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2004 | 2 | 3 | 492-503
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On quantum iterated function systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca

Czasopismo
Rocznik
Tom
2
Numer
3
Strony
492-503
Opis fizyczny
Daty
wydano
2004-09-01
online
2004-09-01
Twórcy
  • Institute of Theoretical Physics, University of Wrocław, 9 Pl. Maxa Borna, 50 204, Wrocław, Poland, ajad@th-phys.edu.hk
Bibliografia
  • [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)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02476427
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