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Theory of Quantum Non-equilibrium Physics

Theory of Quantum Non-equilibrium Physics. -From Introduction to Outlook – Ochanomizu University F. Shibata. （１） Introduction –Outlook of several theoretical methods （２） Projection operator formalism F. S., T. Arimitsu, M. Ban and S. Kitajima,

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Theory of Quantum Non-equilibrium Physics

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  1. Theory of Quantum Non-equilibrium Physics -From Introduction to Outlook – Ochanomizu University F. Shibata

  2. （１） Introduction –Outlook of several theoretical methods （２） Projection operator formalism F. S., T. Arimitsu, M. Ban and S. Kitajima, “Physics of Quanta and Non-equilibrium Systems”, chap. 3, (University of Tokyo Press, 2009, in Japanese) H.-P. Breuer and F. Petruccione, “The Theory of Open Quantum Systems” (2006, Oxford ) （３） Spin relaxation (i ) F.S., C. Uchiyama, J. Phys. Soc. Jpn., 62 (1993) 381. “Rigorous solution to nonlinear spin relaxation process” （4） Spin relaxation (ii ) Y. Hamano, F.S., J. Phys. Soc. Jpn., 51 (1982) 1727. “Theory of spin relaxation for arbitrary time scale”

  3. （5） Low field resonance : exact solution F.S.-I. Sato, Physica A 143 (1987) 468. “Theory of low field resonance and relaxation Ⅰ” （６） Micro-Laser theory C. Uchiyama, F. S., J. Phys. Soc. Jpn., 69 (2000) 2829. “Self-organized formation of atomic coherence via photon exchange in a coupled atom-photon system”. （7） Decoherence control S. Kitajima, M. Ban and F.S., J. Phys. B 43 (2010) 135504. “Theory of decoherence control in a fluctuating environment” （8） Outlook

  4. (1) Introduction – Outline of several theoretical methods Damping theory ：　(a) Projection operator method (b) Schrodinger picture versus Heisenberg picture (c) Time-convolution (TC) type versus Time-convolutionless (TCL) type Path integral theory ：　Feynman – Vernon, Caldeira – Leggett Non-equilibrium Green’s function ：　Schwinger - Kerdysh ・・

  5. (2) Projection operator formalism Basic equations in Interaction picture (Schrodinger's view) ・・ Physics of Quanta and Non-equilibrium Systems”, chap. 3, (University of Tokyo Press, 2009, in Japanese) Hamiltonian Liouville-von Neumann equation where

  6. Time convolutio(TC) type equation

  7. Time convolutionless(TCL) type equation where

  8. Perturbation expansion formulae TC type formula

  9. TCL type formula

  10. where

  11. Heisenberg picture Mori equation where Projection operator

  12. (3) Spin relaxation (Ⅰ)： Rigorous Solution to Nonlinear Spin Relaxation Process J. Phys. Soc. Jpn. 62 (1993) 381 1. Preliminaries Time evolution of the nonlinear spin relaxation process

  13. C-number equation for a normally mapped (quasi-)probability density where

  14. 2. Method of solution For , ・・・(1) where with

  15. An exact solution is given by the form of a continued fraction: where

  16. 3. Averages and Fluctuations The average of the spin operator The second moments of the spin operator

  17. J. Phys. Soc. Jpn. 62 (1993) 381

  18. (4) Spin relaxation (Ⅱ)： Theory of Spin Relaxation for Arbitrary Time Scale J. Phys. Soc. Jpn. 51 (1982) 1727 1. Reduced Density Operator Hamiltonian

  19. Time evolution of a reduced density operator for the relevant system where

  20. ・・ In the Schrodinger picture The moment equations

  21. 2. Longitudinal Relaxation solution

  22. J. Phys. Soc. Jpn. 51 (1982) 1727

  23. 3. Transverse Relaxation solution

  24. J. Phys. Soc. Jpn. 51 (1982) 1727

  25. 4. Comparison with Stochastic Theory

  26. References • F. S., Y. Takahashi and N. Hashitsume, J. Stat. Phys. 17 (1977) 171. • S. Chaturvedi and F. S., Z. Phys. B35 (1979) 297. • F. S. and T. Arimitsu, J. Phys. Soc. Jpn., 49 (1980) 891.

  27. Low field resonance : exact results • Theory of low field resonance and relaxation Ⅰ Physica 143A (1987) 468 1. Basic formulation Hamiltonian Liouville-von Neumann equation in the interaction picture The projection operator

  28. The average of an arbitrary operator The time-convolution (TC) equation

  29. A basic equation The “self-energy”

  30. A power spectrum The longitudinal spectrum The transverse spectrum

  31. 2. Two-state jump Markoff process Longitudinal relaxation Transverse relaxation Non-adiabatic case Non-adiabatic case

  32. The time evolution of the longitudinal function for the low field; (a) for overall and (b) for the short time. The process is the two-state-jump. Physica 143A (1987) 468

  33. The time evolution of the transverse function for the low field; (a) for overall and (b) for the short time. The process is the two-state-jump. Physica 143A (1987) 468

  34. 3. Gaussian-Markoffian process 3.1 The longitudinal relation : Non-adiabatic case

  35. 3.2 The transverse relation : Non-adiabatic case

  36. Physica 143A (1987) 468

  37. Physica 143A (1987) 468

  38. References • R. Kubo and T. Toyabe, in: Proc. of the XIVth Colloque Ampere Ljubljana 1966, Magnetic Resonance and Relaxation, R. Blinc, ed. (North-Holland, Amsterdam, 1967) p.810. • R. S. Hayano, Y. J. Uemura, J. Imazato, N. Nishida, T. Yamazaki and R. Kubo, Phys. Rev. B20 (1979) 850. • Y. J. Uemura and T. Yamazaki, Physica 109 & 110B (1982) 1915; and references cited therein. • Y. J. Uemura, Doctor Thesis, University of Tokyo (1982). • 4) E. Torikai, A. Ito, Y. Takeda, K. Nagamine, K. Nishiyama, Y. Syono and H. Takei, Solid State Commun. 58 (1986) 839.

  39. (6) Micro-Laser theory : Self-organized formation of atomic coherence via photon exchange in a coupled atom-photon system J. Phys. Soc. Jpn., 69 (2000) 2829 1. Basic equations Hamiltonian Liouville-von Neumann equation for a reduced density operator

  40. 2. Method of solution The normally mapped (quasi-)probability density

  41. J. Phys. Soc. Jpn., 69 (2000) 2829

  42. J. Phys. Soc. Jpn., 69 (2000) 2829

  43. J. Phys. Soc. Jpn., 69 (2000) 2829

  44. J. Phys. Soc. Jpn., 69 (2000) 2829

  45. J. Phys. Soc. Jpn., 69 (2000) 2829

  46. J. Phys. Soc. Jpn., 69 (2000) 2829

  47. J. Phys. Soc. Jpn., 69 (2000) 2829

  48. J. Phys. Soc. Jpn., 69 (2000) 2829

  49. (7) Decoherence control : Theory of decoherence control in a fluctuating environment J. Phys. B 43 (2010) 135504 1. Preliminaries The characteristic function

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