Decoherence and emergent phenomena in quantum dynamical transport

The basic concepts of quantum dynamical transport of carriers rely on 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 a generalized 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 práctical 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 stochastic the Schrödinger equation. As a key practical aspect, only a single wave function (either single particle or many-body) 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], H 2 dissociation in the Heyrovsky heterogeneous catalysis [6] and even the “poised-realm” regime of biological electron-transfer in proteins and DNA [7]. This tool could describe the dynamics of electronic excitation induced in attosecond laser spectroscopy and the puzzling observation of intrinsic irreversibility [8] in chaotic many-body dynamics in Loschmidt echo/OTOC experiments in NMR.

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[3] C. J. Cattena, L. J. Fernández-Alcázar, R. A. Bustos-Marún, D. Nozaki, and H. M. Pastawski, J. Phys.: Condens. Matter 26, 345304 (2014).

[4] H. M. Pastawski, Physica B 398, 278(2007)

[5] L. J. Fernández-Alcázar and H. M. Pastawski, 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, 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, Phys. Rev. A 109, 042213 (2024).

[8] C. M. Sánchez, A. K. Chattah, and H. M. Pastawski, Phys. Rev. A 105, 052232 (2022).