Abstract

Electronic friction is an important energy loss channel for atoms and molecules scattering off, reacting, or simply vibrating at metallic surfaces. It represents the first departure from the adiabatic approximation when a continuum of electronic states is available, and it is usually described by mixed classical-quantum approaches in which the nuclei evolve classically according to Langevin-type equations of motion, the electrons follow them adiabatically and their reaction is subsumed in a coordinate-dependent electronic friction kernel [1]. However, classical dynamics falls short when light atoms are involved, which is also the situation where electronic friction becomes the dominant dissipation channel. In fact, it is not even clear how to include electronic friction in a fully quantum setting for the dynamics.

In this talk, I will present some recent developments that overcome these limitations. First, I will present a fully quantum theory of electronic friction at T=0 K [2]. The theory relies on the exact factorization of the electronic-nuclear wavefunction [3] and describes the nuclear dynamics by means of a nonlinear Schrödinger equation that generalises previously known Schrödinger-Langevin equations [4] to coordinate-dependent, tensorial friction kernel. The electronic bath, on the other hand, is entirely general and can be made of independent or interacting electrons, potentially in a strongly correlated state. Next, I will present a recent extension of the theory to finite-temperature situations. This can obtained by framing the pure-state, exactly factorised dynamics in a quantum hydrodynamic setting, and then generalising it to mixed states with the help of the momentum moments [5]. Two different, limiting kinds of mixed-states appear to be relevant for applications at finite temperatures and they will be discussed along with their quantum-classical limit.

[1] M. Head-Gordon and J. C. Tully, J. Chem. Phys. 103, 10137 (1995); W. Dou, G. Miao, and J.E. Subotnik, Phys. Rev. Lett. 119, 046001 (2017) [2] R. Martinazzo and I. Burghardt, Phys. Rev. Lett. 128, 206002 (2022); Phys. Rev. A 105 , 052215 (2022) [3] A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010). [4] M. D. Kostin, J. Chem. Phys. 57, 3589 (1972). [5] I. Burghardt, L.S. Cederbaum, J. Chem. Phys. 115, 10303 (2001); I. Burghardt, K. B. Møller and K. H. Hughes, pp 391–421, in “Quantum Dynamics of Complex Molecular Systems”, Springer, 2007