Theory of time‐dependent nonequilibrium transport through a single molecule in a nonorthogonal basis set

Abstract

A microscopic theory of nonequilibrium electronic transport under time‐dependent bias through a molecule (or quantum dot) embedded between two semi‐infinite metallic electrodes is developed in a nonorthogonal single‐particle basis set using an ab initio formalism of Green's functions. The equilibrium zeroth order electron Green's function and self‐energy are corrected by the corresponding time‐inhomogeneous dynamical contributions derived in the Hartree approximation in a steady‐state linear‐response regime. Nonorthogonality contributes to dynamical response by introducing terms related to the central region‐electrode interface, which appears only in the time‐dependent case. The expression for current is also derived, where a nonorthogonality‐induced dynamical correction gives an additional current that is not present in the orthogonal description. It is shown that the obtained expression for current is gauge‐invariant and demonstrated that the omission of the additional current violates charge conservation. The additional current term vanishes in an orthogonal basis set.

Non-Equilibrium ϕ4 theory for networks: towards memory formations with quantum brain dynamics

“…In figure 1, we show the central region and the N res reservoirs. (This is the generalization to the multiple reservoirs from the two reservoirs described previously [49][50][51][52][53] with tunneling effects [54][55][56][57]. )…”

“…where m is the mass, λ C and λ α ʼs are coupling constants of the interaction, v α ʼs are tunneling coupling constants between the central region C and the reservoir α [49][50][51][52][53]. We shall adopt the closed time path formalism in figure 2, the Keldysh formalism [58,59], labelled by  to describe non-equilibrium phenomena, and use 2-Particle-Irreducible (2PI) effective action technique [60][61][62].…”

Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions

“…Then, we find that the i∆ −1 0 is written by 3 × 3 matrix with zero (−1, 1) and (1, −1) components. The form of the matrix is similar to 3 × 3 matrix in the analysis in open systems, the central region, left and right reservoirs as in [59,[61][62][63]. Hence we can simplify the Kadanoff-Baym equations for dipole fields in an isolated system with the same procedures as those in open systems.…”

“…The analysis in this section is similar to that in open systems (the central region connected to the left and the right region) [59]. Since (−1, 1) and (1, −1) components in i∆ −1 0 (x, y) in Equation 9are zero, the same procedures to rewrite the Kadanoff-Baym equations as those in open systems [59][60][61][62][63] can be adopted. We set t 0 → −∞.…”

Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain

“…The Lagrangian density in open systems (the central region C and the two reservoirs L, R [46][47][48][49] with tunneling effects [50][51][52][53]) depicted in Figure 1 with the background field method [54][55][56][57] is given by,…”