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One-Sided Fourier Transform: Application to Linear Absorption and Emission Spectra

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spectrum
Absorption
Emission
lineshape
Drude-Lorentz
Gaussian
Lorentzian
Fourier parameters
lineshape parameters
time step dt
0.05
reorganization energy λ
half number of steps nt
50
bath frequency Λ
thermal energy
-1
β
One sometimes needs to numerically evaluate the real part of the one-sided Fourier transform of a function
f(t)
. A simple and efficient way to achieve this is to use a fundamental property of the two-sided Fourier transform of a conjugate-even function (i.e.,
f(-t)=
*
f
(t)
) and use the efficient fast Fourier transform (FFT) algorithm. This procedure is applied here to the linear absorption and emission spectra of a single excitation interacting with a thermal environment.
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