Deborah.Esther.SingleQMoment

calc_Q1(
    trM1::AbstractArray, 
    Nf::Int
) -> Vector{Float64}

Compute the first-order quark cumulant $Q_1$ using:

\[Q_1 = N_{\text{f}} \, \text{Tr} \, M^{-1}\]

Arguments

• trM1::AbstractArray: $\text{Tr} \, M^{-1}$ for each configuration index.
• Nf::Int: Number of quark flavors.

Returns

• Vector{Float64}: $Q_1$ values for all configuration indices.

calc_Q2(
    trM1::AbstractArray, 
    trM2::AbstractArray, 
    Nf::Int
) -> Vector{Float64}

Compute the second-order quark cumulant $Q_2$ using:

\[Q_2 = - N_{\text{f}} \, \text{Tr} \, M^{-2} + \left( N_{\text{f}} \, \text{Tr} \, M^{-1} \right)^2\]

Arguments

• trM1::AbstractArray: $\text{Tr} \, M^{-1}$ for each configuration index.
• trM2::AbstractArray: $\text{Tr} \, M^{-2}$ for each configuration index.
• Nf::Int: Number of quark flavors.

Returns

• Vector{Float64}: $Q_2$ values for all configuration indices.

calc_Q3(
    trM1::AbstractArray, 
    trM2::AbstractArray, 
    trM3::AbstractArray, 
    Nf::Int
) -> Vector{Float64}

Compute the third-order quark cumulant $Q_3$ using:

\[Q_3 = 2 \, N_{\text{f}} \, \text{Tr} \, M^{-3} - 3 \, N_{\text{f}}^{2} \, \text{Tr} \, M^{-2} \, \text{Tr}\, M^{-1} + \left( N_{\text{f}} \, \text{Tr} \, M^{-1} \right)^{3}\]

Arguments

• trM1::AbstractArray: $\text{Tr} \, M^{-1}$ for each configuration index.
• trM2::AbstractArray: $\text{Tr} \, M^{-2}$ for each configuration index.
• trM3::AbstractArray: $\text{Tr} \, M^{-3}$ for each configuration index.
• Nf::Int: Number of quark flavors.

Returns

• Vector{Float64}: $Q_3$ values for all configuration indices.

calc_Q4(
    trM1::AbstractArray, 
    trM2::AbstractArray, 
    trM3::AbstractArray, 
    trM4::AbstractArray, 
    Nf::Int
) -> Vector{Float64}

Compute the fourth-order quark cumulant Q₄ using:

\[Q_4 = - 6 \, N_{\text{f}} \, \text{Tr} \, M^{-4} + 8 \, N_{\text{f}}^{2} \, \text{Tr} \, M^{-3} \, \text{Tr} \, M^{-1} + 3 \left( N_{\text{f}} \, \text{Tr} \, M^{-2} \right)^{2} - 6 \, N_{\text{f}} \, \text{Tr} \, M^{-2} \, \left( N_{\text{f}} \, \text{Tr} \, M^{-1} \right)^{2} + \left( N_{\text{f}} \, \text{Tr} \, M^{-1} \right)^{4}\]

Arguments

• trM1::AbstractArray: $\text{Tr} \, M^{-1}$ for each configuration index.
• trM2::AbstractArray: $\text{Tr} \, M^{-2}$ for each configuration index.
• trM3::AbstractArray: $\text{Tr} \, M^{-3}$ for each configuration index.
• trM4::AbstractArray: $\text{Tr} \, M^{-4}$ for each configuration index.
• Nf::Int: Number of quark flavors.

Returns

• Vector{Float64}: $Q_4$ values for all configuration indices.