Bibliography

1

Carmichael, H.: An open systems approach to quantum optics, Lecture Notes in Physics m 18, Springer Verlag, Berlin 1993

2

Dalibard, J. , Castin, Y. and Mølmer K.: ` Wave-function approach to dissipative processes in quantum optics', Phys. Rev. Lett. 68 (1992) 580-583

3

Mølmer, K., Castin, Y. and Dalibard, J.: `Monte Carlo wave-function method in quantum optics', J. Opt. Soc. Am. B 10 (1993) 524-538

4

Dum, R., Zoller, P. and Ritsch, H.: `Monte Carlo simulation of the atomic master equation for spontaneous emission', Phys. Rev. A 45 (1992) 4879-4887

5

Blanchard, Ph., and Jadczyk, A.: "Event-Enhanced-Quantum Theory and Piecewise Deterministic Dynamics", Ann. der Physik 4 (1995) 583-599, hep-th/9409189
(A review paper. Here a rough idea of the proof of the uniqueness of the PDP is sketched for the first time. The idea came from my discussions, in June and July 1994, with Heidi Narnhoffer at the Schrödinger Institute, Wien.)

6

Blanchard, Ph. and Jadczyk, A. : "On the Interaction Between Classical and Quantum Systems", Phys. Lett. A 175 (1993), 157-164 (The very first paper, describing the method of coupling of a quantum and of a classical system via dynamical semigroup. At that time we didn't yet know about piecewise deterministic processes.)

7

Blanchard, Ph. and Jadczyk, A.: "Strongly coupled quantum and classical systems and Zeno's effect", Phys. Lett. A 183 (1993) 272-276, hep-th/9309112
(Here, for the first time, piecewise deterministic process describing individual systems is being mentioned. We wrote: " To the Liouville equation describing the time evolution of statistical states of we will be in position to associate a piecewise deterministic process taking values in the set of pure states of . Knowing this process one can answer all kinds of questions about time correlations of the events as well as simulate the behaviour of individual quantum-classical systems. Let us emphasize that nothing more can be expected from a theory without introducing some explicit dynamics of hidden variables. What we achieved is the maximum of what can be achieved, which is more than orthodox interpretation gives. There are also no paradoxes; we cannot predict, but we can simulate the behaviour of individual systems." At that time we didn't yet know under what conditions our PDP is unique. That is why we used the term "associated" with the Liouville equation, rather than "derived".)

8

Jadczyk, A.: ``Topics in Quantum Dynamics", in Proc. First Caribb. School of Math. and Theor. Phys., Saint-Francois-Guadeloupe 1993, Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras and Fundamental Interactions, ed. R.Coquereaux et al., World Scientific, Singapore 1995, hep-th/9406204
( A review paper. Describes the PDP process. States the problem: "How to determine state of an individual quantum system?" Describes a process on which later was adapted for generation of quantum fractals.)

9

Jadczyk, A.: ``Particle Tracks, Events and Quantum Theory", Progr. Theor. Phys. 93 (1995), 631-646, hep-th/9407157
(A model of particle tracks using a continuous medium of detectors. Gives GRW "spontaneous localization" model as a particular case.)

10

Blanchard, Ph., and Jadczyk, ``Relativistic Quantum Events", Found. Phys 26 (1996) 1669-1681, quant-ph/9610028

11

Blanchard, Ph., Jadczyk, A., " EEQT a way out of the quantum trap", In Open Systems and Measurement in Relativistic Quantum Theory , Breuer, H.-P., Petruccione, F.,(Eds.), Lecture Notes in Physics, Springer-Verlag, 1999, quant-ph/9812081
(A review paper. With FAQ on EEQT.)

12

von Neumann, John: Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955

13

Davis, M. H. A. : Lectures on Stochastic Control and Nonlinear Filtering, Tata Institute of Fundamental Research, Springer Verlag, Berlin 1984
(This is where we have learned for the first time about the use of piecewise deterministic processs (PDP))

14

Davis, M. H. A. : Markov models and optimization, Monographs on Statistics and Applied Probability, Chapman and Hall, London 1993

15

Barnsley, M. F. : Fractals everywhere, Academic Press, San Diego 1988 (The main textbook reference on Iterated Function Systems.)

16

Peitgen, H-O., Hartmut, J., and Saupe, D.: Chaos and Fractals. New Frontiers of Science, Springer, New York 1992.

17

Peigné, Marc : Iterated Function Systems and spectral decomposition of the associated Markov operator, Preprint U.R.A. C.N.R.S. 305, Prépublication 93 -24, Novembre 1993

18

Casati G.: "Quantum mechanics and chaos", in: Chaos and Quantum Physics, eds. M. J. Gianoni, A. Voros and J. Zinn-Justin, North Holland, 1991

19

Casati, G., Maspero, G., and D. L. Shepelyansky, "Quantum fractal eigenstates", Physica D 131 (1999), pp. 311-316

20

Ph. Blanchard, A. Jadczyk, A. Ruschhaupt, "How Events did come into beeing: EEQT, Particle Tracks, Quantum Chaos, and Tunneling Time", in Mysteries, Puzzles and Paradoxes in Quantum Mechanics , Rodolfo Bonifacio, Ed., Woodbury, NY: American Institute of Physics, 1999, [AIP Conference Proceedings, no. 461], J. Mod. Opt. 47 (2000), 2247-2263, quant-ph/9911113
(A review paper: particle tracks, GRW, Born's interpretation, tunneling time, quantum fractals - the tetrahedron model.)

21

Jadczyk, A., Kondrat, G. and Olkiewicz, R. : "On uniqueness of the jump process in quantum measurement theory" , J. Phys. A 30 (1996) 1-18, quant-ph/9512002 //

23

Jadczyk, A.: `IFS Signatures of Quantum States', IFT Uni Wroclaw, internal report, September 1993.

24

Blanchard, Ph., Jadczyk, A., and Olkiewicz, R.: ` Completely Mixing Quantum Open Systems and Quantum Fractals', Physica D 148 (2001) pp. 227-241, quant-ph/9909085
(Quantum fractals from simultaneous measurement of noncommuting observables.)

25

Jastrzebski G.: Interacting classical and quantum systems. Chaos from quantum measurements, Ph. D. thesis, University of Wrocaw (in Polish), 1996