Editing Monte Carlo in the microcanonical ensemble
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The Integral in the right hand side of (Eq. 2) corresponds to the surface of a 3N-dimensional (<math> p_i; i=1,2,3,\cdots 3N </math>) hyper-sphere of radius | The Integral in the right hand side of (Eq. 2) corresponds to the surface of a 3N-dimensional (<math> p_i; i=1,2,3,\cdots 3N </math>) hyper-sphere of radius | ||
<math> r = \left. \sqrt{ 2 m \Delta E } \right. </math> ; | <math> r = \left. \sqrt{ 2 m \Delta E } \right. </math> ; | ||
Therefore: | |||
:<math> \Pi \left( X^{3N}|E \right) \propto \left[ E- U(X^{3N}) \right]^{(3N-1)/2} | :<math> \Pi \left( X^{3N}|E \right) \propto \left[ E- U(X^{3N}) \right]^{(3N-1)/2} | ||
</math> | </math> | ||
See Ref. 1 for an application of Monte Carlo simulation using this ensemble. | See Ref. 1 for an application of Monte Carlo simulation using this ensemble. |