Summary: The course will convey the main ideas of quantum transport as they developed since the pioneering work of P. W. Anderson and R. Landauer. By developing the basic renormalization procedures based on a Green´s function quantum fields formalism I will show that one obtains Generalized Landauer-Büttiker Equations (GLBE) for the density matrix that accounts for quantum dynamics and decoherent phenomena. Some emergent phenomena, such as quantum dynamical phase transitions, already appear at this level. However, through the “quantum-drift model” one can represent this by a stochastic Schrödinger equation analogous to that Ghirardi-Rimini-Weber, for a wave function that provides the information of the density matrix at an much economical computational cost than GLBE.
Didactical Reviews:
`Tight Binding' methods in quantum transport through molecules and small devices:
From the coherent to the decoherent description. H. M. Pastawski and E. Medina, Rev. Mex. Fisica 47s1, 1-23 (2001) cond-mat/0103219
Electron-Phonon interaction and electronic decoherence in molecular conductors. H. M. Pastawski, L. E. F. Foa Torres, E. Medina; Chem. Phys. 281/2-3 pp. 257-278 (2002)
Revisiting the Fermi Golden Rule: Quantum dynamical phase transition as a paradigm shift, Phys. B 398, 278(2007).
Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility P.R. Zangara and H. M. Pastawski, Phys. Scr. 92, 033001(2017)
Recent material:
-- Decoherent time-dependent transport beyond the Landauer-Büttiker formulation: A quantum-drift alternative to quantum jumps, L.J. Fernández-Alcázar and H.M. Pastawski, Phys. Rev. A 91, 022117 (2015)
--Universal stability of coherently diffusive 1D systems with respect to decoherence. F.S. Lozano-Negro, E. Alvarez Navarro, N.C. Chávez, F. Mattiotti, F. Borgonovi, H.M. Pastawski, G.L. Celardo, arXiv.2307.05656 Phys. Rev. A 109, 042213 (2024)