Rigorous bounds prove that the number of complex exponentials needed for non-Markovian bath correlations is bounded independently of T for many spectral densities, with mild T-dependence only for strong singularities.
( S4) to a bound on Jeff (tanh z), note that Re(tanh(x − iy)) = sinh(2x) cosh(2x) + cos(2y) , so the sign of Re(tanh z) is the sign of x
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Provably Efficient Long-Time Exponential Decompositions of Non-Markovian Gaussian Baths
Rigorous bounds prove that the number of complex exponentials needed for non-Markovian bath correlations is bounded independently of T for many spectral densities, with mild T-dependence only for strong singularities.