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 transcript:

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

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

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

Shift from the PMR Paramagnetic Resonance Isotropic models Perturbation

Shift from the PMR Paramagnetic Resonance Isotropic models Perturbation

Studies on the line shape F. Bloch: PR 70 (1946) 460. Nuclear Induction (Bloch equation) J. H. Van Vleck: PR 74 (1948) 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) General theory of relaxation A. Abragam: The principles of Nuclear Magnetism, Oxford Univ. Press (1978)

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

Shift & Width Peak position Peak width

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

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

Frequency sweep abd Field sweep

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

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

Width Magic Angle R.E. Dietz, et al. PRL 26 (1971) T.T. Cheung, et al. PRB 17 (1978) 1266 SM, T. Yoshino, A. Ogasahara JPSJ 68 (1999) 655 parallel magic angleperpendicular

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

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

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

r=0.5 r=0.5 modified

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

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

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

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

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

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

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) General theory of relaxation Y. Hamano and F. Shibata: JPSJ 51 (1982) 1727,2721,2728. M. Saeki: Prog. Theor. Phys. 67 (1982) : relaxation method Prog. Theor. Phys. 115 (2006) 1. : TCLE method POSTER presentation

Dissipative dynamics Quantum Master equation method Quantum master equation quantum dynamics with dissipation F. Bloch: PR 105 (1957) S. Nakajima: PTP 20 (1958) 987, R. Zwanzig: J. Chem. Phys. 33 (1960) 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.

Studies on the line shape F. Bloch: PR 70 (1946) 460. Nuclear Induction (Bloch equation) J. H. Van Vleck: PR 74 (1948) 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) General theory of relaxation A. Abragam: The principles of Nuclear Magnetism, Oxford Univ. Press (1978)

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

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

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

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

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

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

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

Formulation of line-shape with dissipative dynamics

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

Explicit form of the autocorrelation

Dynamical susceptibility Line shape where

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

Paramagnetic Resonance

Exchange narrowing

Dipole-dipole interaction

Resonance and dissipation

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

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

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)

Thank you very much