Abstract
By using a condition of average trace preservation we derive a general class of non-Markovian Gaussian diffusive unravelings [L. Diosi and L. Ferialdi, Phys. Rev. Lett. \textbf{113}, 200403 (2014)], here valid for arbitrary non-Hermitian system operators and noise correlations. The conditions under which the generalized stochastic Schrodinger equation has the same symmetry properties (invariance under unitary changes of operator base) than a microscopic system-bath Hamiltonian dynamics are determined. While the standard quantum diffusion model (standard noise correlations) always share the same invariance symmetry, the generalized stochastic dynamics can be mapped with an arbitrary bosonic environment only if some specific correlation constraints are fulfilled. These features are analyzed for different non-Markovian unravelings equivalent in average. Results based on quantum measurement theory that lead to specific cases of the generalized dynamics [J. Gambetta and H. M. Wiseman, Phys. Rev. A \textbf{66}, 012108 (2002)]\ are studied from the perspective of the present analysis.
Highlights
The theory of open quantum systems is well established when a Markovian approximation applies [1]
This equivalent evolution allow us to recover in a simple way previous generalized stochastic dynamics obtained from quantum measurement theory [25]
We ask if the stochastic Schrodinger equation has the same invariance symmetry property than a microscopic bosonic dynamics able to induce the same system dynamics
Summary
The theory of open quantum systems is well established when a Markovian approximation applies [1]. The main goal of this paper is to develop similar symmetry analysis for the generalized non-Markovian unraveling [36] and to find which constraints on the noise correlations arise. We show that both the generalized non-Markovian Schrodinger equation and its associated density matrix evolution always share the same symmetry property, that is, they are invariant under arbitrary unitary changes of the system operator base. Instead of a path integral formalism, here the wave vector evolution [Eq (12)] is derived by postulating a stochastic density matrix dynamics driven by multiplicative nonwhite Gaussian noises, where an undetermined contribution is obtained from a condition of average trace conservation [14]. In the Appendix we define the main properties of the noise correlations as well as a generalization of Novikov theorem [37] valid for arbitrary multiplicative complex Gaussian noises
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