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equilibrium: Real-time dynamics

Quantum impurity systems out of. equilibrium: Real-time dynamics. Avraham Schiller. Racah Institute of Physics, The Hebrew University. Collaboration : Frithjof B. Anders, Dortmund University. F.B. Anders and AS, Phys. Rev. Lett. 95 , 196801 (2005).

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equilibrium: Real-time dynamics

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  1. Quantum impurity systems out of equilibrium: Real-time dynamics Avraham Schiller Racah Institute of Physics, The Hebrew University Collaboration: Frithjof B. Anders, Dortmund University F.B. Anders and AS, Phys. Rev. Lett. 95, 196801 (2005) F.B. Anders and AS, Phys. Rev. B 74, 245113 (2006)

  2. Outline Confined nano-structures and dissipative systems: Non-perturbative physics out of equilibrium Time-dependent Numerical Renormalization Group (TD-NRG) Benchmarks for fermionic and bosonic baths Spin and charge relaxation in ultra-small dots

  3. Coulomb blockade in ultra-small quantum dots

  4. Coulomb blockade in ultra-small quantum dots Quantum dot

  5. Coulomb blockade in ultra-small quantum dots Leads

  6. Coulomb blockade in ultra-small quantum dots Lead Lead

  7. Coulomb blockade in ultra-small quantum dots Lead Lead

  8. Coulomb blockade in ultra-small quantum dots U Lead Lead

  9. Coulomb blockade in ultra-small quantum dots U Lead Lead

  10. Coulomb blockade in ultra-small quantum dots Dei+U U U Lead Lead

  11. Coulomb blockade in ultra-small quantum dots U Lead Lead

  12. Coulomb blockade in ultra-small quantum dots Conductance vs gate voltage U Lead Lead

  13. Coulomb blockade in ultra-small quantum dots Conductance vs gate voltage U Lead Lead

  14. Coulomb blockade in ultra-small quantum dots Conductance vs gate voltage dI/dV (e2/h) U Lead Lead

  15. The Kondo effect in ultra-small quantum dots

  16. The Kondo effect in ultra-small quantum dots

  17. The Kondo effect in ultra-small quantum dots Tunneling to leads

  18. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed

  19. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed

  20. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed

  21. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed Hybridization width

  22. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed Hybridization width

  23. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed Hybridization width Condition for formation of local moment:

  24. The Kondo effect in ultra-small quantum dots Inter-configurational energiesedandU+ed Hybridization width Condition for formation of local moment:

  25. The Kondo effect in ultra-small quantum dots

  26. The Kondo effect in ultra-small quantum dots TK ed ed+U EF

  27. The Kondo effect in ultra-small quantum dots A sharp resonance of width TK develops at EF when T<TK TK ed ed+U EF

  28. The Kondo effect in ultra-small quantum dots A sharp resonance of width TK develops at EF when T<TK Abrikosov-Suhl resonance TK ed ed+U EF

  29. The Kondo effect in ultra-small quantum dots A sharp resonance of width TK develops at EF when T<TK Unitary scattering for T=0 and <n>=1 TK ed ed+U EF

  30. The Kondo effect in ultra-small quantum dots A sharp resonance of width TK develops at EF when T<TK Unitary scattering for T=0 and <n>=1 Nonperturbative scale: TK ed ed+U EF

  31. The Kondo effect in ultra-small quantum dots A sharp resonance of width TK develops at EF when T<TK Perfect transmission for symmetric structure Unitary scattering for T=0 and <n>=1 Nonperturbative scale: TK ed ed+U EF

  32. Electronic correlations out of equilibrium

  33. Electronic correlations out of equilibrium Steady state dI/dV (e2/h) Differential conductance in two-terminal devices van der Wiel et al.,Science 2000

  34. Electronic correlations out of equilibrium Steady state ac drive dI/dV (e2/h) Differential conductance in two-terminal devices Photon-assisted side peaks van der Wiel et al.,Science 2000 Kogan et al.,Science 2004

  35. Electronic correlations out of equilibrium Steady state ac drive +w dI/dV (e2/h) -w Differential conductance in two-terminal devices Photon-assisted side peaks van der Wiel et al.,Science 2000 Kogan et al.,Science 2004

  36. Nonequilibrium: A theoretical challenge

  37. Nonequilibrium: A theoretical challenge The Goal:The description of nano-structures at nonzero bias and/or nonzero driving fields

  38. Nonequilibrium: A theoretical challenge The Goal:The description of nano-structures at nonzero bias and/or nonzero driving fields Required:Inherently nonperturbative treatment of nonequilibrium

  39. Nonequilibrium: A theoretical challenge The Goal:The description of nano-structures at nonzero bias and/or nonzero driving fields Required:Inherently nonperturbative treatment of nonequilibrium Problem: Unlike equilibrium conditions, density operator is not known in the presence of interactions

  40. Nonequilibrium: A theoretical challenge The Goal:The description of nano-structures at nonzero bias and/or nonzero driving fields Required:Inherently nonperturbative treatment of nonequilibrium Problem: Unlike equilibrium conditions, density operator is not known in the presence of interactions Most nonperturbative approaches available in equilibrium are simply inadequate

  41. Nonequilibrium: A theoretical challenge Two possible strategies Work directly at steady state Evolve the system in time to reach steady state e.g., construct the many-particle Scattering states

  42. Time-dependent numerical RG

  43. Time-dependent numerical RG Consider a quantum impurity (e.g., quantum dot) in equilibrium, to which a sudden perturbation is applied at time t = 0

  44. Time-dependent numerical RG Consider a quantum impurity (e.g., quantum dot) in equilibrium, to which a sudden perturbation is applied at time t = 0 t < 0 Lead Lead Vg

  45. Time-dependent numerical RG Consider a quantum impurity (e.g., quantum dot) in equilibrium, to which a sudden perturbation is applied at time t = 0 t < 0 t > 0 Lead Lead Lead Lead Vg Vg

  46. Time-dependent numerical RG Consider a quantum impurity (e.g., quantum dot) in equilibrium, to which a sudden perturbation is applied at time t = 0

  47. Time-dependent numerical RG Consider a quantum impurity (e.g., quantum dot) in equilibrium, to which a sudden perturbation is applied at time t = 0 Initial density operator Perturbed Hamiltonian

  48. Wilson’s numerical RG

  49. Wilson’s numerical RG Logarithmic discretization of band: e/D 1 -L-1 -L-2 -L-3 L-3 L-2 L-1 -1

  50. Wilson’s numerical RG Logarithmic discretization of band: e/D 1 -L-1 -L-2 -L-3 L-3 L-2 L-1 -1 After a unitary transformation the bath is represented by a semi-infinite chain x0 x1 x2 x3 imp

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