Muutke küpsiste eelistusi

E-raamat: Statistical Mechanics of Superconductivity

  • Formaat: PDF+DRM
  • Sari: Graduate Texts in Physics
  • Ilmumisaeg: 05-May-2015
  • Kirjastus: Springer Verlag, Japan
  • Keel: eng
  • ISBN-13: 9784431554059
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 61,74 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Statistical Mechanics of SuperconductivitySuurem pilt
  • Formaat: PDF+DRM
  • Sari: Graduate Texts in Physics
  • Ilmumisaeg: 05-May-2015
  • Kirjastus: Springer Verlag, Japan
  • Keel: eng
  • ISBN-13: 9784431554059
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction, and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on a coherent state in terms of the Cooper-pair creation operator, a quasiparticle field for describing the excitation, and the variational principle in statistical mechanics. They have the advantage that the phase coherence due to the Cooper-pair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classics-wave superconductors and its extension to the p-wave superfluidity of3He. Later, the mean-field equations are simplified to the Eilenberger and Ginzburg–Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov’s flux-line lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of p-wave superfluidity in liquid 3He. The book serves as a standard reference for advanced courses of statistical mechanics with exercises along with detailed answers.

Muu info

"This book has a unique approach to formulating mean field theory of superconductivity especially in a way most useful for studying inhomogeneous and/or unconventional superconductors. Building up from the fundamental laws of thermodynamics and the basic techniques of statistical mechanics such that it is readable for students, it develops the Bogoliubov-de Gennes formalism of superconductivity. The book culminates in derivation of the quasiclassical theory of superconductivity and its application to description of vortex states. While it is informative and useful for researchers in the field, it is an excellent textbook - either as the main text or for supplementary reading - for a variety of graduate courses ranging from a standard class on statistical mechanics or condensed matter physics to more specialised classes such as one on superconductivity." (Professor K.Tanaka, Department of Physics & Engineering Physics, University of Saskatchewan)
1 Review of Thermodynamics
1(12)
1.1 Thermodynamics and Hiking
1(2)
1.2 Equation of State
3(1)
1.3 Laws of Thermodynamics
4(1)
1.4 Equilibrium Thermodynamics
5(5)
1.4.1 Basic Equation
6(1)
1.4.2 Equilibrium Conditions
6(1)
1.4.3 Legendre Transformation and Free Energy
7(1)
1.4.4 Particle Number as a Variable
8(2)
1.5 Thermodynamic Construction of Entropy and Internal Energy
10(3)
Problems
11(2)
2 Basics of Equilibrium Statistical Mechanics
13(12)
2.1 Entropy in Statistical Mechanics
13(3)
2.2 Deriving Equilibrium Distributions
16(9)
2.2.1 Microcanonical Distribution
17(1)
2.2.2 Canonical Distribution
18(3)
2.2.3 Grand Canonical Distribution
21(2)
Problems
23(1)
References
23(2)
3 Quantum Mechanics of Identical Particles
25(18)
3.1 Permutation
25(1)
3.2 Permutation Symmetry of Identical Particles
26(3)
3.3 Eigenspace of Permutation
29(2)
3.4 Bra-Kets for Many-Body Wave Functions
31(1)
3.5 Orthonormality and Completeness of Bra-Kets
32(1)
3.6 Matrix Elements of Operators
33(1)
3.7 Summary of Two Equivalent Descriptions
33(1)
3.8 Second Quantization for Ideal Gases
34(5)
3.9 Coherent State
39(4)
Problems
41(1)
References
41(2)
4 Statistical Mechanics of Ideal Gases
43(18)
4.1 Bose and Fermi Distributions
43(2)
4.2 Single-Particle Density of States
45(1)
4.3 Monoatomic Gases in Three Dimensions
46(5)
4.3.1 Single-Particle Density of States
46(1)
4.3.2 Connection Between Internal Energy and Pressure
47(1)
4.3.3 Introducing Dimensionless Variables
48(2)
4.3.4 Temperature Dependences of Thermodynamic Quantities
50(1)
4.4 High-Temperature Expansions
51(1)
4.5 Fermions at Low Temperatures
52(4)
4.5.1 Fermi Energy and Fermi Wave Number
52(1)
4.5.2 Sommerfeld Expansion
53(2)
4.5.3 Chemical Potential and Heat Capacity
55(1)
4.6 Bosons at Low Temperatures
56(2)
4.6.1 Critical Temperature of Condensation
56(1)
4.6.2 Thermodynamic Quantities of T < T0
57(1)
4.6.3 Chemical Potential and Heat Capacity for T T0
57(1)
4.7 Bose-Einstein Condensation and Density of States
58(3)
Problems
59(1)
References
60(1)
5 Density Matrices and Two-Particle Correlations
61(12)
5.1 Density Matrices
61(1)
5.2 Bloch-De Dominicis Theorem
62(5)
5.3 Two-Particle Correlations of Monoatomic Ideal Gases
67(6)
Problems
71(1)
References
71(2)
6 Hartree-Fock Equations and Landau's Fermi-Liquid Theory
73(18)
6.1 Variational Principle in Statistical Mechanics
73(1)
6.2 Hartree-Fock Equations
74(6)
6.2.1 Derivation Based on the Variational Principle
74(3)
6.2.2 Derivation Based on Wick Decomposition
77(1)
6.2.3 Homogeneous Cases
78(2)
6.3 Application to Low-Temperature Fermions
80(11)
6.3.1 Fermi Wave Number and Fermi Energy
80(1)
6.3.2 Effective Mass, Density of States, and Heat Capacity
80(2)
6.3.3 Effective Mass and Landau Parameter
82(2)
6.3.4 Spin Susceptibility
84(2)
6.3.5 Compressibility
86(1)
6.3.6 Landau Parameters
87(2)
Problems
89(1)
References
89(2)
7 Attractive Interaction and Bound States
91(10)
7.1 Attractive Potential in Two and Three Dimensions
91(3)
7.1.1 Bound State in Three Dimensions
92(1)
7.1.2 Bound State in Two Dimensions
93(1)
7.2 Consideration in Wave Vector Domain
94(3)
7.3 Cooper's Problem
97(4)
Problems
98(1)
References
99(2)
8 Mean-Field Equations of Superconductivity
101(24)
8.1 BCS Wave Function for Cooper-Pair Condensation
101(2)
8.2 Quasiparticle Field for Excitations
103(2)
8.3 Bogoliubov--de Gennes Equations
105(14)
8.3.1 Derivation Based on Variational Principle
106(7)
8.3.2 Derivation Based on Wick Decomposition
113(2)
8.3.3 Matrix Representation of Spin Variables
115(2)
8.3.4 BdG Equations for Homogeneous Cases
117(2)
8.4 Expansion of Pairing Interaction
119(6)
8.4.1 Isotropic Cases
119(1)
8.4.2 Anisotropic Cases
120(2)
Problems
122(1)
References
122(3)
9 BCS Theory
125(18)
9.1 Self-Consistency Equations
125(3)
9.2 Effective Pairing Interaction
128(4)
9.3 Gap Equation and Its Solution
132(3)
9.4 Thermodynamic Properties
135(4)
9.4.1 Heat Capacity
135(3)
9.4.2 Chemical Potential
138(1)
9.4.3 Free Energy
138(1)
9.5 Landau Theory of Second-Order Phase Transition
139(4)
Problems
141(1)
References
141(2)
10 Superfluidity, Meissner Effect, and Flux Quantization
143(16)
10.1 Superfluid Density and Spin Susceptibility
143(8)
10.1.1 Spin Susceptibility
146(1)
10.1.2 Superfluid Density
147(2)
10.1.3 Leggett's Theory of Superfluid Fermi Liquids
149(2)
10.2 Meissner Effect and Flux Quantization
151(8)
10.2.1 Ampere's Law
152(1)
10.2.2 London Equation
153(1)
10.2.3 Meissner Effect
154(1)
10.2.4 Flux Quantization
155(1)
Problems
156(1)
References
157(2)
11 Responses to External Perturbations
159(16)
11.1 Linear-Response Theory
159(4)
11.1.1 Response in Time Domain
159(2)
11.1.2 Response in Frequency Domain
161(1)
11.1.3 Energy Dissipation
162(1)
11.2 Ultrasonic Attenuation
163(5)
11.3 Nuclear-Spin Relaxation
168(7)
Problems
174(1)
References
174(1)
12 Tunneling, Density of States, and Josephson Effect
175(14)
12.1 Formula for Tunneling Current
175(7)
12.2 NN Junction
182(1)
12.3 SN Junction and Density of States
182(1)
12.4 SS Junction and Josephson Effect
183(6)
Problems
187(1)
References
187(2)
13 P-Wave Superfluidity
189(12)
13.1 Effective Pairing Interaction
189(1)
13.2 Gap Matrix
190(1)
13.3 Two Bulk Phases
191(6)
13.3.1 B Phase
191(3)
13.3.2 A Phase
194(3)
13.4 Gap Anisotropy and Quasiparticle Density of States
197(4)
Problems
199(1)
References
199(2)
14 Gor'kov, Eilenberger, and Ginzburg--Landau Equations
201(28)
14.1 Matsubara Green's Function
201(3)
14.2 Gor'kov Equations
204(9)
14.2.1 Equation of Motion for Field Operators
204(2)
14.2.2 Derivation of the Gor'kov Equations
206(3)
14.2.3 Matrix Representation of Spin Variables
209(1)
14.2.4 Gauge Invariance
210(1)
14.2.5 Gauge-Covariant Wigner Transform
211(2)
14.3 Eilenberger Equations
213(8)
14.3.1 Quasiclassical Green's Function
213(4)
14.3.2 Pair Potential
217(2)
14.3.3 Current Density
219(1)
14.3.4 Summary of the Eilenberger Equations
219(2)
14.4 Ginzburg-Landau Equations
221(8)
Problem
225(2)
References
227(2)
15 Abrikosov's Flux-Line Lattice
229(18)
15.1 Ginzburg-Landau Equations
229(1)
15.2 Microscopic Flux Density and Magnetization
230(1)
15.3 Dimensionless Equations
231(2)
15.4 Upper Critical Field and Distinction Between Type-I and II
233(1)
15.5 Flux-Line Lattice Near Hc2
234(7)
15.5.1 Constructing Basis Functions
234(4)
15.5.2 Minimization of the Free Energy Functional
238(3)
15.6 Lower Critical Field Hc1
241(6)
Problems
245(1)
References
245(2)
16 Surfaces and Vortex Cores
247(18)
16.1 Andreev Reflection
247(4)
16.2 Vortex-Core States
251(3)
16.3 Quasiclassical Study of an Isolated Vortex
254(11)
16.3.1 Eilenberger Equations in Magnetic Fields
254(2)
16.3.2 Transformation to a Riccati-Type Equation
256(1)
16.3.3 Equations for an Isolated Vortex
257(2)
16.3.4 Numerical Procedures
259(2)
16.3.5 Results
261(2)
Problems
263(1)
References
263(2)
17 Solutions to Problems
265(22)
References
286(1)
Index 287
Takafumi Kita is an associate professor at Department of Physics, Hokkaido University, Japan. He obtained a PhD from Department of Applied Physics, the University of Tokyo in 1988. He held positions at Institute of Solid State Physics, the University of Tokyo (1988-1993, research associate), at Department of Physics and Astronomy, University of Illinois at Urbana-Champaign (1991-1993, visiting scientist), and joined Hokkaido University subsequently. He spent a year in Germany (2000-2001) at University of Karlsruhe and at University of Bayreuth (half a year per each) as an overseas research fellow. He has been teaching quantum mechanics, thermodynamics, statistical mechanics, mathematical methods in physics, field theory in statistical mechanics, etc., over 20 years.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97844315540592e.html
Märksõnad: