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Number of results

Journal

2004 | 2 | 3 | 492-503

Article title

On quantum iterated function systems

Content

Title variants

Languages of publication

EN

Abstracts

EN
A Quantum Iterated Function System on a complex projective space is defined through a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.

Publisher

Journal

Year

Volume

2

Issue

3

Pages

492-503

Physical description

Dates

published
1 - 9 - 2004
online
1 - 9 - 2004

Contributors

  • Institute of Theoretical Physics, University of Wrocław, 9 Pl. Maxa Borna, 50 204, Wrocław, Poland

References

  • [1] M.F. Barnsley: Fractals everywhere, Academic Press, San Diego, 1988.
  • [2] L. Skala, K. Bradler and V. Kapsa: “Consistency requirement and operators in quantum mechanics”, Czech. J. Phys., Vol.52, (2002), pp.345–350. http://dx.doi.org/10.1023/A:1014523917212[Crossref]
  • [3] A. Jadczyk and R. Öberg: “Quantum Jumps, EEQT and the Five Platonic Fractals”, Preprint: http://arXiv.org/abs/quant-ph/0204056.
  • [4] G. Jastrzebski: “Interacting classical and quantum systems. Chaos from quantum measurements”, Ph.D. thesis (in Polish), University of Wrocław, 1996.
  • [5] Ö. Stenflo: “Uniqueness of invariant measures for place-dependent random iterations of functions”, IMA Vol. Math. Appl., Vol. 132, (2002), pp. 13–32. (Preprint: http://www.math.su.se/stenflo/IMA.pdf)
  • [6] M.F. Barnsley, S.G. Demko, J.H. Elton and J.S. Geronimo: “Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities”, Ann. Inst. H. Poincaré Probab. Statist, Vol. 24, (1988), pp. 367–294. (Erratum: Vol. 25, (1989), pp. 589–590)
  • [7] A. Jadczyk, G. Kondrat and R. Olkiewicz: “On uniqueness of the jump process in quantum measurement theory”, J. Phys. A, Vol. 30, (1996), pp. 1–18. (Preprinthttp://arXiv.org/abs/quant-ph/9512002)
  • [8] Ph. Blanchard and A. Jadczyk: “On the Interaction Between Classical and Quantum Systems”, Phys. Lett. A, Vol. 175, (1993), pp. 157–164. (Preprinthttp://arXiv.org/abs/quant-ph/9512002) http://dx.doi.org/10.1016/0375-9601(93)90818-K[Crossref]
  • [9] A. Jadczyk: “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. (Preprinthttp://arXiv.org/abs/hep-th/9406204)
  • [10] A. Jadczyk: “IFS Signatures of Quantum States”, IFT Uni Wroclaw, internal report, September 1993.
  • [11] Ph. Blanchard, A. Jadczyk and R. Olkiewicz: “Completely Mixing Quantum Open Systems and Quantum Fractals”, Physica D: Nonlinear Phenomena, Vol.148, (2001), pp.227–241. (Preprinthttp://arXiv.org/abs/quant-ph/9909085) http://dx.doi.org/10.1016/S0167-2789(00)00175-5[Crossref]
  • [12] A. Lozinski, K. Zyczkowski and W. Slomczynski: “Quantum Iterated Function Systems”, (Phys. Rev., Vol. E68, (2003), article 046110. (Preprinthttp://arXiv.org/abs/quant-ph/0210029)

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_BF02476427
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