Low-dimensional Nanoscale Systems on Discrete SpacesThe 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
1 Lattice Structures and Discretizations | 1 |
2 Periodic Quasiperiodic and Confinement Potentials | 17 |
3 Time Discretization Schemes | 41 |
4 Discrete Schrodinger Equations Typical Examples | 57 |
5 Discrete Analogs and LieAlgebraic Discretizations Realizations of HeisenbergWeyl Algebras | 79 |
6 Hopping Hamiltonians Electrons in Electric Field | 99 |
7 Tight Binding Descriptions in the Presence of the Magnetic Field | 133 |
8 The HarperEquation and Electrons on the 1D Ring | 151 |
Other editions - View all
Low-dimensional Nanoscale Systems On Discrete Spaces Erhardt Papp,Codrutza Micu Limited preview - 2007 |
Low-dimensional Nanoscale Systems on Discrete Spaces E. Papp,Codrutza Micu No preview available - 2007 |
Common terms and phrases
1D ring Abramowitz and Stegun Accordingly algebraic boundary condition Brillouin zone characterizing commutation relations concerning continuous limit corresponding denotes derivation dimensionless discrete analog discrete equation discrete space discussed DLC’s easily verified eigenvalue equation electric field electrons established exhibits function given Hamiltonian harmonic oscillator Harper-equation Hatsugai Hermitian Hermitian conjugation hopping hypergeometric influence Inserting integral intentionally left blank interest Kohmoto Krawtchouk lattice leads Lorente Lyapunov exponent magnetic field magnetic flux modulation obtains operator Papp parameter particle periodic polynomials potential proceeds in accord produces q-deformed q-derivative q-difference q-exponential quantum dots quantum number quantum wire radial realizations recurrence relation relativistic reproduces rescaled resorting respectively Schrödinger equation Schrödinger-equation solution tight binding tight binding models total persistent current virtue Wannier wavefunction whereas Wiegmann and Zabrodin yields