Spectral-angular parametrization of open qudit dynamicsTBA
prof. dr hab. Jean-Pierre Gazeau
Chair of Mathematical Physics, 2026-04-17 godz. 9:45 - 11:15
We introduce a parametrization of finite-dimensional quantum states that is particularly well adapted to the study of open-system dynamics. A generic density matrix is decomposed into two sets of variables: spectral parameters, encoding the eigenvalue structure, and angular variables, describing the eigenvectors through a flag-manifold geometry.
The spectral parameters admit a natural Lie-algebraic interpretation as simple-root coordinates, and are constrained within a convex polytope corresponding to a Weyl chamber. This structure provides a clear geometric picture of the state space.
Within this framework, the dynamics generated by a GKLS (Lindblad) evolution exhibits a partial decoupling: the dissipative part governs the spectral variables, while both Hamiltonian and dissipative contributions influence the angular ones.
Low-dimensional cases illustrate the construction, and we briefly discuss applications, including an alternative notion of purity expressed solely in terms of spectral data.
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