Harmonize approximations

src/ElectronicStructureModels.jl

@@ -2,9 +2,6 @@ module ElectronicStructureModels
 
 hello_world() = "Hello, World!"
 
-# temperature
-export FiniteTemperature, ZeroTemperature
-
 # matter model
 export AbstractMatterModel
 
@@ -27,7 +24,7 @@ export AbstractLocalFieldCorrection, NoLocalFieldCorrection
 
 # concrete electron systems
 export IdealElectronSystem
-export AbstractResponseApproximation, NoApprox, NonDegenerated, Degenerated
+export AbstractResponseApproximation, NoApprox, NonDegenerated, Degenerated, ZeroTemperatureApprox
 export response_approximation
 export InteractingElectronSystem
 
@@ -51,7 +48,6 @@ using SpecialFunctions
 include("utils.jl")
 include("units.jl")
 include("constants.jl")
-include("temperature.jl")
 include("interface.jl")
 include("generic.jl")
 include("lookup.jl")
@@ -61,6 +57,7 @@ include("electron_system/interface.jl")
 include("electron_system/generic.jl")
 include("electron_system/ideal/approximations/interface.jl")
 include("electron_system/ideal/approximations/no_approx.jl")
+include("electron_system/ideal/approximations/zero_temperature.jl")
 include("electron_system/ideal/approximations/non_degenerated.jl")
 include("electron_system/ideal/approximations/degenerated.jl")
 include("electron_system/ideal/utils.jl")

src/electron_system/ideal/approximations/degenerated.jl

@@ -24,7 +24,7 @@ function _deg_integral(x::Real)
     end
 end
 
-function _real_lindhard_nonzero_temperature(::Degenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
+function _real_ideal_dynamic_response(::Degenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
 
     prefac = inv(qbar)
     num = _nu_minus(ombar, qbar)
@@ -42,7 +42,7 @@ function _real_lindhard_nonzero_temperature(::Degenerated, ombar::T, qbar::T, bb
     if ombar < 1.0e-4 * qbar
         # fallback on no-approx
         # TODO: find an improved formula for this case!
-        return _real_lindhard_zero_temperature(NoApprox(), ombar, qbar)
+        return _real_ideal_dynamic_response(NoApprox(), ombar, qbar, bbar)
     end
 
     # general degenerated case
@@ -54,7 +54,7 @@ end
 
 # general degenerated case
 # source: AB84, eq. 26
-function _imag_lindhard_nonzero_temperature(::Degenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
+function _imag_ideal_dynamic_response(::Degenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
     prefac = -pi / (2 * qbar * bbar)
 
     num = _nu_minus(ombar, qbar)

src/electron_system/ideal/approximations/interface.jl

@@ -6,14 +6,11 @@ abstract type AbstractResponseApproximation <: AbstractApproximation end
 # most naive implementation
 struct NoApprox <: AbstractResponseApproximation end
 
-# using integral transforms and identities to make integration more stable
-struct TransformedIntegral <: AbstractResponseApproximation end
+# using the zero temperature limit (betabar to infty)
+struct ZeroTemperatureApprox <: AbstractResponseApproximation end
 
 # using the limit for non-degenerated electron gases (betabar << 1)
 struct NonDegenerated <: AbstractResponseApproximation end
 
 # using the limit for degenerated electron gases (betabar >> 1)
 struct Degenerated <: AbstractResponseApproximation end
-
-const AbstractZeroTemperatureApproximation = Union{NoApprox}
-const AbstractFiniteTemperatureApproximation = Union{NoApprox, NonDegenerated, Degenerated}

src/electron_system/ideal/approximations/no_approx.jl

@@ -1,39 +1,3 @@
-# zero temperature Lindhard, without any further approximation
-
-function _imag_lindhardDSF_zeroT_minus(omb::T, qb::T) where {T <: Real}
-    num = _nu_minus(omb, qb)
-
-    if abs(num) >= one(T)
-        return zero(T)
-    end
-    return one(omb) - num^2
-
-end
-
-function _imag_lindhardDSF_zeroT_plus(omb::T, qb::T) where {T <: Real}
-    nup = _nu_plus(omb, qb)
-    if abs(nup) >= one(T)
-        return zero(T)
-    end
-    return one(omb) - nup^2
-
-end
-
-function _imag_lindhard_zero_temperature(::NoApprox, ombar::T, qbar::T) where {T <: Real}
-    return -pi / (2 * qbar) *
-        (_imag_lindhardDSF_zeroT_minus(ombar, qbar) - _imag_lindhardDSF_zeroT_plus(ombar, qbar))
-end
-
-function _real_lindhard_zero_temperature(::NoApprox, ombar::T, qbar::T) where {T <: Real}
-    num = _nu_minus(ombar, qbar)
-    nup = _nu_plus(ombar, qbar)
-
-    term1 = (1 - num^2) / 4 * _stable_log_term(num)
-    term2 = (1 - nup^2) / 4 * _stable_log_term(nup)
-
-    return -2 * (qbar / 2 - term1 + term2) / qbar
-end
-
 # finite temperature Lindhard, without any further approximation
 
 ## Real part
@@ -62,7 +26,7 @@ function _general_integral(nu, beta)
     return -nu^2 * res
 end
 
-function _real_lindhard_nonzero_temperature(::NoApprox, ombar, qbar, bbar)
+function _real_ideal_dynamic_response(::NoApprox, ombar, qbar, bbar)
     num = _nu_minus(ombar, qbar)
     nup = _nu_plus(ombar, qbar)
 
@@ -75,7 +39,7 @@ end
 
 ## Imaginary part
 
-function _imag_lindhard_nonzero_temperature(::NoApprox, ombar::T, qbar::T, bbar::T) where {T <: Real}
+function _imag_ideal_dynamic_response(::NoApprox, ombar::T, qbar::T, bbar::T) where {T <: Real}
 
     prefac = -pi / (2 * qbar)
 

src/electron_system/ideal/approximations/non_degenerated.jl

@@ -5,7 +5,7 @@ function _non_deg_integal(nu, beta)
     return prefac * dawson(nu * sqrt(beta)) * sqrt(pi)
 end
 
-function _real_lindhard_nonzero_temperature(::NonDegenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
+function _real_ideal_dynamic_response(::NonDegenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
     num = _nu_minus(ombar, qbar)
     nup = _nu_plus(ombar, qbar)
 
@@ -14,7 +14,7 @@ function _real_lindhard_nonzero_temperature(::NonDegenerated, ombar::T, qbar::T,
 end
 
 
-function _imag_lindhard_nonzero_temperature(::NonDegenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
+function _imag_ideal_dynamic_response(::NonDegenerated, ombar::T, qbar::T, bbar::T) where {T <: Real}
     prefac = -pi / (2 * qbar * bbar)
 
     num = _nu_minus(ombar, qbar)

src/electron_system/ideal/approximations/zero_temperature.jl

@@ -0,0 +1,35 @@
+# zero temperature Lindhard, without any further approximation
+
+function _imag_lindhardDSF_zeroT_minus(omb::T, qb::T) where {T <: Real}
+    num = _nu_minus(omb, qb)
+
+    if abs(num) >= one(T)
+        return zero(T)
+    end
+    return one(omb) - num^2
+
+end
+
+function _imag_lindhardDSF_zeroT_plus(omb::T, qb::T) where {T <: Real}
+    nup = _nu_plus(omb, qb)
+    if abs(nup) >= one(T)
+        return zero(T)
+    end
+    return one(omb) - nup^2
+
+end
+
+function _imag_ideal_dynamic_response(::ZeroTemperatureApprox, ombar::T, qbar::T, betabar::T) where {T <: Real}
+    return -pi / (2 * qbar) *
+        (_imag_lindhardDSF_zeroT_minus(ombar, qbar) - _imag_lindhardDSF_zeroT_plus(ombar, qbar))
+end
+
+function _real_ideal_dynamic_response(::ZeroTemperatureApprox, ombar::T, qbar::T, betabar::T) where {T <: Real}
+    num = _nu_minus(ombar, qbar)
+    nup = _nu_plus(ombar, qbar)
+
+    term1 = (1 - num^2) / 4 * _stable_log_term(num)
+    term2 = (1 - nup^2) / 4 * _stable_log_term(nup)
+
+    return -2 * (qbar / 2 - term1 + term2) / qbar
+end

src/electron_system/ideal/generic.jl

@@ -10,13 +10,13 @@ function imag_dynamic_response(
 
     if ombar <= zero(ombar)
         if qbar < zero(qbar)
-            return N0 * _imag_ideal_dynamic_response(elsys, approx, -ombar, -qbar)
+            return N0 * _imag_ideal_dynamic_response(approx, -ombar, -qbar, betabar(elsys))
         else
-            return -N0 * _imag_ideal_dynamic_response(elsys, approx, -ombar, qbar)
+            return -N0 * _imag_ideal_dynamic_response(approx, -ombar, qbar, betabar(elsys))
         end
     end
 
-    return N0 * _imag_ideal_dynamic_response(elsys, approx, ombar, qbar)
+    return N0 * _imag_ideal_dynamic_response(approx, ombar, qbar, betabar(elsys))
 end
 
 function real_dynamic_response(
@@ -31,8 +31,8 @@ function real_dynamic_response(
     N0 = KF / (2 * pi^2)
 
     if ombar <= zero(ombar)
-        return N0 * _real_ideal_dynamic_response(elsys, response_approximation(elsys), -ombar, qbar)
+        return N0 * _real_ideal_dynamic_response(response_approximation(elsys), -ombar, qbar, betabar(elsys))
     end
 
-    return N0 * _real_ideal_dynamic_response(elsys, response_approximation(elsys), ombar, qbar)
+    return N0 * _real_ideal_dynamic_response(response_approximation(elsys), ombar, qbar, betabar(elsys))
 end