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Constraint methodtemperatureas functionof time123Nosé - Hoover thermostatShuishi Nosé (1984)Introduce one new degree of freedom sthat describes the heat bath, havingpotential energy:kinetic energy:V() s ( m1) kTlns1Ks ( ) Qs22124
Nosé - Hoover thermostatThis new degree of freedom s couplesto the particle motion through:p sv sx im iii1iOne has a new Hamiltonian:N 2pi1 2 H QsV 2x1,..., xNV( s)2ms2iwhich corresponds to introducea new time scale dt´ = s dt.125Nosé - Hoover thermostatthen theHamiltonequationsgive:ps QsDefine: dxiHpi 2dt pimisds Hps dt psQdpiH V x ,..., x fidt xidpsH1 p dt s s m sx 1 N iN 2i( m 1) kT2 i1i126
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