Can anyone help me in minimizing the following integral equation and finding the roots ?
Here i am posting an integral equation for which i want the minimization code and methods.
Ω =λ^ 4 (σ 2 + ~π2 − v 2 ) 2 − cσ + νqT∫ (d ^3k)/ (2π) ^3 {ln(1 − nq(T, µ)) + ln(1 − nq¯(T, µ))} equation(1)
we have to minimize the above equation with respect to sigma(σ) and in the scond term,there is integration on the momentum vector k, where integration term also contain the sigma variable in the following ways
nq(T, µ) = 1/ (1 + exp((sqrt(k^2+g^2(σ^2+π^2)) − µ)/T ))
nq¯(T, µ))= 1/ (1 + exp((sqrt(k^2+g^2(σ^2+π^2)) +µ)/T ))
where all the other notation like pi,lambda,vq,T are the some parametrs which we can fix like
lambda=87.6 Mev
T = 500(temperature)
vq=12
g=3.8
mu=100
c=13.6
pi=0
so, we have to find ∂Ω/∂σ and corresponding value of sigma at which above equation (1) is minimized .Here i am posting an integral equation for which i want the minimization code and methods.
Ω =λ^ 4 (σ 2 + ~π2 − v 2 ) 2 − cσ + νqT∫ (d ^3k)/ (2π) ^3 {ln(1 − nq(T, µ)) + ln(1 − nq¯(T, µ))} equation(1)
we have to minimize the above equation with respect to sigma(σ) and in the scond term,there is integration on the momentum vector k, where integration term also contain the sigma variable in the following ways
nq(T, µ) = 1/ (1 + exp((sqrt(k^2+g^2(σ^2+π^2)) − µ)/T ))
nq¯(T, µ))= 1/ (1 + exp((sqrt(k^2+g^2(σ^2+π^2)) +µ)/T ))
where all the other notation like pi,lambda,vq,T are the some parametrs which we can fix like
lambda=87.6 Mev
T = 500(temperature)
vq=12
g=3.8
mu=100
c=13.6
pi=0
so, we have to find ∂Ω/∂σ and corresponding value of sigma at which above equation (1) is minimized . Here i am posting an integral equation for which i want the minimization code and methods.
Ω =λ^ 4 (σ 2 + ~π2 − v 2 ) 2 − cσ + νqT∫ (d ^3k)/ (2π) ^3 {ln(1 − nq(T, µ)) + ln(1 − nq¯(T, µ))} equation(1)
we have to minimize the above equation with respect to sigma(σ) and in the scond term,there is integration on the momentum vector k, where integration term also contain the sigma variable in the following ways
nq(T, µ) = 1/ (1 + exp((sqrt(k^2+g^2(σ^2+π^2)) − µ)/T ))
nq¯(T, µ))= 1/ (1 + exp((sqrt(k^2+g^2(σ^2+π^2)) +µ)/T ))
where all the other notation like pi,lambda,vq,T are the some parametrs which we can fix like
lambda=87.6 Mev
T = 500(temperature)
vq=12
g=3.8
mu=100
c=13.6
pi=0
so, we have to find ∂Ω/∂σ and corresponding value of sigma at which above equation (1) is minimized . optimization of equation containing integration MATLAB Answers — New Questions