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In arXiv:1212.2613, we associated a presheaf \Sigma^A with each unitalC*-algebra A. The spectral presheaf \Sigma^A generalises the Gelfand spectrumof an abelian unital C*-algebra. In the present article, we considerone-parameter groups of automorphisms of the spectral presheaf, in particularthose arising from one-parameter groups of inner automorphisms of the algebra.We interpret the spectral presheaf as a (generalised) state space for a quantumsystem and show how one can use flows on the spectral presheaf and onassociated structures to describe the time evolution of non-relativisticquantum systems, both in the Schr\"odinger picture and the Heisenberg picture.

Flows on Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras and Time Evolution of Quantum Systems