Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Accardi, L, Frigerio, A and Lewis, J T, Quantum stochastic processes, Pub. R.I.M.S. Kyoto 18, 1, 97–133 (1982).
Applebaum, D and Hudson R L, Fermion diffusions, to appear in J. Mathematical Phys.
Cockroft, A M and Hudson, R L, Quantum mechanical Wiener processes, J. Multivariate Anal. 7, 107–24 (1978).
Guichardet, A, Symmetric Hilbert spaces and related topics, lecture notes in Mathematics 261, Springer, Berlin (1972).
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).
Hudson, R L, Ion, P D F and Parthasarathy, K R, Time orthogonal unitary dilations II, preprint.
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).
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).
Hudson, R L and Streater, R F, Itô's formula is the chain rule with Wick ordering, Physics letters 86A 277–9 (1981).
Lindblad, G, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119–30 (1976).
Parthasarathy, K R and Hudson, R L, Non-commutative semimartingales and quantum diffusion processes adapted to Brownian motion, preprint.
Segal, I E, Tensor algebras over Hilbert spaces I, Trans. Amer. Math. Soc. 81 106–34 (1956).
Simon, B, Functional integration and quantum physics, Academic Press, New York (1979).
Author information
Authors and Affiliations
Editor information
Rights 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