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Learn the Non-Equilibrium Green's Function (NEGF) equations in this 23-minute lecture from the nanoHUB-U course on quantum transport fundamentals. Explore advanced concepts in non-equilibrium statistical mechanics as applied to nanoelectronics, building upon linear algebra and differential equations to understand current flow at the atomic scale. Discover how the NEGF formalism provides a mathematical framework for analyzing quantum transport phenomena in nanoscale devices, where billions of nanotransistors with active regions spanning just hundreds of atoms enable modern smartphone technology. Examine the theoretical foundations that connect quantized conductance in short ballistic conductors to classical Ohm's law in longer diffusive systems, while addressing fundamental questions about resistance, electricity-heat interconversion, thermodynamics, and information theory at the nanoscale. Gain insights into the mathematical tools essential for understanding how quantum mechanical effects govern electron transport in devices where traditional classical physics approaches become inadequate.
