Advances in the Casimir Effect

Contents......Page 10
1.1 Zero-point oscillations and their manifestations......Page 20
1.2 Connection between van der Waals and Casimir forces......Page 24
1.3 The Casimir effect as a multidisciplinary subject......Page 26
1.4 A guide to this book......Page 27
I: PHYSICAL AND MATHEMATICAL FOUNDATIONS OF THE CASIMIR EFFECT FOR IDEAL BOUNDARIES......Page 34
2.1 The scalar Casimir effect on an interval......Page 36
2.2 The Abel–Plana formula and regularization......Page 40
2.3 The scalar Casimir effect on a circle......Page 43
2.4 Local and global descriptions of the Casimir effect......Page 46
2.5 Elementary approach to the Casimir force between two parallel planes......Page 48
3.1 Field equations for fields of various spins......Page 52
3.2 Various boundaries and boundary conditions......Page 57
3.3 Canonical quantization and the vacuum energy as a mode expansion......Page 59
3.4 Vacuum energy in terms of Green's functions......Page 65
3.5 Path-integral quantization......Page 67
3.6 Propagators with boundary conditions......Page 70
4 Regularization and renormalization of the vacuum energy......Page 74
4.1 Regularization schemes......Page 75
4.2 The divergent part of the vacuum energy......Page 76
4.3 Renormalization of the vacuum energy......Page 84
5.1 The Matsubara formulation......Page 92
5.2 The Casimir effect at low and high temperature......Page 98
6 Approximate and numerical approaches......Page 103
6.1 The multiple-reflection expansion......Page 104
6.2 Semiclassical approaches......Page 107
6.3 World line numerical methods......Page 110
6.4 Pairwise summation......Page 112
6.5 The proximity force approximation......Page 116
7.1 The scalar Casimir effect for parallel planes......Page 122
7.2 The electromagnetic Casimir effect between parallel planes......Page 126
7.3 The radiative corrections to the Casimir force......Page 131
7.4 Two parallel planes at nonzero temperature......Page 136
7.5 The spinor Casimir effect between parallel planes......Page 144
7.6 The Casimir effect for a wedge......Page 147
7.7 The dynamical Casimir effect......Page 150
8.1 The scalar Casimir effect in a rectangle......Page 155
8.2 The scalar Casimir effect in a three-dimensional box......Page 162
8.3 The electromagnetic Casimir effect in a three-dimensional box......Page 167
8.4 Rectangular boxes with different boundary conditions......Page 171
8.5 Rectangular boxes at nonzero temperature......Page 174
9 Single spherical and cylindrical boundaries......Page 185
9.1 Separation of variables and mode summation......Page 187
9.2 The scalar Casimir effect for a spherical shell......Page 197
9.3 The electromagnetic Casimir effect for a spherical shell and for a dielectric ball......Page 212
9.4 The spinor Casimir effect for a sphere......Page 226
9.5 Spherical shell at nonzero temperature......Page 231
9.6 The Casimir effect for a cylinder......Page 234
10 The Casimir force between objects of arbitrary shape......Page 246
10.1 Various approaches to the calculation of the Casimir energy......Page 247
10.2 Casimir attraction between two bodies......Page 255
10.3 Application to cylindrical geometry......Page 258
10.4 Applications to spherical geometry......Page 268
10.5 Corrugated planes......Page 277
11.1 Topologically nontrivial flat spaces......Page 281
11.2 Topologically nontrivial curved spaces......Page 284
11.3 Nontrivial topologies in cosmology......Page 289
11.4 Compactification of extra dimensions......Page 293
11.5 Topological defects......Page 295
II: THE CASIMIR FORCE BETWEEN REAL BODIES......Page 298
12 The Lifshitz theory of the van der Waals and Casimir forces between plane dielectrics......Page 300
12.1 The Lifshitz formula for two semispaces at zero temperature......Page 301
12.2 The Lifshitz formula for stratified and magnetic media......Page 309
12.3 Two semispaces at nonzero temperature......Page 313
12.4 Correlation of energy and free energy......Page 318
12.5 Asymptotic properties of the Lifshitz formula at low and high temperature......Page 320
12.6 Computational results for typical dielectrics......Page 329
12.7 Problems with polar dielectrics......Page 338
12.8 The Lifshitz formula for anisotropic plates......Page 340
12.9 Lifshitz-type formula for radiative heat transfer......Page 342
12.10 Application region of the Lifshitz formula......Page 343
13.1 Perturbation theory in the relative skin depth, and the plasma model......Page 347
13.2 Drude model and the Lifshitz formula at zero temperature......Page 350
13.3 Computations using tabulated optical data......Page 354
13.4 Surface impedance approach......Page 358
13.5 The generalized plasma-like dielectric permittivity......Page 362
14 The Casimir interaction between real metals at nonzero temperature......Page 370
14.1 The problem associated with the zero-frequency term in the Lifshitz formula......Page 371
14.2 Perturbation theory for metals described by the plasma model......Page 374
14.3 Metals described by the Drude model......Page 380
14.4 Leontovich impedance approach at nonzero temperature......Page 399
14.5 The role of evanescent and propagating waves......Page 406
14.6 Metals described by the generalized plasma-like model......Page 411
15.1 An ideal-metal plate and a plate with constant permittivity......Page 420
15.2 Metal and dielectric plates with permittivities depending on frequency......Page 425
15.3 Computational results......Page 432
15.4 Conductivity of a dielectric plate and the Nernst heat theorem......Page 434
16.1 The van der Waals and Casimir–Polder interatomic potentials......Page 438
16.2 The Lifshitz formula for an atom above a plate......Page 441
16.3 Interaction of atoms with a metal wall......Page 444
16.4 Interaction of atoms with a dielectric wall......Page 458
16.5 The impact of magnetic properties on atom–wall interaction......Page 468
16.6 Atom–wall interactions in the nonequilibrium case......Page 470
16.7 Anisotropic materials: interaction of hydrogen atoms with graphite......Page 472
17 The Casimir force between rough surfaces and corrugated surfaces......Page 479
17.1 Method of pairwise summation for real bodies with rough surfaces......Page 480
17.2 The proximity force approximation for real rough bodies......Page 501
17.3 Nonparallel plates as large-scale roughness......Page 505
17.4 Various approaches for short-scale roughness......Page 509
17.5 Sinusoidally corrugated surfaces......Page 513
III: MEASUREMENTS OF THE CASIMIR FORCE AND THEIR APPLICATIONS IN BOTH FUNDAMENTAL PHYSICS AND NANOTECHNOLOGY......Page 530
18.1 Primary achievements of older measurements......Page 532
18.2 General requirements following from the older measurements......Page 538
18.3 Rigorous procedures for comparison of experiment and theory......Page 539
19.1 Experiment with torsion pendulum......Page 549
19.2 Experiments with an atomic force microscope......Page 552
19.3 Experiments with a micromechanical torsional oscillator......Page 568
19.4 Experiment using a configuration of two parallel plates......Page 592
19.5 Related experiments......Page 593
19.6 Prospects for future measurements......Page 597
20 Measurements of the Casimir force with semiconductors......Page 600
20.1 Experiment with gold-coated sphere and silicon plate......Page 601
20.2 Experiment on the difference Casimir force for samples with different charge carrier densities......Page 612
20.3 Experiment on optically modulated Casimir forces......Page 619
20.4 Proposed experiments with semiconductor surfaces......Page 639
21.1 Experiment with a sphere above a corrugated plate......Page 644
21.2 Measurement of the lateral Casimir force......Page 646
21.3 Calculation of the lateral Casimir force in the configuration of a sphere above a plate......Page 651
21.4 Control of the lateral Casimir force......Page 655
21.5 Experiment with a sphere above rectangular trenches......Page 657
22.1 Measurement of the thermal Casimir–Polder force......Page 662
22.2 Experiments on quantum reflection......Page 668
23.1 Combined role of electrostatic and Casimir forces in MEMS and NEMS......Page 674
23.2 Actuation of MEMS by the Casimir force......Page 680
23.3 Nonlinear micromechanical Casimir oscillator......Page 682
23.4 The Casimir–Polder interaction between atoms and carbon nanostructures......Page 685
23.5 Prospective applications......Page 698
24.1 Long-range forces and constraints on them from gravitational experiments......Page 701
24.2 Constraints from older measurements of the Casimir force......Page 706
24.3 Constraints from experiment with gold surfaces using an atomic force microscope......Page 711
24.4 Constraints from experiment using a micromachined oscillator......Page 712
25 Conclusions and outlook......Page 717
References......Page 722
C......Page 764
E......Page 765
N......Page 766
T......Page 767
Z......Page 768