Skip to main content

Construction of quantum diffusions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1055)

Keywords

  • Brownian Motion
  • Gauge Transformation
  • Stochastic Differential Equation
  • Weyl Operator
  • Quantum Diffusion

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Accardi, L, Frigerio, A and Lewis, J T, Quantum stochastic processes, Pub. R.I.M.S. Kyoto 18, 1, 97–133 (1982).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Applebaum, D and Hudson R L, Fermion diffusions, to appear in J. Mathematical Phys.

    Google Scholar 

  3. Cockroft, A M and Hudson, R L, Quantum mechanical Wiener processes, J. Multivariate Anal. 7, 107–24 (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Guichardet, A, Symmetric Hilbert spaces and related topics, lecture notes in Mathematics 261, Springer, Berlin (1972).

    MATH  Google Scholar 

  5. Hudson, R L, Ion, P D F and Parthasarathy, K R, Time-orthogonal unitary dilations and non-commutative Feynman-Kac formulae, Commun. Math. Phys. 83, 261–80 (1982).

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  6. Hudson, R L, Ion, P D F and Parthasarathy, K R, Time orthogonal unitary dilations II, preprint.

    Google Scholar 

  7. Hudson, R L, Karandikar, R L and Parthasarathy, K R, Towards a theory of non-commutative semimartingales adapted to Brownian motion and a quantum Itô's formula, in Theory and application of random fields, ed. Kallianpur, Lecture notes in Control and Information Sciences 49, Springer, Berlin (1983).

    Google Scholar 

  8. Hudson, R L and Parthasarathy, K R, Quantum diffusions, in Theory and application of random fields, ed. Kallianpur, Lecture notes in Control and Information Sciences 49, Springer, Berlin (1983).

    Google Scholar 

  9. Hudson, R L and Streater, R F, Itô's formula is the chain rule with Wick ordering, Physics letters 86A 277–9 (1981).

    CrossRef  ADS  MathSciNet  Google Scholar 

  10. Lindblad, G, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119–30 (1976).

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  11. Parthasarathy, K R and Hudson, R L, Non-commutative semimartingales and quantum diffusion processes adapted to Brownian motion, preprint.

    Google Scholar 

  12. Segal, I E, Tensor algebras over Hilbert spaces I, Trans. Amer. Math. Soc. 81 106–34 (1956).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Simon, B, Functional integration and quantum physics, Academic Press, New York (1979).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Hudson, R.L., Parthasarathy, K.R. (1984). Construction of quantum diffusions. In: Accardi, L., Frigerio, A., Gorini, V. (eds) Quantum Probability and Applications to the Quantum Theory of Irreversible Processes. Lecture Notes in Mathematics, vol 1055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071721

Download citation

  • DOI: https://doi.org/10.1007/BFb0071721

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12915-8

  • Online ISBN: 978-3-540-38798-5

  • eBook Packages: Springer Book Archive