Estimating the digamma and trigamma functions by completely monotonicity arguments

Mortici, Cristinel

doi:10.1016/j.amc.2010.10.023

Cited by 6 publications

(1 citation statement)

References 34 publications

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“…which describes almost exactly the behavior of ψ (1) (z) for |z| > 1 [55]. We also note that this approximation does not change the sign of F(q), which stays positive for all values of the momentum q and the parameters of the model.…”

Section: A Boltzmann Equation Formalismsupporting

confidence: 60%

Resistivity near a nematic quantum critical point: Impact of acoustic phonons

Carvalho

Fernandes

2019

Phys. Rev. B

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We revisit the issue of the resistivity of a two-dimensional electronic system tuned to a nematic quantum critical point (QCP), focusing on the non-trivial impact of the coupling to the acoustic phonons. Due to the unavoidable linear coupling between the electronic nematic order parameter and the lattice strain fields, long-range nematic interactions mediated by the phonons emerge in the problem. By solving the semi-classical Boltzmann equation in the presence of scattering by impurities and nematic fluctuations, we determine the temperature dependence of the resistivity as the nematic QCP is approached. One of the main effects of the nemato-elastic coupling is to smooth the electronic non-equilibrium distribution function, making it approach the simple cosine angular dependence even when the impurity scattering is not too strong. We find that at temperatures lower than a temperature scale set by the nemato-elastic coupling, the resistivity shows the T 2 behavior characteristic of a Fermi liquid. This is in contrast to the T 4/3 low-temperature behavior expected for a lattice-free nematic quantum critical point. More importantly, we show that the effective resistivity exponent α eff (T ) in ρ(T ) − ρ0 ∼ T α eff (T ) displays a pronounced temperature dependence, implying that a nematic QCP cannot generally be characterized by a simple resistivity exponent. We discuss the implications of our results to the interpretation of experimental data, particularly in the nematic superconductor FeSe1−xSx. arXiv:1906.03205v3 [cond-mat.str-el]

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Section: A Boltzmann Equation Formalismsupporting

confidence: 60%