Nose-Hoover thermostat: Difference between revisions

Revision as of 08:29, 31 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

${\displaystyle \mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} + . }$

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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@@ Line 2: / Line 2: @@
 <math>
-\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \hat{\bold{r}}_{i}^{2} + .
+\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} + .
 </math>