content_image/332566.jpg content_image/332565.jpg content_image/332564.jpg content_image/332563.jpg content_image/332562.jpg content_image/332561.jpg
Hermitian Hamiltonian commutes with the group generators those correspond the group eigenvalues θ$_{i}$ where i runs over 1 , · · · , N . The invariance Haar measure is reduced to 

<img src='content_image/332566.jpg'>

where − π ≤ θ$_{i}$ ≤ π for the circular ensemble. The variables ( θ$_{1}$, · · · , θ$_{N}$ ) are the diago- nalized group eigenvalues. The number of adjoint charges is reduced to N$_{adj}$ = N $^{2}$. The normalisation constant N$_{U}$ is determined by 

<img src='content_image/332565.jpg'>

The saddle points of the group eigen-variables accumulate around the origin for the hot and dense nuclear matter under extreme conditions. Subsequently, the canonical ensemble can be written as the Gaussian-like ensemble in the following way, 

Therefore, the invariance Haar measure is approximated to 

<img src='content_image/332564.jpg'>

<img src='content_image/332563.jpg'>

The unimodular condition for the special unitary symmetry group SU ( N ) is imposed by 

Hence, the invariance Haar measure for SU ( N ) becomes 

<img src='content_image/332562.jpg'>

<img src='content_image/332561.jpg'>

