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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Dynamics

MP 3.2: Talk

Monday, March 18, 2024, 15:30–15:50, HL 001

Unique Decompositions of Generators of Dynamical Semigroups — •Frederik vom Ende — Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Since the 1970s it is well known that every generator L of a completely positive, trace-preserving dynamical semigroup is of the form L=−i[H, · ]+Φ−1/2{Φ^*(1), · } for some Hamiltonian H and some completely positive map Φ. We prove that every quantum state gives rise to a unique decomposition of L into its "building blocks" by means of vanishing expectation values: More precisely, for all states ω there exist unique H, Φ with tr(Hω)=0 and tr(Φ(ω·ω))=0 such that the above decomposition holds. As a special case, for ω=1/n one recovers the uniqueness condition of Gorini, Kossakowski, and Sudarshan involving traceless Lindblad operators (which now has a physical interpretation by means of our result). Moreover, this insight allows for a generalization of such unique decompositions to arbitrary separable Hilbert spaces.

Keywords: quantum dynamics; open quantum systems; Lindblad operators; unique decomposition