A universal Hamiltonian for a quantum dot in the presence of spin-orbit interaction

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We derive a universal Hamiltonian for a quantum dot in the presence of spin-orbit interaction in the symmetry limits of a strong spin-dependent Aharonov-Bohm-like term. We also derive a closed expression for the conductance through such a dot, and use it to study the effects of spin-orbit on the conductance peak statistics in the presence of an exchange interaction. For a realistic strength of the exchange interaction, we find that the width of the peak-spacing distribution is sensitive to spin-orbit coupling only in the absence of an orbital magnetic field. We also find that spin-orbit coupling modifies the shape of the peak-spacing distribution and suppresses the peak-height fluctuations.