Editing Metropolis Monte Carlo
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 14: | Line 14: | ||
A configuration is a microscopic realisation of the ''thermodynamic state'' of the system. | A configuration is a microscopic realisation of the ''thermodynamic state'' of the system. | ||
To define a configuration (denoted as <math> \left. X \right. </math> ) we usually require: | To define a configuration (denoted as <math> \left. X \right. </math> ) we usually require: | ||
*The position coordinates of the particles | *The position coordinates of the particles | ||
*Depending on the problem, other variables like volume, number of particles, etc. | *Depending on the problem, other variables like volume, number of particles, etc. | ||
The probability of a given configuration, denoted as <math> \Pi \left( X | k \right) </math>, | The probability of a given configuration, denoted as <math> \Pi \left( X | k \right) </math>, | ||
depends on the parameters <math> k </math> (e.g. | depends on the parameters <math> k </math> (e.g. temperature, pressure) | ||
Example: | Example: | ||
Line 25: | Line 29: | ||
In most of the cases <math> \Pi \left( X | k \right) </math> exhibits the following features: | In most of the cases <math> \Pi \left( X | k \right) </math> exhibits the following features: | ||
* It is a function of many variables | * It is a function of many variables | ||
* Only for a very small fraction of the configurational space the value of <math> \Pi \left( X | k \right) </math> is not negligible | * Only for a very small fraction of the configurational space the value of <math> \Pi \left( X | k \right) </math> is not negligible | ||
Due to these properties, Metropolis Monte Carlo requires the use of '''Importance Sampling''' techniques | Due to these properties, Metropolis Monte Carlo requires the use of '''Importance Sampling''' techniques | ||