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Quantum Transport in Degenerate Systems

  • S. V. Kozyrev
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Abstract

Transport in nonequilibrium degenerate quantum systems is investigated. The transfer rate depends on the parameters of the system. In this paper we investigate the dependence of the flow (transfer rate) on the angle between “bright” vectors (which define the interaction of the system with the environment). We show that in some approximation for the system under investigation the flow is proportional to the cosine squared of the angle between the “bright” vectors. Earlier the author has shown that in this degenerate quantum system excitation of nondecaying quantum “dark” states is possible; moreover, the effectiveness of this process is proportional to the sine squared of the angle between the “bright” vectors (this phenomenon was discussed as a possible model of excitation of quantum coherence in quantum photosynthesis). Thus quantum transport and excitation of dark states are competing processes; “dark” states can be considered as a result of leakage of quantum states in a quantum thermodynamic machine which performs the quantum transport.

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References

  1. 1.
    D. F. Abasto, M. Mohseni, S. Lloyd, and P. Zanardi, “Exciton diffusion length in complex quantum systems: the effects of disorder and environmental fluctuations on symmetry-enhanced supertransfer,” Philos. Trans. R. Soc. London A: Math. Phys. Eng. Sci. 370, 3750–3770 (2012).CrossRefGoogle Scholar
  2. 2.
    L. Accardi, K. Imafuku, and S. V. Kozyrev, “Interaction of 3-level atom with radiation,” Opt. Spectrosc. 94 (6), 904–910 (2003).CrossRefGoogle Scholar
  3. 3.
    L. Accardi and S. Kozyrev, “Lectures on quantum interacting particle systems,” in Quantum Interacting Particle Systems: Lecture Notes of the Volterra–CIRM Int. Sch., Trento, 2000 (World Scientific, Hackensack, NJ, 2002), QP–PQ: Quantum Probab. White Noise Anal. 14, pp. 1–195.CrossRefGoogle Scholar
  4. 4.
    L. Accardi, S. V. Kozyrev, and A. N. Pechen, “Coherent quantum control of Λ-atoms through the stochastic limit,” in Quantum Information and Computing, Ed. by L. Accardi, M. Ohya, and N. Watanabe (World Scientific, Hackensack, NJ, 2006), QP–PQ: Quantum Probab. White Noise Anal. 19, pp. 1–17; arXiv: quant-ph/0403100.CrossRefGoogle Scholar
  5. 5.
    L. Accardi, Y. G. Lu, and I. Volovich, Quantum Theory and Its Stochastic Limit (Springer, Berlin, 2002).CrossRefzbMATHGoogle Scholar
  6. 6.
    G. G. Amosov and S. N. Filippov, “Spectral properties of reduced fermionic density operators and parity superselection rule,” Quantum Inf. Process. 16 (1), 2 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    I. Ya. Aref’eva, “Formation time of quark–gluon plasma in heavy-ion collisions in the holographic shock wave model,” Teor. Mat. Fiz. 184 (3), 398–417 (2015) [Theor. Math. Phys. 184, 1239–1255 (2015)]; arXiv: 1503.02185 [hep-th].MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    I. Aref’eva, “Multiplicity and thermalization time in heavy-ions collisions,” EPJ Web Conf. 125, 01007 (2016).CrossRefGoogle Scholar
  9. 9.
    I. Ya. Aref’eva and M. A. Khramtsov, “AdS/CFT prescription for angle-deficit space and winding geodesics,” J. High Energy Phys. 2016 (4), 121 (2016); arXiv: 1601.02008 [hep-th].MathSciNetGoogle Scholar
  10. 10.
    I. Aref’eva and I. Volovich, “Holographic photosynthesis,” arXiv: 1603.09107 [hep-th].Google Scholar
  11. 11.
    I. Ya. Aref’eva, I. V. Volovich, and S. V. Kozyrev, “Stochastic limit method and interference in quantum manyparticle systems,” Teor. Mat. Fiz. 183 (3), 388–408 (2015) [Theor. Math. Phys. 183, 782–799 (2015)].CrossRefGoogle Scholar
  12. 12.
    C.-K. Chan, G.-D. Lin, S. F. Yelin, and M. D. Lukin, “Quantum interference between independent reservoirs in open quantum systems,” Phys. Rev. A 89 (4), 042117 (2014).CrossRefGoogle Scholar
  13. 13.
    R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).CrossRefzbMATHGoogle Scholar
  14. 14.
    G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mančal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446, 782–786 (2007).CrossRefGoogle Scholar
  15. 15.
    M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84 (22), 5094–5097 (2000); arXiv: quant-ph/0001094.CrossRefGoogle Scholar
  16. 16.
    A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory,” Usp. Mat. Nauk 70 (2), 141–180 (2015) [Russ. Math. Surv. 70, 331–367 (2015)].MathSciNetzbMATHGoogle Scholar
  17. 17.
    S. V. Kozyrev, “Ultrametricity in the theory of complex systems,” Teor. Mat. Fiz. 185 (2), 346–360 (2015) [Theor. Math. Phys. 185, 1665–1677 (2015)].MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    S. V. Kozyrev, A. A. Mironov, A. E. Teretenkov, and I. V. Volovich, “Flows in non-equilibrium quantum systems and quantum photosynthesis,” Infin. Dimens. Anal. Quantum Probab. Relat. Top. 20 (4), 1750021 (2017); arXiv: 1612.00213 [quant-ph].MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    S. Lloyd and M. Mohseni, “Symmetry-enhanced supertransfer of delocalized quantum states,” New J. Phys. 12 (7), 075020 (2010); arXiv: 1005.2579 [quant-ph].CrossRefGoogle Scholar
  20. 20.
    M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik, “Environment-assisted quantum walks in photosynthetic energy transfer,” J. Chem. Phys. 129 (17), 174106 (2008).CrossRefGoogle Scholar
  21. 21.
    R. Monshouwer, M. Abrahamsson, F. van Mourik, and R. van Grondelle, “Superradiance and exciton delocalization in bacterial photosynthetic light-harvesting systems,” J. Phys. Chem. B 101 (37), 7241–7248 (1997).CrossRefGoogle Scholar
  22. 22.
    M. Ohya and I. Volovich, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano-and Bio-systems (Springer, New York, 2011).CrossRefzbMATHGoogle Scholar
  23. 23.
    A. Olaya-Castro, C. F. Lee, F. F. Olsen, and N. F. Johnson, “Efficiency of energy transfer in a light-harvesting system under quantum coherence,” Phys. Rev. B 78 (8), 085115 (2008).CrossRefGoogle Scholar
  24. 24.
    A. N. Pechen and N. B. Il’in, “Existence of traps in the problem of maximizing quantum observable averages for a qubit at short times,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 289, 227–234 (2015) [Proc. Steklov Inst. Math. 289, 213–220 (2015)].MathSciNetzbMATHGoogle Scholar
  25. 25.
    A. N. Pechen and N. B. Il’in, “On the problem of maximizing the transition probability in an n-level quantum system using nonselective measurements,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 294, 248–255 (2016) [Proc. Steklov Inst. Math. 294, 233–240 (2016)].MathSciNetzbMATHGoogle Scholar
  26. 26.
    A. Pechen and N. Il’in, “Control landscape for ultrafast manipulation by a qubit,” J. Phys. A: Math. Theor. 50 (7), 075301 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    A. Pechen and A. Trushechkin, “Measurement-assisted Landau–Zener transitions,” Phys. Rev. A 91 (5), 052316 (2015).CrossRefGoogle Scholar
  28. 28.
    Quantum Effects in Biology, Ed. by M. Mohseni, Y. Omar, G. S. Engel, and M. B. Plenio (Cambridge Univ. Press, Cambridge, 2014).Google Scholar
  29. 29.
    G. D. Scholes, G. R. Fleming, A. Olaya-Castro, and R. van Grondelle, “Lessons from nature about solar light harvesting,” Nature Chem. 3, 763–774 (2011).CrossRefGoogle Scholar
  30. 30.
    M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Univ. Press, Cambridge, 1997).CrossRefGoogle Scholar
  31. 31.
    M. E. Shirokov, “On quantum zero-error capacity,” Usp. Mat. Nauk 70 (1), 187–188 (2015) [Russ. Math. Surv. 70, 176–178 (2015)].MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    A. S. Trushechkin and I. V. Volovich, “Perturbative treatment of inter-site couplings in the local description of open quantum networks,” Europhys. Lett. 113 (3), 30005 (2016).CrossRefGoogle Scholar
  33. 33.
    I. V. Volovich, “Models of quantum computers and decoherence problem,” in Quantum Information: Proc. 1st Int. Conf., Nagoya, 1997 (World Scientific, Singapore, 1999), pp. 211–224; arXiv: quant-ph/9902055.Google Scholar
  34. 34.
    I. V. Volovich, “Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light,” Phys. Lett. A 380 (1–2), 56–58 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    I. V. Volovich and S. V. Kozyrev, “Manipulation of states of a degenerate quantum system,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 294, 256–267 (2016) [Proc. Steklov Inst. Math. 294, 241–251 (2016)].MathSciNetzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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