Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 027, 7 pages      quant-ph/0602224

Anomalously Slow Cross Symmetry Phase Relaxation, Thermalized Non-Equilibrated Matter and Quantum Computing Beyond the Quantum Chaos Border

M. Bienert a, J. Flores a, S.Yu. Kun a, b, c and T.H. Seligman a
a) Centro de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, Mexico
b) Nonlinear Physics Centre, RSPhysSE, ANU, Canberra ACT 0200, Australia
c) Department of Theoretical Physics, RSPhysSE, ANU, Canberra ACT 0200, Australia

Received November 30, 2005, in final form February 08, 2006; Published online February 27, 2006

Thermalization in highly excited quantum many-body system does not necessarily mean a complete memory loss of the way the system was formed. This effect may pave a way for a quantum computing, with a large number of qubits n ≈ 100-1000, far beyond the quantum chaos border. One of the manifestations of such a thermalized non-equilibrated matter is revealed by a strong asymmetry around 90° c.m. of evaporating proton yield in the Bi(γ,p) photonuclear reaction. The effect is described in terms of anomalously slow cross symmetry phase relaxation in highly excited quantum many-body systems with exponentially large Hilbert space dimensions. In the above reaction this phase relaxation is about eight orders of magnitude slower than energy relaxation (thermalization).

Key words: anomalously slow cross symmetry phase relaxation; Bi(γ,p) photonuclear compound reaction; quantum chaos; thermalized non-equilibrated matter; quantum computing.

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  1. Wigner E.P., Characteristic vectors of bordered matrices with infinite dimensions, Ann. Math., 1955, V.62, N 3, 548-564.
    Wigner E.P., Characteristic vectors of bordered matrices with infinite dimensions II, Ann. Math., 1957, V.65, N 2, 203-207.
  2. Wigner E., Statistical properties of nuclei, Editor J.B. Garg, New York - London, Plenum Press, 1972, p. 11.
  3. Anderson P.W., Basic notions of condensed matter physics, Frontiers in Physics, Vol. 55, The Benjamin-Cummings, 1984, 71-72.
  4. Guhr T., Müller-Groeling A., Weidenmüller H.A., Random matrix theories in quantum physics: common concepts, Phys. Rep., 1998, V.299, N 4-6, 189-425 (and references therein), cond-mat/9707301.
  5. Benet L., Izrailev F.M., Seligman T.H., Suárez-Moreno A., Semiclassical properties of eigenfunctions and occupation number distribution for a model of two interacting particles, Phys. Lett. A, 2000, V.277, N 2, 87-93, chao-dyn/9912035.
  6. Benet L., Flores J., Hernandez-Saldana H., Izrailev F.M., Leyvraz F., Seligman T.H., Fluctuations of wavefunctions about their classical average J. Phys. A: Math. Gen., 2003, V.36, N 5, 1289-1297, nlin.CD/0207039.
  7. Flores J., Kun S.Yu., Seligman T.H., Slow phase relaxation as a route to quantum computing beyond the quantum chaos border, Phys. Rev. E, 2005, V.72, N 1, 017201, 4 pages.
  8. Georgeot B., Shepelyansky D.L., Quantum chaos border for quantum computing, Phys. Rev. E, 2000, V.62, N 3, 3504-3507, quant-ph/9909074.
  9. Shepelyansky D.L., Quantum chaos and quantum computers, in Proceedings of Nobel Symposium on Quantum Chaos 2000, Phys. Scripta, 2001, V.90, 112-120, quant-ph/0006073.
  10. Bienert M., Flores J., Kun S.Yu., Experimental proposal for accurate determination of the phase relaxation time in highly excited quantum many-body systems, nucl-ex/0508020.
  11. Kun S.Yu., Novel approach to angular distributions in precompound reactions: Does the Bohr hypothesis always work?, Z. Phys. A, 1994, V.348, N 2, 273-279.
  12. Kun S.Yu., Statistical reactions with memory and thermalized-nonequilibrated nuclear states, Z. Phys. A, 1997, V.357, N 2, 255-269.
  13. Toms M.E., Stephens W.E., Photoprotons from In, Ce, and Bi, Phys. Rev., 1953, V.92, N 2, 362-366.
  14. Blatt J.M., Weisskopf V.F., Theoretical nuclear physics, New York, Dover Publications, Inc., 1991.
  15. Harvey R.R., Caldwell J.T., Bramblett R.L., Fultz S.C., Photoneutron cross sections of Pb206, Pb207, Pb208, and Bi209, Phys. Rev., 1964, V.136, N 1, B126-B131.
  16. Blann M., Preequilibrium decay, Annu. Rev. Nucl. Sci., 1975, V.25, 123-166.
  17. Simon A., Theory of polarized particles and gamma rays in nuclear reactions, Phys. Rev., 1953, V.92, N 4, 1050-1060.
  18. Racah G., Theory of complex spectra. I, Phys. Rev., 1942, V.61, N 3-4, 186-197.
    Racah G., Theory of complex spectra. II, Phys. Rev., 1942, V.62, N 9-10, 438-462.
  19. Blatt J.M., Biedenharn L.C., The angular distributions of scattering and reaction cross sections, Rev. Mod. Phys., 1952, V.24, N 4, 258-272.
  20. Kun S.Yu., Ericson fluctuations for the finite spin relaxation times, Phys. Lett. B, 1993, V.319, N 1, 16-22.
  21. Mitchell G.E., Bilpuch E.G., Shriner J.F., Lane A.M., Amplitude correlations in nuclear resonance spectroscopy, Phys. Rep., 1985, V.117, N 1, 1-74.
  22. Ericson T., Mayer-Kuckuk, Fluctuations in nuclear reactions, Annu. Rev. Nucl. Sci., 1966, V.16, 183-206.
  23. Agassi D., Weidenmüller H.A., Mantzouranis G., The statistical theory of nuclear reactions for strongly overlapping resonances as a theory of transport phenomena, Phys. Rep., 1975, V.22, N 3, 145-179.
  24. Kun S.Yu., Vagov A.V., Greiner W., Quantum-classical correspondence in microscopic and mesoscopic complex collisions, Phys. Rev. C, 2001, V.63, N 1, 014608, 5 pages.
  25. Benet L., Kun S.Yu., Wang Qi, Effect of phase relaxation on quantum superpositions in complex collisions, quant-ph/0503046.
  26. Kun S.Yu., Vagov A.V., Vorov O.K., Coherently rotating hyperdeformed quasimolecules in 12C+24Mg scattering?, Phys. Rev. C, 1999, V.59, N 2, R585-R588.
  27. Kun S.Yu., Robson B.A., Vagov A.V., Oscillating-correlated nonstatistical structures, slow spin decoherence, and hyperdeformed coherent rotational states in 24Mg+24Mg and 28Si+28Si scattering, Phys. Rev. Lett., 1999, V.83, N 3, 504-507.
  28. Kun S.Yu., Chadderton L.T., Vagov A.V., Greiner W., A new probe for coherent many-body dynamics: Nonergodic molecules in continuum, Int. J. Mod. Phys. E, 2002, V.11, N 4, 273-280.
  29. Kun S.Yu., Benet L., Chadderton L.T., Greiner W., Haas F., Macroscopic quantum superpositions in highly excited strongly interacting many-body systems, Phys. Rev. C, 2003, V.67, N 1, 011604, 4 pages, quant-ph/0205036.
  30. Benet L., Kun S.Yu., Wang Qi, Denisov V., Effect of a finite-time resolution on Schrödinger cat states in complex collisions, Phys. Lett. B, 2005, V.605, N 1-2, 101-105, nucl-th/0407029.
  31. Kun S.Yu., Spontaneous coherence and non-equilibrium correlation phase transitions in microscopic and mesoscopic systems, in Proceedings of International Conference "Nonequilibrium and Nonlinear Dynamics in Nuclear and Other Finite Systems" (May 21-25, 2001, Beijing), Editors Zhuxia Li, Ke Wu, Xizhen Wu, Enguang Zhao and F. Sakata, AIP Conference Proceedings, Vol. 597, New York, Melville, 2001, 319-326.
  32. Kun S.Yu., Sensitivity of nucleus-nucleus cross sections and atomic-electron effects in dissipative heavy-ion collisions, Phys. Rev. Lett., 2000, V.84, N 3, 423-426.
  33. Nielsen M.A., Chuang I.L., Quantum computation and quantum information, Oxford, Cambridge University Press, 2000.

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