From 62cd27cbb6a87189062daa92cc1d1e7aca0706fe Mon Sep 17 00:00:00 2001
From: Federico Cerisola <federico@cerisola.net>
Date: Thu, 15 Aug 2024 01:15:24 +0100
Subject: [PATCH] Fix correlations function for LorentzianSD

Old implementation failed to work properly for the critically and
overdamped cases.
---
 src/LorentzianSD.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/LorentzianSD.jl b/src/LorentzianSD.jl
index 1c23b23..507b6d0 100644
--- a/src/LorentzianSD.jl
+++ b/src/LorentzianSD.jl
@@ -42,8 +42,8 @@ sdoverω(J::LorentzianSD, ω) = (J.α*J.Γ/π)/((ω^2 - J.ω0^2)^2 + (J.Γ*ω)^2
 reorganisation_energy(J::LorentzianSD) = J.α/J.ω0^2/2
 
 function correlations_imag(J::LorentzianSD, τ; ωcutoff=Inf)
-    ω1 = sqrt(J.ω0^2 - J.Γ^2/4)
-    return -J.α*exp(-J.Γ*τ/2)*sin(ω1*τ)/(2*ω1)
+    ω1 = sqrt(complex(J.ω0^2 - J.Γ^2/4))
+    return -J.α*exp(-J.Γ*τ/2)*τ*real(sinc(ω1*τ/π))/2
 end
 
 real_memory_kernel_ft(J::LorentzianSD, ω) = (J.α*(J.ω0^2 - ω^2))/((ω^2 - J.ω0^2)^2 + (J.Γ*ω)^2)