Quantum multipole noise

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.

Cited by in corpus (3)

• Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit
• Long-time Markovianity of multi-level systems in the rotating wave approximation
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators