensemble of identical Hamiltonian systems modeled by the backward‐Euler/Langevin method is considered, an integral equation for the equilibrium phase‐space density is derived, and an asymptotic analysis of that integral equation in the limit Δt → 0 is performed. The result of this asymptotic analysis is a second‐order partial differential equation for the equilibrium phase‐space density expressed as a function of the constants of the motion. This equation is solved in two special cases: a system of coupled harmonic oscillators and a diatomic molecule with a stiff bond.

Original language | English (US) |
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Pages (from-to) | 599-645 |

Number of pages | 47 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 43 |

Issue number | 5 |

DOIs | |

State | Published - Jul 1990 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*43*(5), 599-645. https://doi.org/10.1002/cpa.3160430503