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Author Moskalets, Michael V.

Title Scattering matrix approach to non-stationary quantum transport / Michael V. Moskalets
Published London : Imperial College Press ; Singapore ; Hackensack, NJ : World Scientific Pub. [distributor], [2012]
©2012
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Description 1 online resource (xviii, 278 pages) : illustrations
Contents Acknowledgments; Preface; Contents; List of Figures; 1. Landauer-B ttiker formalism; 1.1 Scattering matrix; 1.1.1 Scattering matrix properties; 1.1.1.1 Unitarity; 1.1.1.2 Micro-reversibility; 1.2 Current operator; 1.3 Direct current and the distribution function; 1.3.1 Conservation of a direct current; 1.3.2 Difference of potentials; 1.3.3 Difference of temperatures; 1.4 Examples; 1.4.1 Scattering matrix 1 × 1; 1.4.2 Scattering matrix 2 × 2; 1.4.3 Scattering matrix 3 × 3; 1.4.4 Scatterer with two leads; 1.4.5 Scatterer with a potential contact; 1.4.6 Scatterer embedded in a ring
1.4.6.1 Spectrum1.4.6.2 Circulating current; 2. Current noise; 2.1 Nature of a current noise; 2.1.1 Thermal noise; 2.1.2 Shot noise; 2.1.3 Combined noise; 2.2 Sample with continuous spectrum; 2.2.1 Current correlator; 2.2.2 Current correlator in the frequency domain; 2.2.2.1 Correlator for incoming currents; 2.2.2.2 Correlator for incoming and outgoing currents; 2.2.2.3 Correlator for outgoing currents; 2.2.3 Spectral noise power for energy-independent scattering; 2.2.4 Zero frequency noise power; 2.2.4.1 Noise power conservation law; 2.2.4.2 Sign rule for the noise power
2.2.4.3 Scatterer with two leads2.2.5 Fano factor; 3. Non-stationary scattering theory; 3.1 Schr dinger equation with a potential periodic in time; 3.1.1 Perturbation theory; 3.1.2 Floquet functions method; 3.1.3 Potential oscillating in time and uniform in space; 3.2 Floquet scattering matrix; 3.2.1 Floquet scattering matrix properties; 3.2.1.1 Unitarity; 3.2.1.2 Micro-reversibility; 3.3 Current operator; 3.3.1 Alternating current; 3.3.2 Direct current; 3.4 Adiabatic approximation for the Floquet scattering matrix; 3.4.1 Frozen scattering matrix; 3.4.2 Zeroth-order approximation
3.4.3 First-order approximation3.5 Beyond the adiabatic approximation; 3.5.1 Scattering matrix in mixed energy-time representation; 3.5.2 Dynamic point-like potential; 3.5.3 Dynamic double-barrier potential; 3.5.3.1 Adiabatic approximation; 3.5.4 Unitarity and the sum over trajectories; 3.5.5 Current and the sum over trajectories; 3.5.5.1 Temperature-independent contribution to generated current; 3.5.5.2 Contribution to generated current dependent on temperature; 3.5.5.3 Nature of two contributions to generated current; 4. Direct current generated by the dynamic scatterer
4.1 Steady particle flow4.1.1 Distribution function; 4.1.2 Adiabatic regime: Current linear in the pump frequency; 4.1.3 Current quadratic in the pump frequency; 4.2 Quantum pump effect; 4.2.1 Quasi-particle picture of direct current generation; 4.2.2 Interference mechanism of direct current generation; 4.3 Single-parameter adiabatic direct current generation; 5. Alternating current generated by the dynamic scatterer; 5.1 Adiabatic alternating current; 5.2 External AC bias; 5.2.1 Second quantization operators for incident and scattered electrons; 5.2.2 Alternating current
Summary The aim of this book is to introduce the basic elements of the scattering matrix approach to transport phenomena in dynamical quantum systems of non-interacting electrons. This approach admits a physically clear and transparent description of transport processes in dynamical mesoscopic systems promising basic elements of solid-state devices for quantum information processing. One of the key effects, the quantum pump effect, is considered in detail. In addition, the theory for a recently implemented new dynamical source - injecting electrons with time delay much larger than the electron coheren
Bibliography Includes bibliographical references (pages 261-276) and index
Notes Print version record
Subject S-matrix theory.
Transport theory.
Form Electronic book
ISBN 1848168357 (electronic bk.)
9781848168350 (electronic bk.)