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Relaxation and Decoherence in Quantum Impurity Models: From Weak to Strong Tunneling

Quantum impurity models (spin-boson, Kondo, Schmid, BSG, ....) Dynamics From weak to strong tunneling. Quantum relaxation Decoherence. Relaxation and Decoherence in Quantum Impurity Models: From Weak to Strong Tunneling. Ulrich Weiss Institute for Theoretical Physics

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Relaxation and Decoherence in Quantum Impurity Models: From Weak to Strong Tunneling

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  1. Quantum impurity models (spin-boson, Kondo, Schmid, BSG, ....) • Dynamics • From weak to strong tunneling • Quantum relaxation • Decoherence Relaxation and Decoherence in Quantum Impurity Models:From Weak to Strong Tunneling Ulrich Weiss Institute for Theoretical Physics University of Stuttgart H. Saleur (USCLA) A. Fubini (Florence) H. Baur (Stuttgart) Quantum Mechanics on the Large Scale Banff, Alberta

  2. solvent bath dynamics dissipation decoherence tunneling acceptor donor classical rate theory Marcus theory of ET activationless ET inverted regime nonadiabatic ET adiabatic ET biological electron transport molecular electronics quantum dots molecular wires charge transport in nanotubes Electron transfer (ET): Quantum Mechanics on the Large Scale Banff, Alberta

  3. a b Spin-boson model with ultracold atoms: Recati et al. 2002 Quantum Mechanics on the Large Scale Banff, Alberta

  4. System Heat bath T Physical baths: Phonons Conduction electrons (Fermi liquid) 1d electrons (Luttinger liquid) BCS quasiparticles Electromagn env. (circuits, leads) Nuclear spins Solvent Electromagnetic modes > 1 super-Ohmic = 1 Ohmic < 1 sub-Ohmic s Global system: Spectral density of the coupling: phonons (d > 1) e-h excitations RC transmission line Quantum Mechanics on the Large Scale Banff, Alberta

  5. TSS: stochastic force: driven TSS: Truncated double well: T T Spin-boson Hamiltonian: stochastic force Quantum Mechanics on the Large Scale Banff, Alberta

  6. spin flip scattering conduction band spin polarization conserved Anisotropic Kondo model Correspondence with spin-boson model: universal in the regime ferromagnetic Kondo regime antiferromagn. Kondo regime Quantum Mechanics on the Large Scale Banff, Alberta

  7. Schmid model: particle in a tilted cosine potential TB limit • Current-biased Josephson junction (charge-phase duality) • Impurity scattering in 1d quantum wire • Point contact tunneling between quantum Hall edges • Boundary sine-Gordon model • Exact selfduality in the Ohmic scaling limit • Scaling function for transport and noise at T=0 is known in analytic form A. Schmid, Phys. Rev. Lett. 51, 1506 (1983) P.Fendley, A.W.W. Ludwig, and H. Saleur, Phys. Rev. B 52, 8934 (1995) Quantum Mechanics on the Large Scale Banff, Alberta

  8. Density matrix: Global system: Reduced description: partial trace full dynamics:W(t) reduced dynamics: time-local interactions time-nonlocal interactions Quantum Mechanics on the Large Scale Banff, Alberta

  9. Tight-binding model: charges Influence functional: Absorption and emission of energy according to detailed balance Quantum Mechanics on the Large Scale Banff, Alberta

  10. Laplace representation in the limit : Keldysh contour Quantum Mechanics on the Large Scale Banff, Alberta

  11. Ohmic scaling limit: Spectral density: Pair interaction between tunneling transitions: Kondo scale: TSS model Schmid model at fixed Kondo scale Quantum Mechanics on the Large Scale Banff, Alberta

  12. noise (Gaussian filter) friction phase factor noise integral N=2: N=5: charges: scaling limit: Quantum Mechanics on the Large Scale Banff, Alberta

  13. noise integral noise integral phase factor phase factor Incoherent tunneling: golden rule limit: { } to from is probability for transfer of energy the bath Quantum Mechanics on the Large Scale Banff, Alberta

  14. Order + c.c. = + c.c. + c.c. + c.c. = + c.c. = + c.c. = (1) (2) (3) (4) Quantum Mechanics on the Large Scale Banff, Alberta

  15. Up-hill partial rates are zero • Scaling property general! particular! Formidable relations between the various noise integrals of same order l Noise integrals: _ _ Quantum Mechanics on the Large Scale Banff, Alberta

  16. Only minimal number of transitions contribute to the rate • All rates can be reconstructed from the known mobility Results: Schmid model: cancelled contributes • Knowledge of all statistical fluctuations (full probability distribution) H. Saleur and U.Weiss, Phys. Rev. B 63, 201302(R) (2001) TSS model: • Exact relations between rates of the Schmid and TSS model Quantum Mechanics on the Large Scale Banff, Alberta

  17. Im(z) C Re(z) Weak-tunneling expansion Integral representation H. Baur, A. Fubini, and U.Weiss, cond-mat/0211046 Quantum Mechanics on the Large Scale Banff, Alberta

  18. Strong-tunneling expansion The case K<1: Leading asymptotic term: Quantum Mechanics on the Large Scale Banff, Alberta

  19. Strong-tunneling expansion The case K>1: Quantum Mechanics on the Large Scale Banff, Alberta

  20. weak tunneling large bias strong tunneling small bias Quantum Mechanics on the Large Scale Banff, Alberta

  21. strong tunneling large bias weak tunneling small bias Quantum Mechanics on the Large Scale Banff, Alberta

  22. Decoherence Conjecture:holds in all known special cases Strong-tunneling expansion: Quantum Mechanics on the Large Scale Banff, Alberta

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