Update to v0.4v0.4

  feature: compute the 2-point correlation function in easyeq.

  feature: compute the Fourier transform of the 2-point correlation function
           in anyeq and easyeq.

  feature: compute the local maximum of the 2-point correlation function and
           its Fourier transform.

  feature: compute the compressibility for anyeq.

  feature: allow for linear spacing of rho's.

  feature: print the scattering length.

  change: ux and uk now return real numbers.

  fix: error in the computation of the momentum distribution: wrong
       definition of delta functions.

  fix: various minor bugs.

  optimization: assign explicit types to variables.

1 files changed, 46 insertions, 12 deletions

diff --git a/src/potentials.jl b/src/potentials.jl
index 46cafc0..b480db0 100644
--- a/src/potentials.jl
+++ b/src/potentials.jl
@@ -1,4 +1,4 @@
-## Copyright 2021 Ian Jauslin
+## Copyright 2021-2023 Ian Jauslin
 ## 
 ## Licensed under the Apache License, Version 2.0 (the "License");
 ## you may not use this file except in compliance with the License.
@@ -13,10 +13,15 @@
 ## limitations under the License.
 
 # exponential potential in 3 dimensions
-@everywhere function v_exp(k,a)
+@everywhere function v_exp(
+  k::Float64,
+  a::Float64
+)
   return 8*pi/(1+k^2)^2*a
 end
-@everywhere function a0_exp(a)
+@everywhere function a0_exp(
+  a::Float64
+)
   if a>0.
     return log(a)+2*MathConstants.eulergamma+2*besselk(0,2*sqrt(a))/besseli(0,2*sqrt(a))
   elseif a<0.
@@ -27,15 +32,24 @@ end
 end
 
 # exp(-x)-a*exp(-b*x) in 3 dimensions
-@everywhere function v_expcry(k,a,b)
+@everywhere function v_expcry(
+  k::Float64,
+  a::Float64,
+  b::Float64
+)
   return 8*pi*((1+k^2)^(-2)-a*b*(b^2+k^2)^(-2))
 end
-@everywhere function a0_expcry(a,b)
+@everywhere function a0_expcry(
+  a::Float64,
+  b::Float64
+)
   return 1.21751642717932720441274114683413710125487579284827462 #ish
 end
 
 # x^2*exp(-|x|) in 3 dimensions
-@everywhere function v_npt(k)
+@everywhere function v_npt(
+  k::Float64
+)
   return 96*pi*(1-k^2)/(1+k^2)^4
 end
 @everywhere function a0_npt()
@@ -43,7 +57,9 @@ end
 end
 
 # 1/(1+x^4/4) potential in 3 dimensions
-@everywhere function v_alg(k)
+@everywhere function v_alg(
+  k::Float64
+)
   if(k==0)
     return 4*pi^2
   else
@@ -53,32 +69,50 @@ end
 a0_alg=1. #ish
 
 # (1+a x^4)/(1+x^2)^4 potential in 3 dimensions
-@everywhere function v_algwell(k)
+@everywhere function v_algwell(
+  k::Float64
+)
   a=4
   return pi^2/24*exp(-k)*(a*(k^2-9*k+15)+k^2+3*k+3)
 end
 a0_algwell=1. #ish
 
 # potential corresponding to the exact solution c/(1+b^2x^2)^2
-@everywhere function v_exact(k,b,c,e)
+@everywhere function v_exact(
+  k::Float64,
+  b::Float64,
+  c::Float64,
+  e::Float64
+)
   if k!=0
     return 48*pi^2*((18+3*sqrt(c)-(4-3*e/b^2)*c-(1-2*e/b^2)*c^1.5)/(4*(3+sqrt(c))^2*sqrt(c))*exp(-sqrt(1-sqrt(c))*k/b)+(-18+3*sqrt(c)+(4-3*e/b^2)*c-(1-2*e/b^2)*c^1.5)/(4*(3-sqrt(c))^2*sqrt(c))*exp(-sqrt(1+sqrt(c))*k/b)+(1-k/b)/2*exp(-k/b)-c*e/b^2*(3*(9-c)*k/b+8*c)/(8*(9-c)^2)*exp(-2*k/b))/k
   else
     return 48*pi^2*(-sqrt(1-sqrt(c))/b*(18+3*sqrt(c)-(4-3*e/b^2)*c-(1-2*e/b^2)*c^1.5)/(4*(3+sqrt(c))^2*sqrt(c))-sqrt(1+sqrt(c))/b*(-18+3*sqrt(c)+(4-3*e/b^2)*c-(1-2*e/b^2)*c^1.5)/(4*(3-sqrt(c))^2*sqrt(c))-1/b-c*e/b^2*(27-19*c)/(8*(9-c)^2))
   end
 end
-@everywhere function a0_exact(b,c,e)
+@everywhere function a0_exact(
+  b::Float64,
+  c::Float64,
+  e::Float64
+)
   return 1. #ish
 end
 
 # tent potential (convolution of soft sphere with itself): a*pi/12*(2*|x|/b-2)^2*(2*|x|/b+4) for |x|<b
-@everywhere function v_tent(k,a,b)
+@everywhere function v_tent(
+  k::Float64,
+  a::Float64,
+  b::Float64
+)
   if k!=0
     return (b/2)^3*a*(4*pi*(sin(k*b/2)-k*b/2*cos(k*b/2))/(k*b/2)^3)^2
   else
     return (b/2)^3*a*(4*pi/3)^2
   end
 end
-@everywhere function a0_tent(a,b)
+@everywhere function a0_tent(
+  a::Float64,
+  b::Float64
+)
   return b #ish
 end