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 harmonics. Odd-even parity effects and the flux dependent oscillations of total persistent currents in discretized rings can also be invoked. Technological developments are then provided by conductance calculations characterizing 1D conductors, junctions between rings and leads or rings and dots, and by quantum LC-circuits. Accordingly, the issues presented in this book are important starting points for the design of novel nanodevices.

Contents:

• Lattice Structures and Discretizations
• Periodic Quasiperiodic and Confinement Potentials
• Time Discretization Schemes
• Discrete Schr�dinger 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

View Full Text (1,801 KB)