1. The University of Tokyo Seiji Miyashita
10 Aug. 2010
Kyoto Yukawa
Reduction of the system dynamics from the total system including the environments
The University of Tokyo
Seiji Miyashita

2. Projection operator method

4. For the master equation

5. Real part

6. Phonon Bottleneck phenomena in V15
Plateau induced by thermal effect
sample
Heat flow
Heat bath
Chiorescu, W. Wernsdorfer,
A. Mueller, H. Boegge, B. Barbara,
Phys. Rev. Lett. 84 (2000) 3454.

7. Field sweeping with thermal bath
Fast sweeping
Slow sweeping
Magnetic
Foehn Effect
LZS
K. Saito & SM.
JPSJ (2001) 3385.

8. Nonadiabatic Tr. & Heat-inflow
LZ transition
Magnetic Foehn Effect

9. Fe2 Fe-rings Y. Shapira, et al PRB59 (1999) 1046 Y. Ajiro & Y. Inagaki
Y. Narumi & K. Kindo
H. Nakano & SM, JPSJ 70(2001) 2151

10. Fast Magnetization Tunneling in Tetranicke(II) SMM
[Ni(hmp)(dmb)Cl]4
v=0.0512, ....,
V=0.002, , 0.28T/s
En-Che Yang,et al: Inorg. Chem. 45 (2006) 529

11. Boson system

12. Spin-boson system
from QMEnote (SM and T. Mori)

13. Relation between the equation of motion and its steady solution
Equation of motion up to the second order
(a situational solution)
we may add any traceless W
The diagonal elements are arbitrary in the order of
Master equation leads the system to the equilibrium of the system
The off-diagonal elements aredetermined in the order of
T. Mori and SM: JPSJ 77 (2008) (1-9).
Complex admittance
C. Uchiyama, M. Aihara, M. Saeki and S. Miyashita: PRE 80 (2009) (1-18).
M. Saeki, C. Uchiyama, T. Mori and S. Miyashita: PRE 81, (2010) (1-33)

14. The University of Tokyo Seiji Miyashita
10 Aug. 2010
Kyoto Yukawa
Study on the line shapes of the response function --Origins of the Width--
The University of Tokyo
Seiji Miyashita

15. ESR line shape in strongly interacting spin systems
Temperature-dependence of the shift and width in low-dimensional quantum spin systems
Spin trimer: 3CuCl2 ・2Dioxane F F AF
(S=1/2)x3
paramagnetic
S=3/2
EPR
correlated state
Y. Ajiro, et al: JPSJ 63 (1994) 859.

16. Shift and width of the line shape
Intrinsic width due to assembly of the delta-functions
Quantum broadening due to quantum fluctuation of the field
Transmission spectrum (input-output modes)
Broadening width due to the interaction with the thermal bath

17. Microscopic expression of the line shape from　the Hamiltonian of the system
R. Kubo & K.Tomita JPSJ (1954) 888.
Kubo formula
R. Kubo: JPSJ 12 (1957) 570.
Isotropic models (Paramagnetic Resonance)
Perturbation

18. Expression of the admittance
Eigenvalue and eigenvectors of the Hamiltonian
shift
width

19. Frequency sweep and Field sweep

20. 1D AF Heisenberg Chain

21. Nagata-Tazuke effect One-dimensional Heisenberg antiferromagnet
K.Nagata and Y.Tazuke, JPSJ 32(1972)337.
(J. Kanamori & M.Tachiki : JPSJ 48 (1962) 50)
One-dimensional Heisenberg antiferromagnet 21

22. Demonstration of the Nagata-Tazuke effects
R.E. Dietz, et al. PRL 26 (1971) 1186.
T.T. Cheung, et al. PRB 17 (1978) 1266
SM, T. Yoshino, A. Ogasahara: JPSJ 68 (1999) 655.

23. Line shape of a spin chane with a staggered DM interaction
S. El Shawish, O. Cepas, and SM: PRB81, (2010).

24. Line shape of a spin chain with a staggered DM interaction
cf.
S. El Shawish, O. Cepas, and SM: PRB81, (2010).

25. Models
Staggered DM model
XXZ model
Equivalence
Difference

26. Consideration on the line shape
relaxation time
moments of

27. Memory function (short time)

28. Memory function (long time)

29. Memory function (Gaussian form : KT)

30. Double peak structure

31. Estimated line shape in infinite chain
Exact short range + spin diffusion long time tail
with various cut-off times (tau_0,tau_c)

32. Width of the line shape
self-consistent

33. Memory function (2D kagome)

34. Line shape and width (2D kagome)

35. Derivative of line shape ZnCu3(OH3)Cl2

36. Shift and width of the line shape
Intrinsic width due to assembly of the delta-functions
Quantum broadening due to quantum fluctuation of the field
Transmission spectrum (input-output modes)
Broadening width due to the interaction with the thermal bath

37. Coupling between spin system and cavity phonon system
Cavity photon system
Coupling
Transmission

38. Coupling between spin system and cavity phonon system
Cavity photon system
Coupling
Transmission

39. Jaynes-Cumming model and ESR spectrum
I. Chiorescu and S. Miyashita: PRB (2010) in press
Model for ESR
Rabi-oscillation
Absorption spectrum
Jaynes-Cummings model

40. Interaction with photon The Jaynes-Cummings model
Photon couples all the spins.
Total spin is conserved

41. Enhancement of Rabi-oscillation and the vacuum-field Rabi splitting
Y. Kaluzny, P. G. , M. Gross, J. M. Raimond and S. Haroche, PRL 51, 1175 (1983)
The vacuum-field Rabi splitting in the transmission spectrum
G. S. Agarwal:, PRL 53, 1732 (1984).

42. Splitting of PMR of DPPH
The vacuum-field
Rabi-splitting
G. S. Agarwal:, PRL 53, 1732 (1984).
DPPH
I. Chiorescu, N. Groll, S. Bertaina, T. Mori and SM: PRB (2010) in press. ( )

43. N-diamond
arXiv

44. arXiv
Rubby S=3/2 Cr3+

45. Multi-photon effect N=nmax ( , 0) ( , 1) ( , N) nmax: number of cavity
Super-radiance?
( , 0)
...
( , 1)
...
( , N)
...
At N=nmax, a wide distribution of
the Rabi frequences
nmax: number of cavity
photons in the ground
state of spin system

46. Eigenvalues and the transmission spectrum
The vacuum-field
Rabi-splitting
G. S. Agarwal:, PRL 53, 1732 (1984).

47. Photon emission spectrum

48. Shift and width of the line shape
Intrinsic width due to assembly of the delta-functions
Quantum broadening due to quantum fluctuation of the field
Transmission spectrum (input-output modes)
Broadening width due to the interaction with the thermal bath

49. Line shape of the transmission

50. Thermal bath method

55. Transmission in a steady state
j-1 j j+1
j=0

58. Input-output formulation

60. Shift and width of the line shape
Intrinsic width due to assembly of the delta-functions
Quantum broadening due to quantum fluctuation of the field
Transmission spectrum (input-output modes)
Broadening width due to the interaction with the thermal bath
C. Uchiyama, M. Aihara, M. Saeki and S. Miyashita: PRE 80 (2009)

61. Summary Explicit expression of the the spectrum line shape:
Quantum broadening due to quantum fluctuation of the field
Transmission spectrum (steady flow method) vs
Broadening width due to the interaction with the thermal bath
Line shale of a ring Heisenberg model with DM interaction
Coupling of spin system and cavity photons

62. Thank you very much