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Quantum diffusions on involutive algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 1442)

Abstract

We introduce a refinement of the notion of quantum diffusion which has the advantage over the earlier definition that the algebraic conditions which are necessary for existence are always satisfied. In this framework every quantum stochastic parallel transport process induces horizontal lifts. Applications are given to group respresentations and a factorisation property is obtained for parallel transport processes driven by classical Brownian motion on the d × d matrices.

Keywords

  • Rotation Number
  • Parallel Transport
  • Complex Hilbert Space
  • Hermitian Structure
  • Horizontal Lift

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References

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© 1990 Springer-Verlag

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Applebaum, D. (1990). Quantum diffusions on involutive algebras. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications V. Lecture Notes in Mathematics, vol 1442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085502

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  • DOI: https://doi.org/10.1007/BFb0085502

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53026-8

  • Online ISBN: 978-3-540-46311-5

  • eBook Packages: Springer Book Archive