Abstract
Some aspects of open quantum dynamics are discussed. We make use of Liouville space notation [1], whereby operators are represented by ‘kets’ and ‘bras’, on which act superoperators (supops for short). We first derive in a concise way the complete positivity (CP) of ‘closed’ dynamical semigroups, and the Kossakowski-Lindblad (KL) form of their generators [2]. The two main master equations, ‘memory’ and ‘cumulant’, are next derived [3]. It is emphasized that these two equations treated to a given order in the system-bath interaction amount to different approximations. This is illustrated with a ‘static’ system in a thermal bath of oscillators with uncorrelated initial state [4], which also provides an instance of non-CP reduced dynamics. Finally we obtain the reduced Wigner function of an oscillator in a bath of oscillators, for arbitrary initial states. (Notation: We often write f(t) = f t).
This is a preview of subscription content, log in via an institution to check access.
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
A. Royer, (a) Phys. Rev. A 43, 44 (1991); (b) ibid. 45, 793 (1992). In these references, {A B} ≡ (2πℏ)TrA † B, whence different prefactors. Also, M° is denoted M*.
V. Gorini, A. Kossakowski and E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976); L. Lindblad, Commun. Math. Phys. 48, 119 (1976)
H.P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, (Oxford University Press, Oxford, 2002)
D. Braun, F. Haake and W. Strunz, Phys. Rev. Lett. 86, 2913 (2001)
F. Benatti, R. Floreanini and R. Romano, J. Phys. A 35, L551 (2002)
R.A. Horn and C.R. Johnson, Matrix Analysis, (Cambridge University Press, Cambridge, 1985) p. 135
A. Royer, Phys. Rev. Lett. 77, 3272 (1996)
(a) R. Kubo, J. Phys. Soc. Japan 17, 1100 (1962); J. Math. Phys. 4, 174 (1963); (b) A. Royer, Phys. Rev. A 6, 1741 (1972); (c) R.F. Fox, Phys. Rep. 48, 179 (1978)
A. Royer, Phys. Rev. A 7, 1078 (1973); ibid. 22, 1625 (1980); Acta Phys. Pol. A54, 805 (1978)
(a) M. Hillery, R.F. O’Connell, M.O. Scully and E.P. Wigner, Phys. Rep. 106, 121 (1984); (b) A. Royer, Am. J. Phys. 64, 1393 (1996)
See, e.g., R.G. Littlejohn, Phys. Rep. 138, 193 (1986)
This result is implicit in: G.R. Folland, Harmonic Analysis in Phase Space, (Princeton University Press, Princeton, 1989)
H. Dekker, Phys. Rev. A 16, 2116 (1977); A.O. Caldeira and A.J. Leggett, Physica 121A, 587 (1983); F. Haake and R. Reibold, Phys. Rev. A 32, 2462 (1985); W.G. Unruh and W.H. Zurek, Phys. Rev. D 40, 1071 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Royer, A. (2003). Aspects of Open Quantum Dynamics. In: Benatti, F., Floreanini, R. (eds) Irreversible Quantum Dynamics. Lecture Notes in Physics, vol 622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44874-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-44874-8_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40223-7
Online ISBN: 978-3-540-44874-7
eBook Packages: Springer Book Archive