The structures of state space concerning Quantum Dynamical Semigroups

TL;DR

This paper explores the structural decomposition of state spaces in finite-dimensional quantum dynamical semigroups, highlighting differences between discrete and continuous evolutions and their relation to quantum processes like decay and decoherence.

Contribution

It provides a detailed analysis of how the state space decomposes in quantum dynamical semigroups and distinguishes features unique to discrete versus continuous time evolutions.

Findings

Decomposition of state space into decay and stationary subspaces.

Differences between discrete and continuous semigroup evolutions.

Identification of relations between space structure and quantum processes.

Abstract

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to decay, orthogonal subspaces support the stationary states. Specialities where the complete positivity of evolutions is actually needed for analysis, mainly for evolution of coherence, are highlighted. Decompositions are done the same way for evolutions in discrete as in continuous time, but evolutions may show differences, only for discrete semigroups there may appear cases of sudden decay and of perpetual oscillation. Concluding the analysis we identify the relation of the state space structure to the processes of Decay, Decoherence, Dissipation and Dephasing.