Kinetic theory of quantum transport at the nanoscale

Abstract

We present a quantum-kinetic scheme for the calculation of non-equilibrium transport properties in nanoscale systems. The approach is based on a Liouville-master equation for a reduced density operator and represents a generalization of the well-known Boltzmann kinetic equation. The system, subject to an external electromotive force, is described using periodic boundary conditions. We demonstrate the feasibility of the approach by applying it to a double-barrier resonant tunneling structure.

Stochastic time-dependent current-density-functional theory: A functional theory of open quantum systems

“…It is important to realize that an approach based on the SSE (15) does not suffer from this drawback: the density matrix (21) constructed from the SSE is by definition positive at any time.…”

A method for performing fully quantum mechanical simulations of gated silicon quantum wire structures

“…Moreover, the broadening of the delta function will not be apparent when we reverse the Fourier transform of (30), as the area under the spectral density remains normalized to unity [38]. Since our recursion in (20) is in the site representation, rather than in a mode representation, we have to reverse the Fourier transform in (30) to get the x-axis variation, and do a mode-to-site unitary transformation to get the self-energy in the form necessary for the recursion. This is the subject of the rest of this section, where we discuss the different phonon scattering processes.…”

“…The imaginary term is constant throughout the device, and therefore fails to consider the inhomogeneous density in the out of equilibrium system. This approach has also been questioned as not conserving current [19], but this fails to properly consider the entire dissipative current [20]. Dissipation may also be included through the use of Büttiker probes [21,22].…”

Scattering in quantum simulations of silicon nanowire transistors

“…The imaginary term is constant throughout the device, and therefore fails to consider the inhomogeneous density in the out of equilibrium system. This approach has also been questioned as not conserving current [35], but this fails to properly consider the entire dissipative current [36]. Dissipation may also be included through the use of Büttiker probes [37].…”