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md2011-05-note_Part_5 - Nos-Hoover method[W Hoower...

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Nosé-Hoover method [W. Hoower, Phys.Rev.A 31, 1695 (1985)] I The Hamiltonian is modified by adding a virtual degree of freedom (time-scale variable s ) with its own K s and U s . I This introduces a dimensionless friction factor with virtual mass Q , which controls the rate of change in T . I The Hamiltonian and equations of motion become H = X i p i 2 m i + U ( q i ) + p 2 s 2 Q + gk B T ln ( s ) (30) d q i d t = p i m 1 ; d p i d t = - d V d q i - p s p i ; d p s d t = i p i m i - gk B T Q . (31) I Modified equations of motion guarantee that the original degrees of freedom follow properly the isotherm. I Nosé suggested Q gk B T ( g is the number of degrees of freedom in the system). Notes
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Nosé-Hoover Chain Method [Tobias et al., J.Phys.Chem. 97, 12959 (1993)] I A chain is formed of the parameters s so that one always controls the previous one. I This is needed for some cases to avoid ergodicity problems with the standard Nosé-Hoover method. I In the Massive Nosé-Hoover chain method, a thermostat is connected to every degree of freedom.
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