We calculate the magnetic field dependence of quasiparticle transport properties in the vortex state of a d-wave superconductor arising solely from the quasiparticle's Doppler shift in the superflow field surrounding the vortex. Qualitative features agree well with experiments on cuprate and heavy fermion superconductors at low fields and temperatures. We derive scaling relations in the variable T /H 1/2 valid at sufficiently low temperatures T and fields H, but show that these relations depend on the scattering phase shift, and are in general fulfilled only approximately even in the clean limit, due to the energy dependence of the quasiparticle relaxation time.PACS Numbers: 74.25.Fy,74.60.Ec Introduction. While the origins of high-temperature superconductivity and the non-Fermi liquid nature of the normal state in the cuprates are not understood, recently a consensus has been emerging that the superconducting state itself is not particularly exotic, in the sense that it consists of a BCS-like pair state with well-defined quasiparticle excitations above it. Although the order parameter in these materials is now thought to display d-wave symmetry, ranking them among the few known "unconventional" superconductors, it has been argued that the prediction of observable properties in the superconducting state is now a relatively routine task.In the study of transport properties, however, questions arise which prevent one from drawing such sanguine conclusions. Recent measurements of thermal conductivity in both the LSCO-214 and BSCCO-2212 systems have hinted at qualitatively new physics in the vortex state at low temperatures and fields. [1,2] In the LSCO case, a logarithmic dependence on field has been found suggestive of quantum interference effects; in the BSCCO case, a kink in the thermal conductivity as a function of field occurs, apparently signaling a transition to a new superconducting phase at higher fields.In order to extract which aspects of the new phenomena are due to qualitatively "new" physics, one needs first to understand which aspects can be attributed to the perhaps more mundane but still largely unexplored phenomenology of quasiparticles in the d-wave vortex state. A fundamental observation regarding the thermodynamics of this state was made by Volovik, who pointed out that, in contrast to classic superconductors, in d-wave systems the entropy and density of states was dominated by contributions from extended quasiparticle states rather than the bound states associated with vortex cores. The remarkable consequence of this observation, which occurs due to the existence of order parameter nodes in the clean d-wave state, is a term in the specific heat of the superconductor in a field varying as √ HT rather than as HT as in the classic case. Other calculations, dependent only on the Dirac-like spectrum of nodal quasiparticles excited at low temperature, gave the field dependence of the density of states N (ω; H) [4] and predicted the specific heat should scale as C(T ; H)/T 2 ∼ F C (X), where X ≡ T...