H. M. Pastawski,^1,2 F. S. Lozano-Negro,^1,2 and L. J. Fernández-Alcázar^3,4

¹Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba (UNC), Córdoba, Argentina
²Instituto de Física Enrique Gaviola (UNC-CONICET)
³Institute for Modeling and Innovative Technology, IMIT (CONICET – UNNE), Corrientes, Argentina
⁴Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes, Argentina

This presentation will start with a tutorial on the basic concepts of quantum dynamical transport of carriers developed upon the pioneering work of P. W. Anderson, R. Landauer, and M. Büttiker. Starting from the renormalization procedures of the quantum field density Green’s functions in the formalism of Keldysh and Kadanoff-Baym, it is easy to describe open systems in the thermodynamic limit [1,2]. The requirement of the conservation laws in the linear regime yields the Generalized Landauer-Büttiker Equations (GLBE), equivalent to the Kirchhoff law for a quantum circuit [3]. The GLBE accounts for quantum dynamics and decoherence processes using a non-Hermitian Hamiltonian concatenated with a self-consistent evolution of the density. This enables to describe emergent phenomena, of which the Quantum Dynamical Phase Transition (QDPT) becomes a paradigmatic example [4]. However, the numerical solution of the dynamics only becomes accessible within the “quantum-drift model” (DQM), which represents the “collapse” imposed by the environmental interactions as a stochastic noise imposed upon Schrödinger dynamics [5]. This procedure recovers all known results from other approaches such as the Carmichael and Dalibard-Casting “quantum jumps” model and the Haken-Strobl model. Moreover, the QDM has a fundamental connection with the Ghirardi-Rimini-Weber generalization of the Schrödinger equation. As a key practical aspect, only a single wave function is stored, allowing the evaluation of observables and their fluctuations. This has a very low computational cost as compared with the GLBE or the Lindblad equation. We will mention the main achievement in describing Giant Magnetoresistance (GMR), Sound Amplification (SASER) [5], H₂ dissociation in the Heyrovsky heterogeneous catalysis [6] and even the “poised-realm” regime of biological electron-transfer in proteins and DNA [7]. The possible progress of experiments on dynamics of electronic excitation enabled by attosecond laser spectroscopy and the observation of intrinsic irreversibility [8] in chaotic many-body dynamics.

References:
[1] H. M. Pastawski, Classical and Quantum Transport from Generalized Landauer-Büttiker Equations II: Time dependent tunneling. Phys. Rev. B 46, 4053 (1992).
[2] H. M. Pastawski, L. E. F. Foa Torres, and E. Medina, Electron-phonon interaction and electronic decoherence in molecular conductors. Chem. Phys. 281, 257 (2002).
[3] C. J. Cattena, L. J. Fernández-Alcázar, R. A. Bustos-Marún, D. Nozaki, and H. M. Pastawski, Generalized multi-terminal decoherent transport: recursive algorithms and applications to SASER and giant magnetoresistance. J. Phys.: Condens. Matter 26, 345304 (2014).
[4] H. M. Pastawski, Revisiting the Fermi Golden Rule: Quantum dynamical phase transition as a paradigm shift. Physica B 398, 278(2007).
[5] L. J. Fernández-Alcázar and H. M. Pastawski, Decoherent time-dependent transport beyond the Landauer-Büttiker formulation: A quantum-drift alternative to quantum jumps. Phys. Rev. A 91, 022117 (2015).
[6] F. S. Lozano-Negro, M. A. Ferreyra-Ortega, D. Bendersky, L. J. Fernández-Alcázar, and H. M. Pastawski, Simulating a catalyst induced quantum dynamical phase transition of a Heyrovsky reaction with different models for the environment. J. Phys. Condens. Matt. 34, 214006 (2022).
[7] F. S. Lozano-Negro, E. Alvarez Navarro, N. C. Chávez, F. Mattiotti, F. Borgonovi, H. M. Pastawski, and G. L. Celardo, Universal stability of coherently diffusive 1D systems with respect to decoherence. Phys. Rev. A 109, 042213 (2024).
[8] C. M. Sánchez, A. K. Chattah, and H. M. Pastawski, Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR. Phys. Rev. A 105, 052232 (2022).