Dependence of the indicators of spin coherence and the degree of entanglement on Fermi energy and spin–orbit coupling strength. (a) and (c) Three-dimensional display of the magnitude of the spin polarization vector | P | and van Neumann entropy S versus the Fermi energy ε f and the spin–orbit coupling strength t_so for the cavity shape marked as ⋆ in Fig. 1, where the classical dynamics are fully chaotic. (b) and (d) Similar 3D plot but for the case marked as • in Fig. 1, where the classical dynamics are of the mixed type. (e) The value of | P | averaged over a relatively large interval of the Fermi energy versus t_so for case ⋆ (solid curve) and case • (dashed curve). (f) The corresponding average value of entropy S versus t_so for the cases in (e). Both ε f and t_so are measured in units of t₀, the hopping energy of any pair of nearest sites in the square lattice as a result of discretization of the two-dimensional Schrödinger equation.