On the integrated density of states of random Pauli Hamiltonians (Q816496)

The author proves that the difference of the integrated densities of states (IDS) of the two components of a random Pauli Hamiltonian is equal to a constant given in terms of the expectation of the magnetic field. This formula is a random version of \textit{Y. Aharonov} and \textit{A. Casher}'s theory [``Ground state of a spin-\( 1/2 \) charged particle in a two-dimensional magnetic field'', Phys. Rev. 19, No. 6, 2461--2462 (1979)]. Applying this formula, the IDS is shown to jump at \( 0 \) if the expectation of the magnetic field is nonzero. For a zero magnetic field a lower estimate of the asymptotics of the IDS at \( 0 \) is found. This lower estimate demonstrates that the IDS decays slower than known results for random Schrödinger operators whose infimum of the spectrum is \(0 \). Moreover the strong-magnetic-field limit of the IDS is identified in a general setting.