We review recent progress in the understanding of the quasiparticle properties of d-wave superconductors in a magnetic field within a semiclassical treatment. We demonstrate that threre exists quantitative agreement between theory and experimental data of YBa_2Cu_3O_(7- delta ) (YBCO) for he field applied aolong the c-axis. We suggest that the field dependence of the NMR magnetization in the regime where the single relaxation time approximation breaks down can be used as a probe of the quasiparticle properties. We also show that for the field applied in the a-b plane the density of states and thermodynamic properties depend on the angle between the applied field and the order parameter nodes, resulting in fourfold oscillations of the electronic specific heat and anisotropy of the thermodynamic coefficients. We arguethat this anisotropy can serve as a test of gap symmetry in the bulk, and as a further probe of the nodal quasiparticles.
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