Nose-Hoover thermostat: Difference between revisions

Revision as of 14:10, 29 May 2019

In the approach by Nosé and Hoover^[1]^[2]^[3] an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate $s$ which is introduced into the Lagrangian of the system. This Lagrangian for an $N$ is written as

${\mathcal {L}}=\sum \limits _{i=1}^{N}{\frac {m_{i}}{2}}s^{2}\mathbf {\dot {r}} _{i}^{2}$

References

[nose:jcp:1984-1] S. Nosé, J. Chem. Phys. 81, 511 (1984).

[nose:ptp:1991-2] S. Nosé, Prog. Theor. Phys. Suppl. 103, 1 (1991).

[hoover:pra:1985-3] W. G. Hoover, Phys. Rev. A 31, 1695 (1985).

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[2]

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-In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}} an extra degree of freedom is introduced in the Hamiltonian.
+In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}} an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for an <math>N</math> is written as
+<math>
+\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \mathbf{\dot{r}}_{i}^{2}
+</math>
 == References ==