This book employs nonequilibrium quantum transport, based on the use of mixed Hilbert space representations and real time quantum superfield transport theory, to explain various topological phases of systems with entangled chiral degrees of freedom. It presents an entirely new perspective on topological systems, entanglement-induced localization and delocalization, integer quantum Hall effect (IQHE), fractional quantum Hall effect (FQHE), and its respective spectral zones in the Hofstadter butterfly spectrum. A simple and powerful, intuitive, and wide-ranging perspective on chiral transport dynamics.

This book presents the first comprehensive treatment of discrete phase-space quantum mechanics and the lattice Weyl-Wigner formulation of energy band dynamics, by the originator of these theoretical techniques. The author's quantum superfield theoretical formulation of nonequilibrium quantum physics is given in real time, without the awkward use of artificial time contour employed in previous formulations. These two main quantum theoretical techniques combine to yield general (including quasiparticle-pairing dynamics) and exact quantum transport equations in phase-space, appropriate for nanodevices. The derivation of transport formulas in mesoscopic physics from the general quantum transport equations is also treated. Pioneering nanodevices are discussed in the light of the quantum-transport physics equations, and an in-depth treatment of the physics of resonant tunneling devices is given. Operator Hilbert-space methods and quantum tomography are discussed. Discrete phase-space quantum mechanics on finite fields is treated for completeness and by virtue of its relevance to quantum computing. The phenomenological treatment of evolution superoperator and measurements is given to help clarify the general quantum transport theory. Quantum computing and information theory is covered to demonstrate the foundational aspects of discrete quantum dynamics, particularly in deriving a complete set of multiparticle entangled basis states.