Low-dimensional nanoscale systems on discrete spaces - Papp, E. (World Scientific, 2007)
Includes bibliographical references (p. 241-257) and index
Lattice structures and discretizations -- Periodic quasiperiodic and confinement potentials -- Time discretization schemes -- Discrete Schr·odinger equations. Typical examples -- Discrete analogs and lie-algebraic discretizations. Realizations of Heisenberg-Weyl algebras -- Hopping Hamiltonians. Electrons in electric field -- Tight binding descriptions in the presence of the magnetic field -- The Harper-Equation and electrons on the 1D ring -- The q-symmetrized Harper equation -- Quantum oscillations and interference effects in nanodevices -- Conclusions
The area of low-dimensional quantum systems on discrete spaces is a rapidly growing research field lying at the interface between quantum theoretical developments, like discrete and q-difference equations, and tight binding superlattice models in solid-state physics. Systems on discrete spaces are promising candidates for applications in several areas. Indeed, the dynamic localization of electrons on the 1D lattice under the influence of an external electric field serves to describe time-dependent transport in quantum wires, linear optical absorption spectra, and the generation of higher harmo