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Quantum Field Theory of Non-equilibrium States [Hardback]

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(Umeå Universitet, Sweden)
  • Formāts: Hardback, 552 pages, height x width x depth: 254x181x30 mm, weight: 1230 g
  • Izdošanas datums: 19-Jul-2007
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521874998
  • ISBN-13: 9780521874991
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Quantum Field Theory of Non-equilibrium StatesPalielināt
  • Formāts: Hardback, 552 pages, height x width x depth: 254x181x30 mm, weight: 1230 g
  • Izdošanas datums: 19-Jul-2007
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521874998
  • ISBN-13: 9780521874991
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780521874991.html
Keywords:
Quantum field theoretical applications for graduate students in statistical mechanics and condensed matter physics.

Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.

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Review of the hardback: 'The information is there, well presented and comprehensive ' Contemporary Physics

Papildus informācija

Quantum field theoretical applications for graduate students in statistical mechanics and condensed matter physics.
Preface xi
Quantum fields
1(32)
Quantum mechanics
2(3)
N-particle system
5(9)
Identical particles
6(3)
Kinematics of fermions
9(2)
Kinematics of bosons
11(2)
Dynamics and probability current and density
13(1)
Fermi field
14(9)
Bose field
23(6)
Phonons
25(1)
Quantizing a classical field theory
26(3)
Occupation number representation
29(2)
Summary
31(2)
Operators on the multi-particle state space
33(20)
Physical observables
33(4)
Probability density and number operators
37(3)
Probability current density operator
40(2)
Interactions
42(6)
Two-particle interaction
42(3)
Fermion-boson interaction
45(1)
Electron-phonon interaction
45(3)
The statistical operator
48(4)
Summary
52(1)
Quantum dynamics and Green's functions
53(26)
Quantum dynamics
53(7)
The Schrodinger picture
54(2)
The Heisenberg picture
56(4)
Second quantization
60(2)
Green's functions
62(8)
Physical properties and Green's functions
62(2)
Stable of one-particle Green's functions
64(6)
Equilibrium Green's functions
70(7)
Summary
77(2)
Non-equilibrium theory
79(42)
The non-equilibrium problem
79(2)
Ground state formalism
81(3)
Closed time path formalism
84(19)
Closed time path Green's function
87(3)
Non-equilibrium perturbation theory
90(4)
Wick's theorem
94(9)
Non-equilibrium diagrammatics
103(10)
Particles coupled to a classical field
104(2)
Particles coupled to a stochastic field
106(1)
Interacting fermions and bosons
107(6)
The self-energy
113(6)
Non-equilibrium Dyson equations
116(1)
Skeleton diagrams
117(2)
Summary
119(2)
Real-time formalism
121(30)
Real-time matrix representation
121(2)
Real-time diagrammatics
123(4)
Feynman rules for a scalar potential
123(2)
Feynman rules for interacting bosons and fermions
125(2)
Triagonal and symmetric representations
127(6)
Fermion-boson coupling
129(2)
Two-particle interaction
131(2)
The real rules: the RAK-rules
133(2)
Non-equilibrium Dyson equations
135(3)
Equilibrium Dyson equation
138(2)
Real-time versus imaginary-time formalism
140(9)
Imaginary-time formalism
140(2)
Imaginary-time Green's functions
142(1)
Analytical continuation procedure
143(5)
Kadanoff-Baym equations
148(1)
Summary
149(2)
Linear response theory
151(28)
Linear response
151(8)
Density response
152(3)
Current response
155(3)
Conductivity tensor
158(1)
Conductance
159(1)
Linear response of Green's functions
159(5)
Properties of response functions
164(1)
Stability of the thermal equilibrium state
165(4)
Fluctuation-dissipation theorem
169(4)
Time-reversal symmetry
173(1)
Scattering and correlation functions
174(4)
Summary
178(1)
Quantum kinetic equations
179(38)
Left-right subtracted Dyson equation
179(2)
Wigner or mixed coordinates
181(3)
Gradient approximation
184(4)
Spectral weight function
185(1)
Quasi-particle approximation
186(2)
Impurity scattering
188(10)
Boltzmannian motion in a random potential
192(1)
Brownian motion
193(5)
Quasi-classical Green's function technique
198(13)
Electron-phonon interaction
200(6)
Renormalization of the a.c. conductivity
206(1)
Excitation representation
207(2)
Particle conservation
209(2)
Impurity scattering
211(1)
Beyond the quasi-classical approximation
211(5)
Thermo-electrics and magneto-transport
215(1)
Summary
216(1)
Non-equilibrium superconductivity
217(36)
BCS-theory
219(13)
Nambu or particle-hole space
225(3)
Equations of motion in Nambu Keldysh space
228(3)
Green's functions and gauge transformations
231(1)
Quasi-classical Green's function theory
232(6)
Normalization condition
235(1)
Kinetic equation
236(1)
Spectral densities
236(2)
Trajectory Green's functions
238(4)
Kinetics in a dirty superconductor
242(7)
Kinetic equation
244(2)
Ginzburg-Landau regime
246(3)
Charge imbalance
249(2)
Summary
251(2)
Diagrammatics and generating functionals
253(60)
Diagrammatics
254(16)
Propagators and vertices
255(3)
Amplitudes and superposition
258(3)
Fundamental dynamic relation
261(4)
Low order diagrams
265(5)
Generating functional
270(11)
Functional differentiation
272(2)
From diagramiriatics to differential equations
274(7)
Connection to operator formalism
281(1)
Fermions and Grassmann variables
282(2)
Generator of connected amplitudes
284(12)
Source derivative proof
284(6)
Combinatorial proof
290(4)
Functional equation for the generator
294(2)
One-particle irreducible vertices
296(10)
Symmetry broken states
301(1)
Green's functions and one-particle irreducible vertices
302(4)
Diagrammatics and action
306(1)
Effective action and skeleton diagrams
307(5)
Summary
312(1)
Effective action
313(60)
Functional integration
313(7)
Functional Fourier transformation
314(1)
Gaussian integrals
315(4)
Fermionic path integrals
319(1)
Generators as functional integrals
320(10)
Euclid versus Minkowski
323(1)
Wick's theorem and functionals
324(6)
Generators and 1PI vacuum diagrams
330(3)
1PI loop expansion of the effective action
333(6)
Two-particle irreducible effective action
339(12)
The 2PI loop expansion of the effective action
346(5)
Effective action approach to Bose gases
351(21)
Dilute Bose gases
351(1)
Effective action formalism for bosons
352(4)
Homogeneous Bose gas
356(3)
Renormalization of the interaction
359(4)
Inhomogeneous Bose gas
363(2)
Loop expansion for a trapped Bose gas
365(7)
Summary
372(1)
Disordered conductors
373(76)
Localization
373(15)
Scaling theory of localization
374(3)
Coherent backscattering
377(11)
Weak localization
388(20)
Quantum correction to conductivity
388(4)
Cooperon equation
392(6)
Quantum interference and the Cooperon
398(4)
Quantum interference in a magnetic field
402(2)
Quantum interference in a time-dependent field
404(4)
Phase breaking in weak localization
408(15)
Electron-phonon interaction
410(6)
Electron-electron interaction
416(7)
Anomalous magneto-resistance
423(5)
Magneto-resistance in thin films
424(4)
Coulomb interaction in a disordered conductor
428(9)
Mesoscopic fluctuations
437(11)
Summary
448(1)
Classical statistical dynamics
449(52)
Field theory of stochastic dynamics
450(10)
Langevin dynamics
450(1)
Fluctuating linear oscillator
451(3)
Quenched disorder
454(1)
Dynamical index notation
455(2)
Quenched disorder and diagrammatics
457(2)
Over-damped dynamics and the Jacobian
459(1)
Magnetic properties of type-II superconductors
460(4)
Abrikosov vortex state
460(2)
Vortex lattice dynamics
462(2)
Field theory of pinning
464(5)
Effective action
467(2)
Self-consistent theory of vortex dynamics
469(3)
Hartree approximation
470(2)
Single vortex
472(15)
Perturbation theory
473(1)
Self-consistent theory
474(2)
Simulations
476(1)
Numerical results
476(6)
Hall force
482(5)
Vortex lattice
487(6)
High-velocity limit
488(1)
Numerical results
489(3)
Hall force
492(1)
Dynamic melting
493(7)
Summary
500(1)
Appendices
501(22)
Path integrals
503(8)
Path integrals and symmetries
511(2)
Retarded and advanced Green's functions
513(4)
Analytic properties of Green's functions
517(6)
Bibliography 523(8)
Index 531


Jorgen Rammer is a Professor in the Department of Physics at Umea University, Sweden. He has also worked in Denmark, Germany, Norway, Canada and the USA. His past research interests are partly reflected in the topics of this book; his main current interests are in decoherence and charge transport in nanostructures.