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Quantum response in dissipative environments University of Tokyo S. Miyashita 5 Nov. 2007 Linear Response 50 Equilibrium & NE response collaborators: Akira.

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Presentation on theme: "Quantum response in dissipative environments University of Tokyo S. Miyashita 5 Nov. 2007 Linear Response 50 Equilibrium & NE response collaborators: Akira."— Presentation transcript:

1 Quantum response in dissipative environments University of Tokyo S. Miyashita 5 Nov. 2007 Linear Response 50 Equilibrium & NE response collaborators: Akira Ogasahara, Keiji Saito, Chikako Uchiyama, and Mizuhiko Saeki

2 ESR line shape in strongly interacting spin systems Temperature-dependence of the shift and width in low-dimensional quantum spin systems Y. Ajiro, et al: JPSJ 63 (1994) 859. Spin trimer: 3CuCl2 ・ 2Dioxane FF AF

3 Microscopic expression of the line shape from Hamiltonian Kubo Formula R. Kubo: JPSJ 12 (1957) 570 R. Kubo & K.Tomita JPSJ (1954) 888 Pure quantum dynamics

4 Shift from the PMR Paramagnetic Resonance Isotropic models Perturbation

5 Shift from the PMR Paramagnetic Resonance Isotropic models Perturbation

6 Studies on the line shape F. Bloch: PR 70 (1946) 460. Nuclear Induction (Bloch equation) J. H. Van Vleck: PR 74 (1948) 1168. Dipolar broadening, and exchange narrowing N. Bloembergen, E. M. Purcell and R. V. Pound: PR 73 (1948) 679. Relaxation Effects in Nuclear Magnetic Resonance Absorption. I. Solomon: PR 99 (1955) 559. Relaxation processes in a system of two spins F. Bloch: PR 105 (1957) 1206. General theory of relaxation A. Abragam: The principles of Nuclear Magnetism, Oxford Univ. Press (1978)

7 Expression of the admittance Pure quantum dynamics Eigenvalue and eigenvectors of the Hamiltonian

8 Shift & Width Peak position Peak width

9 Nagata-Tazuke Dependence (J. Kanamori & M.Tachiki JPSJ 48 (1962) 50) K. Nagata and Y. Tazuke: JPSJ 32 (1972) 337 1D Heisenberg model with Dipole-dipole interaction

10 1D Heisenberg model Dipole-dipole interaction Paramagnetic resonance N=4 Constant H

11 Frequency sweep abd Field sweep

12 Line shape as an ensemble of delta-function N=8

13 Shift 1D Heisenberg AF Temperature Dependence Angle Dependence SM, T. Yoshino, A. Ogasahara JPSJ 68 (1999) 655

14 Width Magic Angle 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 parallel magic angleperpendicular

15 Zigzag Chain A. Ogasahara and S. Miyashita J. Phys. Soc. Jpn. Suppl. B 72,44-52 (2003).

16 Spiral structure Dipole-dipole interaction DM interaction parallel perpendicular 12 3 r=1 a

17 Spriral structure Dipole-dipole interaction r r=0.1 parallelr=0.2

18 r=0.5 r=0.5 modified

19 Spiral structure DM interaction d(x,z) (0,0) r=0.5 parallel (0,0) r=0.5 perpendicular

20 DM parallel d(1,0) (1,0) r=0.5 parallel (1,0) r=0.5 perpendicular D

21 DM perpendicular d(0,1) (0,1) r=0.5 parallel(0,1) r=0.5 perpendicular

22 d(0,5) (0,5) r=0.5 parallel (0,5) r=0.5 perpendicular

23 d(1,1) (1,1) r=0.5 x (1,1) r=0.5 z

24 d(3,3) (3,3) r=0.5 x(3,3) r=0.5 z

25 Response in dissipative dynamics pure quantum dynamics quantum dynamics with dissipation Relaxation effects: I. Solomon: PR 99 (1955) 559. Relaxation processes in a system of two spins F. Bloch: PR 105 (1957) 1206. General theory of relaxation Y. Hamano and F. Shibata: JPSJ 51 (1982) 1727,2721,2728. M. Saeki: Prog. Theor. Phys. 67 (1982) 1313. : relaxation method Prog. Theor. Phys. 115 (2006) 1. : TCLE method POSTER presentation

26 Dissipative dynamics Quantum Master equation method Quantum master equation quantum dynamics with dissipation F. Bloch: PR 105 (1957) 1206. S. Nakajima: PTP 20 (1958) 987, R. Zwanzig: J. Chem. Phys. 33 (1960) 1338. A. G. Redfield: Adv. Magn. Reson. 1 (1965) 1. H. Mori: PTP 33 (1965) 423. M. Tokuyama and H. Mori: PTP 55 (1976) 411. N. Hashitsume, F. Shibata and M. Shingu: J. Stat. Phys. 17 (1977) 155 & 171. T. Arimitsu and H. Umezawa: PTP 77 (1987) 32.

27 Studies on the line shape F. Bloch: PR 70 (1946) 460. Nuclear Induction (Bloch equation) J. H. Van Vleck: PR 74 (1948) 1168. Dipolar broadening, and exchange narrowing N. Bloembergen, E. M. Purcell and R. V. Pound: PR 73 (1948) 679. Relaxation Effects in Nuclear Magnetic Resonance Absorption. I. Solomon: PR 99 (1955) 559. Relaxation processes in a system of two spins F. Bloch: PR 105 (1957) 1206. General theory of relaxation A. Abragam: The principles of Nuclear Magnetism, Oxford Univ. Press (1978)

28 Time evolution of the density matrix in dissipative system K. Saito, S. Takesue and SM. Phys. Rev. B61 (2000) 2397. Independent phonon bath

29 Quantum dynamics of magnetization Molecular magnets V6 Cu3 Ni4 V15 Mn12 Fe8

30 Phonon-bottleneck effect I. Chiorescu, W. Wernsdorfer, A. Mueller, H. Boegge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454. K. Saito & SM. JPSJ (2001) 3385. Plateau in the magnetization process due to thermal contact with the bath

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

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

33 Fast sweep region? V=0.002,....., 0.28T/s [Ni(hmp)(dmb)Cl] 4 En-Che Yang,et al: Inorg. Chem. 45 (2006) 529

34 LZ transition + Thermal relaxation + MFE v=0.0512,...., 0.0002

35 Formulation of line-shape with dissipative dynamics

36 Eigenmode of time-evolution operator I. Knezevic and D. K. Ferry: Phys. Rev. E66(2003) 016131, Phys. Rev.A 69 (2004) 012104. S. Miyashita and K. Saito: Physica B 329-333 (2003) 1142.

37 Explicit form of the autocorrelation

38 Dynamical susceptibility Line shape where

39 Condition for relaxation to the equilibrium distribution KMS relation for correlation of the bath Steady state

40 Paramagnetic Resonance

41 Exchange narrowing

42 Dipole-dipole interaction

43 Resonance and dissipation

44 Summary Direct numerical estimation of the line shape Ensemble of the delta-functions Geometrical effects Estimation of the width due to dissipative dynamics Quantum Master equation method Width due to the dissipative dynamics Analysis of the themal bath: Coupling to the system : X Relaxation function: Φ short-relaxation approximation? Exchange narrowing Motional narrowing? Other related topics Quantum narrowing effect in the spin-Peierls transition Micro-wave heating in quantum system

45 Quantum narrowing effect H. Onishi and SM: JPSJ 72(2003) 392 ◆ effects of quantum lattice fluctuation becomes small when m small Spin-Peierls systems

46 Effect of AC field in complicated system -- Micro-wave heating -- M. Machida, K. Saito and SM: JPSJ 71(2002) 2427 Relation between the eigen state of the Hamiltonian and that of the Floquet operator: (POSTER by Hijii)

47 Thank you very much

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