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Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint [Pehme köide]

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(, Instituto de Fisica, UNAM, Mexico City, Mexico), (, Director, Raman Research Institute, Bangalore, India)
  • Formaat: Paperback / softback, 418 pages, kõrgus x laius x paksus: 234x158x21 mm, kaal: 583 g, 30 b/w line illustrations
  • Ilmumisaeg: 29-Jul-2010
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198525834
  • ISBN-13: 9780198525837
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Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy ViewpointSuurem pilt
  • Formaat: Paperback / softback, 418 pages, kõrgus x laius x paksus: 234x158x21 mm, kaal: 583 g, 30 b/w line illustrations
  • Ilmumisaeg: 29-Jul-2010
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198525834
  • ISBN-13: 9780198525837
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780198525837.html
This book presents the statistical theory of complex wave scattering and quantum transport in classically chaotic and disordered systems. The novel approach is a maximum-entropy viewpoint, which reveals the statistical regularity of the phenomena in a natural way. The book contains many worked-through exercises

The aim of this book is to present a statistical theory of wave scattering by complex systems -systems which have a chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or possess quenched randomness, as in the case of disordered conductors-- with emphasis on mesoscopic fluctuations.

The universal character of the statistical behavior of these phenomena is incorporated in a natural way by approaching the problem from a Maximum-Entropy viewpoint -Shannon's information entropy is maximized, subject to the symmetries and constraints that are physically relevant-- within the powerful, non-perturbative Theory of Random Matrices. This book also collects in one place the material and notions -derived from the published work of the authors in collaboration with several co-workers, as well as from the work of others-- which are scattered through research journals and textbooks on the subject.

To make the book self-contained, we present in Chapters 2 and 3 the quantum theory of scattering, set in the context of quasi-one-dimensional, multichannel systems, thus related directly to scattering problems in mesoscopic physics. Chapter 4 discusses the linear-response theory of quantum electronic transport, adapted to the context of mesoscopic systems. These chapters, together with Chapter 5 on the Maximum-Entropy Approach and Chapter 8 on weak localization, have been written in a pedagogical style, and can be used as part of a graduate course. Chapters 6 and 7 discuss the problem of electronic transport through classically chaotic cavities and quasi-one-dimensional disordered systems. There are many exercises, most of them worked out in detail, distributed throughout the book. This should help graduate students, their teachers and the research scholars interested generally in the subject of quantum transport through disordered and chaotic systems in their preparation for it, and beyond.

Arvustused

`Its great strength is that it provides a consistent, systematic introduction to the major ideas of the field and includes a lot of related material that provides important intellectual context. ' Allan MacDonald, University of Texas at Austin `A most important and timely topic. [ ...] There are other books, but not at the same level of depth. ' John Spence, Arizona State University

1 Introduction
1(14)
1.1 Atomic nuclei and microwave cavities
2(2)
1.2 Wave localization and fluctuations
4(1)
1.3 Mesoscopic conductors: time- and length-scales
5(8)
1.3.1 Ballistic mesoscopic cavities
7(1)
1.3.2 Diffusive mesoscopic conductors
7(1)
1.3.3 Statistical approach to mesoscopic fluctuations
8(5)
1.4 Organization of the book
13(2)
2 Introduction to the quantum mechanical time-independent scattering theory I: one-dimensional scattering
15(105)
2.1 Potential scattering in infinite one-dimensional space
16(54)
2.1.1 The Lippman-Schwinger equation; the free Green function; the reflection and the transmission amplitudes
16(7)
2.1.2 The T matrix
23(2)
2.1.3 The full Green function
25(5)
2.1.4 The S matrix
30(14)
2.1.5 The transfer or M matrix
44(4)
2.1.6 Combining the S matrices for two scatterers in series
48(3)
2.1.7 Transformation of the scattering and the transfer matrices under a translation
51(2)
2.1.8 An exactly soluble example
53(4)
2.1.9 Scattering by a step potential
57(11)
2.1.10 Combination of reflection and transmission amplitudes for a one-dimensional disordered conductor: invariant imbedding equations
68(2)
2.2 Potential scattering in semi-infinite one-dimensional space: resonance theory
70(50)
2.2.1 A soluble model for the study of resonances
71(2)
2.2.2 Behavior of the phase shift
73(5)
2.2.3 Behavior of the wave function
78(6)
2.2.4 Analytical study of the internal amplitude of the wave function near resonance
84(3)
2.2.5 The analytic structure of S(k) in the complex-momentum plane
87(3)
2.2.6 Analytic structure of S(E) in the complex-energy plane
90(3)
2.2.7 The R-matrix theory of scattering
93(16)
2.2.8 The `motion' of the S matrix as a function of energy
109(11)
3 Introduction to the quantum mechanical time-independent scattering theory II: scattering inside waveguides and cavities
120(67)
3.1 Quasi-one-dimensional scattering theory
120(48)
3.1.1 The reflection and transmission amplitudes; the Lippman-Schwinger coupled equations
120(18)
3.1.2 The S matrix
138(3)
3.1.3 The transfer matrix
141(4)
3.1.4 Combining the S matrices for two scatterers in series
145(1)
3.1.5 Transformation of the scattering and transfer matrices under a translation
146(1)
3.1.6 Exactly soluble example for the two-channel problem
147(8)
3.1.7 Extension of the S and M matrices to include open and closed channels
155(13)
3.2 Scattering by a cavity with an arbitrary number of waveguides
168(13)
3.2.1 Statement of the problem
168(3)
3.2.2 The S matrix; the reflection and transmission amplitudes
171(10)
3.3 The R-matrix theory of two-dimensional scattering
181(6)
4 Linear response theory of quantum electronic transport
187(39)
4.1 The system in equilibrium
188(3)
4.2 Application of an external electromagnetic field
191(2)
4.3 The external field in the scalar potential gauge
193(16)
4.3.1 The charge density and the potential profile
194(14)
4.3.2 The current density
208(1)
4.4 The external field in the vector potential gauge
209(12)
4.5 Evaluation of the conductance
221(5)
5 The maximum-entropy approach: an information-theoretic viewpoint
226(18)
5.1 Probability and information entropy: the role of the relevant physical parameters as constraints
227(7)
5.1.1 Properties of the entropy
229(4)
5.1.2 Continuous random variables
233(1)
5.2 The role of symmetries in motivating a natural probability measure
234(1)
5.3 Applications to equilibrium statistical mechanics
235(6)
5.3.1 The classical microcanonical ensemble
236(1)
5.3.2 The classical canonical ensemble
236(3)
5.3.3 The quantum mechanical canonical ensemble
239(2)
5.4 The maximum-entropy criterion in the context of statistical inference
241(3)
6 Electronic transport through open chaotic cavities
244(35)
6.1 Statistical ensembles of S matrices: the invariant measure
245(4)
6.2 The one-channel case
249(2)
6.3 The multichannel case
251(2)
6.4 Absence of prompt (direct) processes
253(9)
6.4.1 Averages of products of S: weak localization and conductance fluctuations
253(5)
6.4.2 The distribution of the conductance in the two-equal-lead case
258(4)
6.5 Presence of prompt (direct) processes
262(2)
6.5.1 The case β = 2
262(2)
6.5.2 The case β = 1
264(1)
6.6 Numerical calculations and comparison with theory
264(6)
6.6.1 Absence of prompt (direct) processes
265(3)
6.6.2 Presence of prompt (direct) processes
268(2)
6.7 Dephasing effects: comparison with experimental data
270(9)
6.7.1 The limit of large NΦ
272(2)
6.7.2 Arbitrary NΦ
274(2)
6.7.3 Physical experiments
276(3)
7 Electronic transport through quasi-one-dimensional disordered systems
279(51)
7.1 Ensemble of transfer matrices; the invariant measure; the combination law and the Smoluchowski equation
280(8)
7.1.1 The invariant measure
284(2)
7.1.2 The ensemble of transfer matrices
286(2)
7.2 The Fokker-Planck equation for a disordered one-dimensional conductor
288(10)
7.2.1 The maximum-entropy ansatz for the building block
289(2)
7.2.2 Constructing the probability density for a system of finite length
291(7)
7.3 The Fokker-Planck equation for a quasi-one-dimensional multichannel disordered conductor
298(20)
7.3.1 The maximum-entropy ansatz for the building block
298(3)
7.3.2 Constructing the probability density for a system of finite length
301(1)
7.3.3 The diffusion equation for the orthogonal universality class, β = 1
302(8)
7.3.4 The diffusion equation for the unitary universality class, β = 2
310(8)
7.4 A unified form of the diffusion equation for the various universality classes describing quasi-one-dimensional disordered conductors: calculation of expectation values
318(7)
7.4.1 The moments of the conductance
319(6)
7.5 The correlations in the electronic transmission and reflection from disordered quasi-one-dimensional conductors
325(5)
8 An introduction to localization theory
330(32)
8.1 Strong localization
331(4)
8.2 Mobility edge
335(2)
8.3 Coherent back-scattering (CBS)
337(3)
8.4 Scaling theory
340(2)
8.5 Weak localization: quantum correction to the conductivity
342(8)
8.5.1 The Hamiltonian and the Green function
343(6)
8.5.2 Ensemble-averaged Green's function in the self-consistent Born approximation
349(1)
8.6 Electrical conductivity of a disordered metal and quantum corrections: weak localization
350(12)
8.6.1 Classical (Drude) conductivity
354(3)
8.6.2 Weak localization (WL) and quantum correction to the classical (Drude) conductivity: the maximally-crossed diagrams
357(3)
8.6.3 Scale dependence of the conductivity
360(2)
A The theorem of Kane-Serota-Lee
362(5)
B The conductivity tensor in RPA
367(9)
C The conductance in terms of the transmission coefficient of the sample
376(4)
D Evaluation of the invariant measure
380(9)
D.1 The orthogonal case, β = 1
382(3)
D.2 The unitary case, β = 2
385(4)
References 389(8)
Index 397
Pier Mello is Distinguished Professor at the Universidad Nacional Autónoma de México (UNAM). He took his B.S. degree in Physics at UNAM in 1962, and his PhD there in 1965. he was a member of the Institute for Advanced Study, Princeton, 1965-67, and has been Full Professor of Physics at the Instituto de Física, UNAM, Mexico, since 1974. He was a member of the Wissenschaftkolleg (Institute for Advanced Study) in Berlin, Germany, 1992-93 and became Distinguished Professor at UNAM, Mexico in 1994. He was a Lecturer at the Les Houches International School on Mesoscopic Quantum Physics in 1994.

Narendra Kumar is Director at the Raman Research Institute, Bangalore. He has been recognised with several awards, including the Shanti Swarup Bhatnagar (SSB) Prize for Physics in 1985 by CSIR, India

the Third World Academy of Sciences (TWAS) Prize for Physics (1992), the C.V. Raman Birth Centenary award (1999-2000), and the Meghnad Saha Medal (2000). He was elected Fellow of the Indian Academy of Sciences, Bangalore (1987), Fellow of the American Physical Society (1994), Fellow of TWAS (1995), Fellow of INSA (1987), and Fellow of the National Academy of Sciences, India (1994).