Fluctuations and localization in mesoscopic electron systems
Fluctuations and localization
Janssen, M. (Martin)
creator
text
bibliography
Electronic book.
Electronic books.
si
Singapore
River Edge, N.J
World Scientific
©2001
2001
monographic
eng
1 online resource (xii, 205 pages) : illustrations
The quantum phenomena of tunneling and interference show up not only in the microscopic world of atoms and molecules, but also in cold materials of the real world, such as metals and semiconductors. Though not fully macroscopic, such mesoscopic systems contain a huge number of particles, and the holistic nature of quantum mechanics becomes evident already in simple electronic measurements. The measured quantity fluctuates as a function of applied fields in an unpredictable, yet reproducible way. Despite this fingerprint character of fluctuations, their statistical properties are universal, i.e. they are the same for a large class of different mesoscopic systems, having only very few parameters in common. Localization of electrons is a dramatic effect of destructive interference. As a consequence a metal can become an insulator while reaching mesoscopic scales. Based on elementary quantum and statistical physics, this text introduces the theory of mesoscopic electron systems. It focuses on universal characteristics of fluctuations and on the localization mechanism. General concepts and methods are stressed, such as scaling laws for distribution functions. Tools from condensed matter theory are used flexibly. Involved technical details are skipped so as to present a broad overview of the field, including topics like quantum dots, the quantum Hall effect and a number of the most recent developments.
Ch. 1. Introduction -- ch. 2. Experimental facts. 2.1. Aharonov-Bohm effect. 2.2. Conductance fluctuations. 2.3. Localization. 2.4. Quantum Hall effects. 2.5. Quantum dots -- ch. 3. Basic theoretical models and tools. 3.1. Relevant scales and observables. 3.2. The independent electron approximation. 3.3. Model Hamiltonian and Green's function. 3.4. Disorder diagrams and field theory. 3.5. Scattering matrix modeling. 3.6. Fokker-Planck equations -- ch. 4. Idealized systems. 4.1. Localized systems. 4.2. Delocalized systems. 4.3. Random matrices and symmetry -- ch. 5. Towards realistic systems. 5.1. Concept of scaling. 5.2. Distributions and typical values. 5.3. Corrections at finite conductances. 5.4. Quasi-one-dimensional systems -- ch. 6. The localization-delocalization transition. 6.1. Finite size scaling. 6.2. Real-space renormalization. 6.3. Multifractality of critical states. 6.4. Point-contact conductance. 6.5. Order parameter and scaling variable.
Martin Janssen.
Includes bibliographical references (pages 191-198) and index.
Fluctuations (Physics)
Quantum theory
Mesoscopic phenomena (Physics)
SCIENCE
Physics
Condensed Matter
Fluctuations (Physics)
Mesoscopic phenomena (Physics)
Quantum theory
Física do estado sólido
QC6.4.F58 J36 2001eb
530.4/1
Fluctuations and localization in mesoscopic electron systems
Janssen, M. (Martin).
Singapore ; River Edge, N.J. : World Scientific, ©2001
(DLC) 2001275377
(OCoLC)47978870
World Scientific lecture notes in physics ; v. 64
9789812798923
9812798927
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