Describing nonHermitian dynamics using a Generalized ThreeTime NEGF for a Partitionfree Molecular Junction with ElectronPhonon Coupling
Abstract
In this paper we develop the NonEquilibrium Green's Function (NEGF) formalism for a dissipative molecular junction that consists of a central molecular system with onedimensional electronic transport coupled to a phonon environment and attached to multiple electronic leads. Our approach is partitionless  initial preparation of the system places the whole system in the correct canonical equilibrium state  and is valid for an external bias with arbitrary time dependence. Using path integrals as an intermediary tool, we apply a twotime HubbardStratonovich transformation to the phonon influence functional with mixed real and imaginary times to obtain an exact expression for the electronic density matrix at the expense of introducing coloured Gaussian noises whose properties are rigorously derived from the environment action. This results in a unique stochastic Hamiltonian on each branch of the KonstantinovPerel' contour (upper, lower, vertical) such that the time evolution operators in the Liouville equation no longer form a Hermitian conjugate pair, thus corresponding to nonHermitian dynamics. To account for this we develop a generalized threetime NEGF which is sensitive to all branches of the contour, and relate it to the standard NEGF in the absence of phonons via a perturbative expansion of the noises. This approach is exact and fully general, describing the nonequilibrium driven dynamics from an initial thermal state while subject to inelastic scattering, and can be applied to nonHermitian dynamics in general.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.05133
 Bibcode:
 2021arXiv210805133L
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Quantum Physics
 EPrint:
 27 pages, 2 figures