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We present a numerical approach to construct a non-equilibrium many-bodystatistical operator $\hat{\rho}_\mathrm{rel}$ for an adaptive subspace ofrelevant quasi-bound electronic states in a semiconductor nanowire-basedfield-effect transistor (NWFET). As a constraint for $\hat{\rho}_\mathrm{rel}$,we assume that the single-particle density matrix $\rho_1$ is a given quantity,resulting from a non-equilibrium Green's function (NEGF) calculation for theNWFET for a given set of applied voltages. Two different orthonormal (ON)eigenbases for $\hat{\rho}_\mathrm{rel}$ are considered: (A) a Slaterdeterminant basis of natural orbitals (eigenstates of $\rho_1$) and (B) theeigenbasis of the projected many-body Hamiltonian $\hat{H}_\mathrm{rel}$ withina relevant Fock subspace of the system. As for the eigenvalues $w_n$ of$\hat{\rho}_\mathrm{rel}$, we furthermore assume that $w_n$ have a generalizedBoltzmann form, parameterized by effective electrochemical potentials ofnatural orbitals and a given temperature. From the determined$\hat{\rho}_\mathrm{rel}$, in turn, one can calculate expectation values forany many-body observable within the relevant subspace. As an example, weanalyze the electron density and the covariance of the density-densitycorrelation function for representative electronic preparations of the NWFET.

Numerical determination of a non-equilibrium many-body statistical operator for quasi-bound electrons in a gated nanowire system