Electron-phonon thermalization in a scalable method for real-time quantum dynamics

Abstract

We present a quantum simulation method that follows the dynamics of out-of-equilibrium many-body systems of electrons and oscillators in real time. Its cost is linear in the number of oscillators and it can probe time scales from attoseconds to hundreds of picoseconds. Contrary to Ehrenfest dynamics, it can thermalize starting from a variety of initial conditions, including electronic population inversion. While an electronic temperature can be defined in terms of a nonequilibrium entropy, a Fermi-Dirac distribution in general emerges only after thermalization. These results can be used to construct a kinetic model of electron-phonon equilibration based on the explicit quantum dynamics.

Interactions between low energy electrons and DNA: a perspective from first-principles simulations

“…While electronic excitation processes are captured correctly by this approach [84], the meanfield character of Ehrenfest distorts the characteristics of energy transfer from electrons to phonons, e.g. Ehrenfest cannot describe properly ubiquitous phenomena such as Joule heating [85] or the thermalisation between electronic and nuclear degrees of freedom [81]. A second limitation is related to the exchange-correlation approximations used in TDDFT.…”

“…TDHF), or TDDFT. Model hamiltonians are good for developing new methodologies [81], while tight-binding models, especially the so-called density-functional tight-binding (DFTB) approach, has proved useful for describing electron dynamics in large systems [82,83]. Introducing the nuclear dynamics also requires approximations for the electronnuclear correlation.…”

“…Although CEID is still rather young and costly, it has emerged as a powerful tool for problems in which the transfer of energy between electrons and nuclei is crucial. A cost-effective alternative that limits the nuclear motion to harmonic phonons, named Effective CEID, has been proposed recently [81], and applied to inelastic electron transport in water chains [89]. It is important to remark that none of these methods is presently mature enough to allow for the dynamical simulation of the dissociative electron attachment process.…”

Inelastic electron injection in a water chain

“…Second, we retain only single-phonon processes by ignoring terms of the form , . This leads to the following equations9…”

“…The mesoscale nature of this problem makes it especially challenging for non-adiabatic quantum electron-nuclear simulations. We have recently reported a method, called Effective Correlated Electron-Ion Dynamics (ECEID), designed for such simulations9. In this paper we combine ECEID with electronic Open Boundaries (OB)10 to simulate in real time the injection of LEEs and their inelastic dynamical interaction with phonons.…”