Monte Carlo in the microcanonical ensemble: Difference between revisions
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== Integration of the kinetic degrees of freedom == | |||
Considering a system of <math> \left. N \right. </math> identical particles, with total energy <math> \left. H \right. </math> given by: | |||
: <math> H = \sum_{i=1}^{3N} \frac{p_i^2}{2m} + U \left( X^{3N} \right). </math> | |||
where the first term on the right hand side is the kinetic energy, whereas the second one is | |||
the potential energy (function of the position coordinates) | |||
From the partition function in the [[microcanonical ensemble]] we can integrate | |||
PEOPLE AT WORK, SORRY FOR ANY INCONVENIENCE | |||
Revision as of 15:54, 28 February 2007
Integration of the kinetic degrees of freedom
Considering a system of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. N \right. } identical particles, with total energy Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. H \right. } given by:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H = \sum_{i=1}^{3N} \frac{p_i^2}{2m} + U \left( X^{3N} \right). }
where the first term on the right hand side is the kinetic energy, whereas the second one is the potential energy (function of the position coordinates)
From the partition function in the microcanonical ensemble we can integrate
PEOPLE AT WORK, SORRY FOR ANY INCONVENIENCE