Quantum multipole noise

Quantum multipole noise is defined as a family of creation and annihilation operators with commutation relations proportional to derivatives of delta function of difference of the times, $[c^-_n(t),c^+_n(τ)]\approx δ^{(n)}(τ-t)$. In this paper an explicit operator representation of the quantum multipole noise is constructed in a suitable pseudo-Hilbert space (i.e., in a Hilbert space with indefinite metric). For making this representation, we introduce a class of Hilbert spaces obtained as completion of the Schwartz space in specific norms. Using this representation, we obtain an asymptotic expansion as a series in quantum multipole noise for multitime correlation functions which describe the dynamics of open quantum systems weakly interacting with a reservoir.

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