We present a study of thermal conductivity, κ, in undoped and doped strontium titanate in a wide temperature range (2-400 K) and detecting different regimes of heat flow. In undoped SrTiO_{3}, κ evolves faster than cubic with temperature below its peak and in a narrow temperature window. Such behavior, previously observed in a handful of solids, has been attributed to a Poiseuille flow of phonons, expected to arise when momentum-conserving scattering events outweigh momentum-degrading ones. The effect disappears in the presence of dopants. In SrTi_{1-x}Nb_{x}O_{3}, a significant reduction in lattice thermal conductivity starts below the temperature at which the average inter-dopant distance and the thermal wavelength of acoustic phonons become comparable. In the high-temperature regime, thermal diffusivity becomes proportional to the inverse of temperature, with a prefactor set by sound velocity and Planckian time (τ_{p}=(ℏ/k_{B}T)).
Recently we have shown that a one-parameter scaling, T coh , describes the physical behavior of several heavy fermions in a region of their phase diagram. In this paper we fully characterize this region, obtaining the uniform susceptibility, the resistivity and the specific heat in terms of the coherence temperature T coh . This allows for an explicit evaluation of the Wilson and the Kadowaki-Woods ratios in this regime. These quantities turn out to be independent of the distance |δ| to the quantum critical point (QCP). The theory of the one-parameter scaling corresponds to a local interacting model. Although spatial correlations are irrelevant in this case, time fluctuations are critically correlated as a consequence of the quantum character of the transition. PACS Nos. 71.27+a 75.30Mb 71.10Hf 75.45+j 64.60Kw
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