Ultracold Quantum Fields

By: Henk T. C. Stoof (Editor), D. B. M. Dickerscheid (Editor), Koos Gubbels (Editor)

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Hardcover | 1 November 2008

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500 Pages

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24.13 x 16.51 x 1.91

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On June 19th 1999, the European Ministers of Education signed the Bologna Dec laration, with which they agreed that the European university education should be uniformized throughout Europe and based on the two cycle bachelor master's sys tem. The Institute for Theoretical Physics at Utrecht University quickly responded to this new challenge and created an international master's programme in Theoret ical Physics which started running in the summer of 2000. At present, the master's programme is a so called prestige master at Utrecht University, and it aims at train ing motivated students to become sophisticated researchers in theoretical physics. The programme is built on the philosophy that modern theoretical physics is guided by universal principles that can be applied to any sub?eld of physics. As a result, the basis of the master's programme consists of the obligatory courses Statistical Field Theory and Quantum Field Theory. These focus in particular on the general concepts of quantum ?eld theory, rather than on the wide variety of possible applica tions. These applications are left to optional courses that build upon the ?rm concep tual basis given in the obligatory courses. The subjects of these optional courses in clude, for instance, Strongly Correlated Electrons, Spintronics, Bose Einstein Con densation, The Standard Model, Cosmology, and String Theory.

Industry Reviews

From the reviews:

"The book offers a substantial and self-consistent introduction into this exciting and challenging subject of present day research. ... Important items in basic quantum theory ... fine and hyperfine spectral structure, are presented in a new way. ... Most appreciable in this essentially theoretical text is the continuous correspondence with events from the laboratories: actually by the extended bibliography laboratories get very close to the reader." (Bassano Vacchini, Zentralblatt MATH, Vol. 1177, 2010)

"The book has evidently been put together with great care and is very well written. It provides detailed textual explanations to guide the reader through the equations, and includes the intermediate steps in derivations. ... found friendly and understandable by students including, in many cases, senior undergraduates. ... It is pleasure to commend it warmly to those entering, teaching or working in the burgeoning field of ultracold atomic gases as well as in many-particle physics more generally." (Peter V. E. McClintock, Contemporary Physics, Vol. 52 (2), 2011)

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Paperback

Published: 1st November 2014

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Introduction	p. 1
Ultracold Atomic Quantum Gases	p. 2
Outline	p. 6
Part 1	p. 6
Part 2	p. 8
Part 3	p. 10

Gaussian Integrals	p. 15
The Gaussian Integral over Real Variables	p. 15
Generating Function	p. 16
Multi-Dimensional Gaussian Integral	p. 18
Complex Analysis	p. 20
Differentiation and Contour Integrals	p. 20
Laurent Series and the Residue Theorem	p. 22
Gaussian Integrals over Complex Variables	p. 25
Grassmann Variables	p. 26
Problems	p. 28
Quantum Mechanics	p. 33
Hilbert Spaces	p. 34
Observables	p. 35
Schrödinger vs. Heisenberg Picture	p. 39
Bosonic Harmonic Oscillator	p. 41
Creation and Annihilation Operators	p. 42
Three-Dimensional Harmonic Oscillator	p. 43
Coherent States	p. 45
Fermionic Harmonic Oscillator	p. 47
Spin	p. 49
Perturbation Theory	p. 52
Scattering Theory	p. 53
Many-particle Quantum Mechanics	p. 57
Problems	p. 57
Statistical physics	p. 59
Legendre Transformations	p. 59
Statistical Physics	p. 61
Spin Chain	p. 61
Canonical Ensemble	p. 64
Grand-Canonical Ensemble	p. 65
Ideal Gases	p. 67
Ideal Maxwell-Boltzmann Gas	p. 68
Ideal Bose Gas: Bose-Einstein Condensation	p. 72
Ideal Fermi Gas	p. 77
Density Matrix	p. 80
Problems	p. 83
Path Integrals	p. 85
Functionals and Functional Derivatives	p. 85
Principle of Least Action	p. 87
Phase-Space Representation	p. 89
The Feynman Path Integral	p. 90
Continuum Limit and Fluctuation Expansion	p. 93
Gel'fand-Yaglom Method	p. 95
Matrix Elements and Time Ordering	p. 99
Quantum-Mechanical Partition Function	p. 103
Expectation Values	p. 104
Hubbard-Stratonovich Transformation	p. 105
Problems	p. 106
Second Quantization	p. 109
Many-Body Hamiltonian	p. 110
Fock Space	p. 111
Creation and Annihilation Operators	p. 114
Second-Quantized Hamiltonian	p. 116
Field Operators	p. 117
Equivalence of First and Second Quantization	p. 119
Coherent States	p. 122
Problems	p. 125

Functional Integrals	p. 131
Grand-Canonical Partition Function	p. 131
Ideal Quantum Gases	p. 134
Semiclassical Method	p. 135
Matsubara Expansion	p. 137
Green's Function Method	p. 142
Wick's Theorem	p. 146
Problems	p. 149
Interactions and Feynman Diagrams	p. 151
Quasiparticles	p. 152
The Lehmann Representation	p. 153
The Spectral-Weight Function	p. 156
Collective Excitations	p. 158
Perturbation Theory	p. 159
Dyson's Equation	p. 164
Hartree-Fock Approximation	p. 167
Variational Approach	p. 168
Hubbard-Stratonovich Transformation	p. 171
Hartree Theory	p. 172
Fock Theory	p. 176
Hartree-Fock Theory for an Atomic Fermi Gas	p. 178
The Jellium Model	p. 182
Field-Theory Approach	p. 184
Effective Action	p. 185
Dispersion and Screened Coulomb Interaction	p. 188
Problems	p. 190
Landau Theory of Phase Transitions	p. 193
Ising Model in d Dimensions	p. 194
Landau Approach	p. 199
Hubbard-Stratonovich Transformation	p. 203
Gaussian Fluctuations	p. 205
Spontaneous Symmetry Breaking	p. 208
Problems	p. 211
Atomic Physics	p. 213
Atomic Structure	p. 214
Fine Structure	p. 215
Hyperfine Structure	p. 216
Zeeman Effect	p. 217
Two-body Scattering in Vacuum	p. 219
Two-Body Transition Matrix	p. 220
Partial-Wave Expansion	p. 222
Scattering from a Square-Well Potential	p. 224
Two-Body Scattering in a Medium	p. 227
Physical Regimes	p. 230
Problems	p. 232
Bose-Einstein Condensation	p. 235
Definitions for a Bose-Einstein Condensate	p. 236
Superfluidity	p. 238
Landau Criterion	p. 239
Superfluid Density	p. 240
Field-Theory Approach	p. 241
Bogoliubov Theory and the Gross-Pitaevskii Equation	p. 243
Dyson Equation	p. 245
Quasiparticle Dispersion	p. 246
Thermodynamic Potential for Bosons	p. 248
Bogoliubov-de Gennes Equation	p. 251
Popov Theory	p. 253
Hydrodynamic-Like Approach	p. 255
Time-Dependent Gross-Pitaevskii Equation	p. 255
Collective Modes	p. 257
Rotating Bose-Einstein Condensates	p. 259
Attractive Interactions	p. 262
Effective Action	p. 263
Breathing Mode	p. 265
Metastability of the Condensate	p. 268
Problems	p. 269
Condensation of Fermionic Pairs	p. 273
Introduction	p. 273
Thouless Criterion	p. 274
Hubbard-Stratonovich Transformation	p. 276
Bardeen-Cooper-Schrieffer Theory	p. 278
Critical Temperature	p. 280
Gap Equation	p. 283
Thermodynamic Potential for Fermions	p. 286
The BEC-BCS Crossover	p. 288
Theoretical Results	p. 289
Comparison with Experiment	p. 292
Problems	p. 294
Symmetries and Symmetry Breaking	p. 299
Effective Actions	p. 300
Noether's Theorem	p. 303
Ward Identities	p. 305
Hugenholtz-Pines Theorem	p. 309
Bragg Scattering	p. 310
RF Spectroscopy	p. 313
Second-Order Perturbation Theory	p. 317
Ladder Summations	p. 319
Absence of Clock Shift	p. 320
Absence of Vertex Corrections	p. 324
Phase Diffusion	p. 325
Problems	p. 328
Renormalization Group Theory	p. 329
The Renormalization-Group Transformation	p. 330
Scaling	p. 333
Interactions	p. 335
Quantum Effects	p. 340
Interactions	p. 343
Nonuniversal Quantities	p. 346
Renormalization Group for Fermions	p. 347
Renormalization-Group Equations	p. 348
Extremely-Imbalanced Case	p. 350
Homogeneous Phase Diagram	p. 352
Problems	p. 354

Low-Dimensional Systems	p. 359
Modified Popov Theory	p. 360
Phase Fluctuations	p. 360
Many-Body T Matrix	p. 362
Long-Wavelength Physics	p. 363
Comparison with Popo Theory	p. 364
One Dimension	p. 364
Two Dimensions	p. 366
Three Dimensions	p. 370
Vortices in Two Dimensions	p. 371
Kosterlitz-Thouless Phase Transition	p. 373
Trapped Bose Gases	p. 377
Density Profiles	p. 379
Phase Fluctuations	p. 381
Comparision with Exact Results	p. 385
Problems	p. 389
Optical Lattices	p. 391
Introduction	p. 392
Coupling between Atoms and Light	p. 393
Two-Level Approximation	p. 393
Fine Structure	p. 395
Band Structure	p. 397
Hubbard Models	p. 397
Superfluid-Mott Insulator Transition	p. 400
Bogoliubov Approximation	p. 402
Decoupling Approximation	p. 406
Hubbard-Stratonovich Transformation	p. 413
Fluctuations	p. 418
Mott Insulator	p. 420
Superfluid Phase	p. 421
Bragg Spectroscopy	p. 423
Problems	p. 428
Feshbach Resonances	p. 431
Example of a Feshbach Resonance	p. 432
Bare Atom-Molecule Theory	p. 439
Ladder Summations	p. 447
Effective Atom-Molecule theory	p. 453
Scattering Properties	p. 454
Bound-State Energy	p. 455
Molecular Density of States	p. 456
Bogoliubov Theory for the Bose-Einstein Condensed Phase	p. 458
Experiments	p. 462
Josephson Frequency	p. 466
Problems	p. 471
References	p. 475
Index	p. 481
Table of Contents provided by Ingram. All Rights Reserved.

Ultracold Quantum Fields

At a Glance

Hardcover

Industry Reviews

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