Error Bounds of Continued Fractions for Complex Transport Coefficients and Spectral Functions

Abstract

We study the calculation of complex transport coefficients x (ω) and power spectra in terms of complex continued fractions. In particular, we establish classes of dynamical equilibrium and non-equilibrium systems for which we can obtain a posteriori bounds for the truncation error | x (ω) - x⁽ⁿ⁾(ω)| ≦ c (ω) | x⁽ⁿ⁾(ω) - x^(n-1)(ω)| when the transport coefficient is approximated by its n-th continued fraction approximant x⁽ⁿ⁾(ω).