Asymptotic equality of the isolated and the adiabatic susceptibility

Many-particle systems with a hamiltonian of the form H = A + hB, h being a parameter, are discussed. In particular, for a certain class of these systems, a criterion is derived for the asymptotic equality of the isolated and the adiabatic susceptibility or, equivalently, for the ergodicity of B. This criterion states that, for sufficiently large particle number, any hermitian operator polynomial in h of any degree J that commutes with H(h) can be written as a linear combination of the powers H⁰, …, H^J with polynomial coefficients.