Quantum multipole noise

TL;DR

This paper introduces quantum multipole noise, constructs an explicit operator representation in a pseudo-Hilbert space, and derives an asymptotic expansion for multitime correlation functions in open quantum systems.

Contribution

It provides the first explicit operator representation of quantum multipole noise in a pseudo-Hilbert space, enabling new analysis of open quantum system dynamics.

Findings

Constructed an explicit operator representation in a pseudo-Hilbert space.

Derived an asymptotic expansion for multitime correlation functions.

Applied the framework to analyze weakly interacting open quantum systems.

Abstract

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, $[c^-_n(t),c^+_n(\tau)]\approx \delta^{(n)}(\tau-t)$. 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.