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Upper limit to some response functions
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Neutrino155 committed Nov 2, 2023
1 parent 1e153c5 commit 57465fd
Showing 1 changed file with 3 additions and 7 deletions.
10 changes: 3 additions & 7 deletions src/ResponseFunctions.jl
Original file line number Diff line number Diff line change
Expand Up @@ -95,12 +95,8 @@ See F. Peeters and J. Devreese 1984: https://doi.org/10.1016/S0081-1947(08)60312
See also [`polaron_mobility`](@ref), [`polaron_complex_conductivity`](@ref)
"""
function inverse_frohlich_mobility(v, w, α, ω, β)
if β == Inf
return zero(β)
else
structure_factor(t) = frohlich_structure_factor(t, v, w, α, ω, β)
return abs(imag(general_memory_function(structure_factor; limits = [0, 1e4]))) / ω
end
structure_factor(t) = frohlich_structure_factor(t, v, w, α, ω, β)
return abs(imag(general_memory_function(structure_factor; limits = [0, 1e5]))) / ω
end

"""
Expand Down Expand Up @@ -246,7 +242,7 @@ function inverse_Hellwarth_mobility(v, w, α, ω, β)
b = R * ω * β / sinh* β * v / 2) # Feynman1962 version; page 1010, Eqn (47b)
a = sqrt((ω * β / 2)^2 + R * ω * β * coth* β * v / 2))
k(u, a, b, v) = (u^2 + a^2 - b * cos(v * u))^(-3 / 2) * cos(u) # integrand in (2)
K = quadgk(u -> k(u, a, b, v), 0, Inf)[1] # numerical quadrature integration of (2)
K = quadgk(u -> k(u, a, b, v), 0, 1e5)[1] # numerical quadrature integration of (2)

# Right-hand-side of Eqn 1 in Hellwarth 1999 // Eqn (4) in Baggio1997
RHS = α / (3 * sqrt(π)) ** β)^(5 / 2) / sinh* β / 2) * (v^3 / w^3) * K
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