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Quantum diffusions on the rotation algebras and the quantum hall effect

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Quantum Probability and Applications V

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

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References

  1. Accardi, L., Frigerio, A and Lewis, J.T., Quantum Stochastic Processes, Proc. Res. Inst. Math. Sci. Kyoto 18, 94–133 (1982)

    MathSciNet  MATH  Google Scholar 

  2. Hudson, R.L. and Parthasarathy, K.R., Quantum Ito’s Formula and Stochastic Evolutions, Commun. Math. Phys. 93, 301–323 (1984).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Hudson, R.L., Algebraic Theory of Quantum Diffusions, Stochastic Mechanics and Stochastic Processes, Swansea Proceedings, eds. I. Davies, A. Truman (1986).

    Google Scholar 

  4. Evans, M.P. and Hudson, R.L., Multidimensional Quantum Diffusions, Quantum Probability and Applications III, proceedings Oberwolfach, eds. Accardi, L. and von Waldenfels, W., 1303, Springer-Verlag (1987).

    Google Scholar 

  5. Hudson, R.L., Robinson, P., Quantum Diffusions and the Noncommutative Torus, Lett. Math. Phys. 15, 47–53 (1988).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Rieffel, M.A., C*-algebras Associated with Irrational Rotations, Pacific J. Math. 93, 415–429 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  7. Hudson, R.L., Quantum Stochastic Calculus in Fock space: a review, Fundamental Aspects of Quantum Theory, eds. Frigerio, A. and Gorini, V., Plenum Press, New York and London (1986).

    Chapter  Google Scholar 

  8. Bellisard, J., C*-algebras in Solid State Physics, in D. Evans (ed.), Proc. Anglo-American Conf. on Operator ALgebras, Warwick (1987), to appear.

    Google Scholar 

  9. Srivastava, Y., Beyond the Hall Effect: Practical Engineering form Relativistic Quantum Field Theory, Fundamental Aspects of Quantum Theory, eds. Frigerio, A., and Gorini, V., Plenum Press, New York and London (1986).

    Google Scholar 

  10. Robinson, P., Nottingham PhD thesis (1988).

    Google Scholar 

  11. Streda, P., Theory of quantised Hall conductivity in two dimensions, J. Phys. C. 15, L717–L723 (1982).

    Article  ADS  Google Scholar 

  12. Connes, A., A survey of Foliations and Operator Algebras, chapter 13, Proc. Symposia in Pure Mathematics, Operator Algebras and Applications, American Math. Soc. 38 (part 1), 616–628 (1982).

    Google Scholar 

  13. Hudson, R.L., Lindsay, J.M., Uses for non-Fock Quantum Brownian motion and a quantum Martingale representation theorem, Proceedings of the 2nd workshop on Quantum Probability and its applications, eds. Accardi, L. and von Waldenfels, W., 1136, Springer-Verlag (1985).

    Google Scholar 

  14. Prange, R.E., Girvin, S.M. (eds.), Quantum Hall Effect, Graduate Texts in Contemporary Physics, New York, Springer (1987).

    Google Scholar 

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Luigi Accardi Wilhelm von Waldenfels

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© 1990 Springer-Verlag

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Robinson, P. (1990). Quantum diffusions on the rotation algebras and the quantum hall effect. 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/BFb0085526

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  • DOI: https://doi.org/10.1007/BFb0085526

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53026-8

  • Online ISBN: 978-3-540-46311-5

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