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Excitons and Cooper Pairs: Two Composite Bosons in Many-Body Physics [Hardback]

(Directeur de Recherche CNRS Emeritus, Institute de NanoSciences de Paris, Université Pierre-et-Marie-Curie), (Assistant Research Fellow, Department of Physics and National Centre of Theoretical Sciences, National Cheng Kung University)
  • Formāts: Hardback, 560 pages, height x width x depth: 248x186x33 mm, weight: 1262 g
  • Sērija : Oxford Graduate Texts
  • Izdošanas datums: 10-Dec-2015
  • Izdevniecība: Oxford University Press
  • ISBN-10: 019875373X
  • ISBN-13: 9780198753735
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Excitons and Cooper Pairs: Two Composite Bosons in Many-Body PhysicsPalielināt
  • Formāts: Hardback, 560 pages, height x width x depth: 248x186x33 mm, weight: 1262 g
  • Sērija : Oxford Graduate Texts
  • Izdošanas datums: 10-Dec-2015
  • Izdevniecība: Oxford University Press
  • ISBN-10: 019875373X
  • ISBN-13: 9780198753735
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780198753735.html
This book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons, the authors raise fundamental questions of current interest: how does the Pauli exclusion principle wield its power on the fermionic components of bosonic particles at a microscopic level and how this affects the macroscopic physics? What can we learn from Wannier and Frenkel excitons and from Cooper pairs that helps us understand "bosonic condensation" of composite bosons and its difference from Bose-Einstein condensation of elementary bosons? The authors start from solid mathematical and physical foundation to derive excitons and Cooper pairs. They further introduce Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or graduate students in physics with no prior background will benefit from this book. The developed concepts and methodology should also be useful to present researches on ultracold atomic gases, exciton-polaritons, and quantum information.

Recenzijas

In this book a new and fascinating light is shined on an old question. It is must reading for anyone interested in this subject. Leon Cooper, Brown University This new book provides a thorough and interesting account of the microscopic theories behind superconductors, excitons and Bose condensates, drawing parallels between all three areas. It promises to be a useful textbook for postgraduates as well as a stimulating monograph for current practitioners in the fields of condensed matter physics. Derek Lee, Imperial College London I strongly recommend this clear, accessible book gathering for the first time two aspects of pair formation in condensed matter, namely excitons in semiconductors and Cooper pairs in superconductors. Claude Cohen-Tannoudji, Ecole Normale Superieure Composite bosons consist of two fermions and hence do not obey the usual bosonic commutation relations. The authors here develop comprehensive techniques and diagrams to describe such systems, focusing on two important examples: particle-hole excitons in semiconductors and two-particle Cooper pairs in superconductors. Future work will doubtless illuminate the important and relatively new field of BCS-BEC crossover involving paired fermions in ultra-cold dilute atomic gases. Alexander Fetter, Stanford University ... full of insight and clarity, combining deep theoretical insight with a demand for intuitive and comprehensible behaviours. This link between excitons and Cooper pairs brings together two fields where there is fertile ground for connection and new ideas. Jeremy Baumberg, University of Cambridge The book by the noted many-body theorist Monique Combescot and Shiue-Yuan Shiau presents a novel theory of interacting excitons based on the fermion character of their constituent electron and hole and a unique unification of the concepts of Wannier and Frenkel excitons and Cooper pairs. L. J. Sham, University of California San Diego The topic is timely and interesting - in particular the similarities and differences between exciton condensates and condensation of Cooper pairs. There are books on excitons and there are books on superconductivity - this combination is rather unique and worth reading. Pawel Hawrylak, University of Ottawa

1 Introduction
1(14)
1.1 Technical aspects
7(2)
1.2 On the possible ways to draw diagrams
9(6)
Part I Excitons
2 The Exciton Concept
15(19)
2.1 The physical picture
16(3)
2.2 Relevant Coulomb processes
19(4)
2.3 Exciton-photon coupling
23(1)
2.4 Many-body effects
24(4)
2.5 Thermal effects
28(2)
2.6 The semiconductor Hamiltonian
30(4)
3 Wannier Excitons
34(74)
3.1 Phenomenological approach
34(15)
3.2 Microscopic derivation
49(16)
3.3 One Wannier exciton
65(14)
3.4 Many-body effects
79(29)
4 Frenkel Excitons
108(70)
4.1 Atomic states and the tight-binding approximation
109(4)
4.2 Second quantization formulation
113(18)
4.3 One Frenkel exciton
131(8)
4.4 Spin and orbital degrees of freedom
139(9)
4.5 Many-body effects
148(30)
5 Elementary Bosons, Wannier Excitons, and Frenkel Excitons
178(15)
5.1 Physical pictures
180(1)
5.2 Commutation relations and Pauli scatterings
181(2)
5.3 Interaction scatterings
183(4)
5.4 Closure relations
187(1)
5.5 Normalization factors
187(1)
5.6 Many-body parameters
188(1)
5.7 Hamiltonian mean values
189(4)
Part II Cooper Pairs
6 The Cooper Pair Problem
193(9)
6.1 The four main approaches to BCS superconductivity
194(2)
6.2 Effective attraction between two electrons
196(6)
7 The Bardeen-Cooper-Schrieffer Approach
202(20)
7.1 The Cooper problem
204(2)
7.2 The BCS problem
206(1)
7.3 The BCS approach to the BCS problem
207(3)
7.4 Hamiltonian mean value
210(2)
7.5 Mean value minimization
212(2)
7.6 Ground-state energy
214(2)
7.7 Physical meaning of the condensation energy
216(2)
7.8 The energy gap
218(4)
8 The Bogoliubov Approach
222(16)
8.1 The Bogoliubov procedure
223(2)
8.2 Diagonalization of the Bogoliubov Hamiltonian
225(3)
8.3 Eigenstates of the Bogoliubov Hamiltonian
228(3)
8.4 Ground-state energy of the BCS Hamiltonian
231(3)
8.5 Ground-state wave function of the BCS Hamiltonian
234(3)
8.6 Discussion
237(1)
9 The Gorkov Approach
238(9)
9.1 The mean-field Hamiltonian
239(2)
9.2 Gorkov equations for T = 0
241(3)
9.3 The energy gap
244(1)
9.4 Gorkov equations and the energy gap for T ≠ 0
245(2)
10 Richardson-Gaudin Exact Solution
247(23)
10.1 Commutator formalism for zero-momentum fermion pairs
250(5)
10.2 One-pair eigenstates (The Cooper problem)
255(2)
10.3 Two-pair eigenstates
257(3)
10.4 Three-pair eigenstates
260(2)
10.5 Richardson-Gaudin equations for N pairs
262(1)
10.6 Analytical solution of the Richardson-Gaudin equations
263(2)
10.7 Hints on the analytical resolution of the Richardson-Gaudin equations
265(4)
10.8 Many-body parameter for Cooper pairs
269(1)
11 Links Between Cooper Pairs and Excitons
270(43)
11.1 Degrees of freedom
272(3)
11.2 Potentials
275(7)
11.3 One composite boson
282(3)
11.4 Two composite bosons
285(5)
11.5 N composite bosons
290(4)
11.6 Many-body parameters
294(3)
11.7 Wave functions
297(11)
11.8 Density regimes
308(5)
Part III Particles Related to Excitons
12 Trions, Biexcitons, and Polaritons
313(5)
12.1 A brief description
313(2)
12.2 Spin and orbital degrees of freedom
315(3)
13 Trions
318(22)
13.1 The X- trion as an exciton interacting with an electron
320(6)
13.2 Trion creation operator
326(4)
13.3 Trion-photon coupling
330(7)
13.4 More on Sz = 0 trion
337(3)
14 Biexcitons
340(11)
14.1 The biexciton as two interacting excitons
342(4)
14.2 Biexciton creation operator
346(1)
14.3 Biexciton-photon coupling
347(4)
15 Polaritons
351(32)
15.1 Formal description
353(2)
15.2 One polariton
355(2)
15.3 Many-body effects
357(4)
15.4 Microscopic derivation
361(22)
Part IV Bosonic Condensation
16 From Elementary to Composite Boson Condensates
383(7)
16.1 Elementary bosons
385(2)
16.2 Elementary fermions
387(1)
16.3 Composite bosons
388(2)
17 Elementary Bosons
390(27)
17.1 Noninteracting bosons for T = 0
391(1)
17.2 Noninteracting bosons for T ≠ 0
391(6)
17.3 Momentum and spin fragmentation of the condensate
397(5)
17.4 Interacting bosons for T = 0
402(15)
18 Elementary Fermions
417(16)
18.1 Free fermions for T = 0
418(1)
18.2 Free fermions for T ≠ 0
419(1)
18.3 Interacting electrons for T = 0
420(7)
18.4 Interacting electrons and holes
427(6)
19 Composite Bosons
433(32)
19.1 T = 0 ground state
434(14)
19.2 Momentum, spin, and dark-bright fragmentation
448(17)
Appendix A Some Mathematical Results
465(8)
A.1 Kronecker symbol and delta function
466(3)
A.2 Fourier transform and series expansion
469(2)
A.3 Coulomb scatterings
471(2)
Appendix B Second Quantization Formalism
473(3)
Appendix C The Hamiltonian for Wannier Excitons
476(6)
C.1 The semiconductor Hamiltonian in first quantization
477(1)
C.2 Bloch states
478(1)
C.3 The semiconductor Hamiltonian on the Bloch basis
479(3)
Appendix D Valence Electron Operator Versus Hole Operator
482(6)
D.1 Valence electron absence
483(1)
D.2 Spin 1/2
484(2)
D.3 L = 1 orbital momentum
486(2)
Appendix E "The Coboson Bible"
488(5)
Appendix F Direct Coulomb Scatterings for Wannier Excitons
493(9)
F.1 Creation potential
494(4)
F.2 Direct Coulomb scatterings
498(3)
F.3 Symmetry properties
501(1)
Appendix G Concerning N Ground-State Wannier Excitons
502(11)
G.1 Normalization factor
503(5)
G.2 Hamiltonian mean value
508(5)
Appendix H Photon-Semiconductor Interaction
513(15)
H.1 Electromagnetic field in vacuum
515(1)
H.2 The electron Hamiltonian in a photon field
516(2)
H.3 Linear coupling
518(5)
H.4 Quadratic coupling
523(3)
H.5 Complex polarization vectors
526(2)
Appendix I Photon-Exciton Interaction
528(5)
I.1 Photon-exciton coupling
529(2)
I.2 The sum rule between photon-exciton couplings
531(2)
References 533(10)
Index 543
M. Combescot is a former student of the Ecole Normale Superieure in Paris, France (Mathematics and Physics majors). In 1973, she obtained her Ph.D. in condensed matter many-body theory from the University of Paris, France (adviser Prof. Ph. Nozičres). After two years of postdoc at Cornell University, USA, she returned as a research member at CNRS in Paris, permanently. Yet, she likes teaching very much --- she has been first at the "Aggregation de Physique", a competitive exam for high school teachers. For many years, she taught undergraduate courses at universities and engineering schools in Paris. Over the last two decades, she also gave various courses at the graduate level, in Paris and in many other places in the world. This book is based on one of these lectures.

Dr. Shiue-Yuan Shiau obtained his B.S. in 1998 and M.S. in 2002 from National Taiwan University. In 2007, he received his Ph.D in condensed matter physics from the University of Wisconsin-Madison, USA. After postdocs in INAC/SPSM, CEA at Grenoble, France and in RCAS, Academia Sinica at Taipei, Taiwan, he is currently assistant research fellow at National Cheng Kung University, Taiwan.