Courses ¨
DISSIPATIVE QUANTUM MECHANICS OF ELECTRONS IN NANOSTRUCTURES
(A.D. Zaikin)

  1. Path Integrals in Quantum Mechanics. The concept of the effective action. Description of interaction with the quantum thermostat. The theory of functional Feynman-Vernon influence.
  2. Dissipation in quantum mechanics. Theory Kaldeyry-Leggetta. Semiclassical Langevin equation.
  3. Quantum tunneling with dissipation. The limits of weak and strong dissipation. Macroscopic quantum tunneling in Josephson contacts.
  4. The idea of macroscopic quantum coherence. Coherence and dissipation. Quantum dynamics of two-level systems with dissipation. The notion of qubits.
  5. Second quantization and coherent states. The functional integration of systems of fermions. Matsubaru temperature technique.
  6. Physical observables and Grin functions. Grin functions of nonequilibrium system. Functional integration in the Keldysh technique.
  7. Coulomb interaction of fermions. Transformation of the Hubbard-Stratonovich and the effective action of fermions in terms of Bose fields.
  8. Actioon of Ambegaokar-Ekern-Shen for tunneling contacts.
  9. Coulomb blockade, P(E)-theory. Quasi-charge. Instantons and weak Coulomb blockade.
  10. The nonlinear equation for the density matrix of interacting electrons. Effective action and the Pauli exclusion principle.
  11. Quantum corrections to the conductivity of disordered conductors. Weak localization.
  12. Electron-electron interaction and phase decoherence of electrons. Fundamental sequences of low temperature saturation of decoherence time.
  13. Scattering matrix. The Landauer formula, shot noise, third cumulant of current, full-counting statistics.
  14. Disordered conductors, σ-model. Fluctuations of the conductivity, the distribution of transmissivity.
  15. Scattering matrix method and electron-electron interaction in disordered conductors. Effective action for arbitrary scatterers. Example of point contacts.
  16. Coulomb corrections to the conductance and shot noise. Influence of electron-electron interaction on the higher correlators current, limits of low and high transparency. Communication of interaction effects and full-counting statistics.
  17. The effects of interactions in quantum dots. Systems of quantum dots as a general model of disordered conductors.
  18. Modern understanding of the ground state and low-temperature transport properties of disordered conductors.
  • REFERENCES
  • Principal:
    1. R. Feynman, A. Hibs, Quantum Mechanics and Path Integrals. M. Izd. Moscow University, 1998.
    2. U. Weiss, Quantum dissipative systems, World Scientific, Singapore, 1999.
    3. J.W. Negele, H. Orland , Quantum many-particle systems, Westview Press, Boulder , 1998.
  • MORE:
    1. G. Schön and A. Zaikin, Quantum coherent effects, phase transitions, and the dissipative dynamics of ultra small tunnel junctions. Physics Reports, vol 198 (1990), p. 237.
    2. D.S. Golubev, A.V. Galaktionov, and A.D. Zaikin, Electron transport and current fluctuations in short coherent conductors. Physical Review B, vol.72 (2005), p. 205417
    3. D.S. Golubev, A.D. Zaikin, and G. Schön, On low temperature dephasing by electron-electron interaction. Journal of Low Temperature Physics, vol. 126 (2002), p. 1355.
    4. D.S. Golubev and A.D. Zaikin, Weak localization in arrays of metallic quantum dots: Combined scattering matrix formalism and nonlinear σ-model, Physical Review B, vol. 74 (2006), p. 245329.

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