PL EN


Preferences help
enabled [disable] Abstract
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
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
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_BF02476427
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.