Nose-Hoover thermostat: Difference between revisions

Revision as of 14:11, 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

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

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).

[1]

[2]

[3]

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