Application of a semiclassical model for the second-quantized many-electron Hamiltonian to nonequilibrium quantum transport: The resonant level model

Abstract

A semiclassical approach is developed for nonequilibrium quantum transport in molecular junctions. Following the early work of Miller and White [J. Chem. Phys. 84, 5059 (1986)], the many-electron Hamiltonian in second quantization is mapped onto a classical model that preserves the fermionic character of electrons. The resulting classical electronic Hamiltonian allows for real-time molecular dynamics simulations of the many-body problem from an uncorrelated initial state to the steady state. Comparisons with exact results generated for the resonant level model reveal that a semiclassical treatment of transport provides a quantitative description of the dynamics at all relevant timescales for a wide range of bias and gate potentials, and for different temperatures. The approach opens a door to treating nontrivial quantum transport problems that remain far from the reach of fully quantum methodologies.

Symmetry breaking and restoration using the equation-of-motion technique for nonequilibrium quantum impurity models

“…In general, this many body out-of-equilibrium problem cannot be solved exactly but for a few simple cases [4][5][6][7] . Excluding recent developments based on brute-force approaches such as time-dependent numerical renormalization-group techniques [8][9][10] , iterative [11][12][13] or stochastic 14-18 diagrammatic techniques to real time path integral formulations, wave function based approaches 19 , or reduced dynamic approaches 20,21 , all suitable to relatively simple model systems, most theoretical treatments of quantum transport rely on approximations of some sort.…”

Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions

“…Perturbative treatments (in either the molecule-leads coupling parameter or the electron-phonon interaction energy) are commonly used, including the nonequilibrium Green's function technique [4][5][6][7][8] and Master equation approaches [5,[9][10][11][12][13]. For following the real-time dynamics of such systems, involved methods have been recently developed, e.g., semiclassical approaches [14,15].…”

A quasi-classical mapping approach to vibrationally coupled electron transport in molecular junctions

“…81,83,85 We enforce quantum statistics on the initial conditions for each DoF by setting the initial occupation to either 0 or 1 such that its expectation value, averaged over the set of initial conditions, satisfies the Fermi-Dirac distribution …”

“…72,[75][76][77][78][79][80] Recently, similar mapping strategies have been proposed for the many-electron problem inherent in the transport scenario. Swenson et al 81 have adopted a mapping approach based on the early work of Miller and White, 82 constructing a classical Hamiltonian corresponding to the general second-quantized Hamiltonian operator for a many-electron system in which all the creation and annihilation operators for the spin orbitals were substituted by a set of classical action angle variables. This scheme was employed to calculate the current of the resonant level model with and without electron-vibrational coupling, 81,83 ignoring in both cases electron-electron interactions.…”

“…Swenson et al 81 have adopted a mapping approach based on the early work of Miller and White, 82 constructing a classical Hamiltonian corresponding to the general second-quantized Hamiltonian operator for a many-electron system in which all the creation and annihilation operators for the spin orbitals were substituted by a set of classical action angle variables. This scheme was employed to calculate the current of the resonant level model with and without electron-vibrational coupling, 81,83 ignoring in both cases electron-electron interactions. This mapping approach provides semiquantitative results for a range of system parameters, i.e., different source-drain voltages, temperatures, and electron-vibrational couplings.…”