Advances in the Casimir effect:
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| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2009
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| Edition: | 1. publ. |
| Series: | International series of monographs on physics
145 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [703] - 743 |
| Physical Description: | XVII, 749 S. graph. Darst. |
| ISBN: | 9780199238743 019923874X |
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| _version_ | 1804142741286813696 |
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| adam_text | Titel: Advances in the Casimir effect
Autor: Bordag, Michael
Jahr: 2009
CONTENTS
1 Introduction 1
1.1 Zero-point oscillations and their manifestations 1
1.2 Connection between van der Waals and Casimir forces 5
1.3 The Casimir effect as a multidisciplinary subject 7
1.4 A guide to this book 8
I PHYSICAL AND MATHEMATICAL FOUNDATIONS OF THE
CASIMIR EFFECT FOR IDEAL BOUNDARIES
2 Simple models of the Casimir effect 17
2.1 The scalar Casimir effect on an interval 17
2.2 The Abel-Plana formula and regularization 21
2.3 The scalar Casimir effect on a circle 24
2.4 Local and global descriptions of the Casimir effect 27
2.5 Elementary approach to the Casimir force between two parallel
planes 29
3 Field quantization and vacuum energy in the presence of
boundaries 33
3.1 Field equations for fields of various spins 33
3.2 Various boundaries and boundary conditions 38
3.3 Canonical quantization and the vacuum energy as a mode
expansion 40
3.4 Vacuum energy in terms of Green s functions 46
3.5 Path-integral quantization 48
3.6 Propagators with boundary conditions 51
4 Regularization and renormalization of the vacuum energy 55
4.1 Regularization schemes 56
4.2 The divergent part of the vacuum energy 57
4.2.1 The divergent part in the cutoff regularization 57
4.2.2 The divergent part in the zeta function regularization
and the heat kernel expansion 59
4.3 Renormalization of the vacuum energy 65
4.3.1 Smooth background fields 66
4.3.2 Singular background fields and boundary conditions 69
4.3.3 Finiteness of the Casimir force between separate bodies 71
5 The Casimir effect at nonzero temperature 73
5.1 The Matsubara formulation 73
5.2 The Casimir effect at low and high temperature 79
Contents
Approximate and numerical approaches 84
6.1 The multiple-reflection expansion 85
6.2 Semiclassical approaches 88
6.3 World line numerical methods 91
6.4 Pairwise summation 93
6.5 The proximity force approximation 97
The Casimir effect for two ideal-metal planes 103
7.1 The scalar Casimir effect for parallel planes 103
7.1.1 Dirichlet boundary conditions 103
7.1.2 Mixed boundary conditions 106
7.2 The electromagnetic Casimir effect between parallel planes 107
7.2.1 Ideal-metal planes 107
7.2.2 An ideal-metal plane and an infinitely permeable plane 110
7.3 The radiative corrections to the Casimir force 112
7.4 Two parallel planes at nonzero temperature 117
7.4.1 General case 117
7.4.2 The limit of low temperature 122
7.4.3 The limit of high temperature 124
7.5 The spinor Casimir effect between parallel planes 125
7.6 The Casimir effect for a wedge 128
7.7 The dynamical Casimir effect 131
7.7.1 Uniformly moving plane 131
7.7.2 Particle creation from an accelerated plane 131
The Casimir effect in rectangular boxes 136
8.1 The scalar Casimir effect in a rectangle 136
8.1.1 Regularization using the Abel-Plana formula 137
8.1.2 Regularization using the Epstein zeta function 139
8.1.3 A Casimir piston in a rectangle 142
8.2 The scalar Casimir effect in a three-dimensional box 143
8.3 The electromagnetic Casimir effect in a three-dimensional box 148
8.4 Rectangular boxes with different boundary conditions 152
8.5 Rectangular boxes at nonzero temperature 155
8.5.1 The scalar Casimir effect 156
8.5.2 The electromagnetic Casimir effect 160
Single spherical and cylindrical boundaries 166
9.1 Separation of variables and mode summation 168
9.1.1 Spherical symmetry 168
9.1.2 Mode summation for the interior problem 170
9.1.3 Mode summation for the exterior problem 172
9.1.4 Cylindrical symmetry 175
9.2 The scalar Casimir effect for a spherical shell 178
9.2.1 Boundarv conditions and mode-generating functions 178
Contents xi
9.2.2 Analytic continuation for regularized vacuum energy
and divergent contributions 180
9.2.3 The renormalized vacuum energy for a massive scalar
field 185
9.2.4 The vacuum energy for a massless scalar field 188
9.3 The electromagnetic Casimir effect for a spherical shell and
for a dielectric ball 193
9.3.1 Boundary conditions and separation of polarizations 193
9.3.2 The mode-generating functions 195
9.3.3 The electromagnetic Casimir effect for a conducting
spherical shell 196
9.3.4 The Casimir effect for a dielectric ball 200
9.4 The spinor Casimir effect for a sphere 207
9.5 Spherical shell at nonzero temperature 212
9.5.1 Low-temperature expansion 212
9.5.2 High-temperature expansion 214
9.6 The Casimir effect for a cylinder 215
9.6.1 Conducting cylindrical shell 216
9.6.2 Dielectric cylinder 221
10 The Casimir force between objects of arbitrary shape 227
10.1 Various approaches to the calculation of the Casimir energy 228
10.1.1 Functional-determinant representation for the case of
boundary conditions on separate bodies 228
10.1.2 T-matrix approach for potentials with disjoint support 232
10.2 Casimir attraction between two bodies 236
10.3 Application to cylindrical geometry 239
10.3.1 Two parallel cylinders and a cylinder parallel to a plane 240
10.3.2 Cylinder parallel to a plane at large separation 245
10.3.3 The limit of short separations, and corrections beyond
the proximity force approximation 246
10.4 Applications to spherical geometry 249
10.4.1 General formulas for two spheres and for a sphere in
front of a plane 250
10.4.2 A sphere and a plane at large separation 254
10.4.3 Corrections beyond the proximity force approximation
at small separations 255
10.5 Corrugated planes 258
11 Spaces with non-Euclidean topology 262
11.1 Topologically nontrivial fiat spaces 262
11.1.1 Three-dimensional space-time 262
11.1.2 Four-dimensional space-time 264
11.2 Topologically nontrivial curved spaces 265
11.2.1 Three-dimensional space-time 266
xii Contents
11.2.2 Four-dimensional space-time 268
11.3 Nontrivial topologies in cosmology 270
11.4 Compactification of extra dimensions 274
11.5 Topological defects 276
II THE CASIMIR FORCE BETWEEN REAL BODIES
12 The Lifshitz theory of the van der Waals and Casimir
forces between plane dielectrics 281
12.1 The Lifshitz formula for two semispaces at zero temperature 282
12.1.1 Representation in terms of imaginary frequencies 284
12.1.2 Representation in terms of real frequencies 288
12.1.3 The limiting cases of small and large separations 289
12.2 The Lifshitz formula for stratified and magnetic media 290
12.3 Two semispaces at nonzero temperature 294
12.3.1 Representation in terms of Matsubara frequencies 294
12.3.2 Representation in terms of real frequencies 298
12.4 Correlation of energy and free energy 299
12.5 Asymptotic properties of the Lifshitz formula at low and high
temperature 301
12.5.1 Finite static dielectric permittivity 302
12.5.2 Static conductivity of the dielectric material and the
third law of thermodynamics 307
12.6 Computational results for typical dielectrics 310
12.6.1 Dielectric permittivity along the imaginary frequency
axis 310
12.6.2 Free energy and pressure as functions of separation and
temperature 312
12.6.3 The inclusion of dc conductivity 316
12.7 Problems with polar dielectrics 319
12.8 The Lifshitz formula for anisotropic plates 321
12.8.1 Uniaxial crystals 321
12.8.2 Casimir torque 322
12.9 Lifshitz-type formula for radiative heat transfer 323
12.10 Application region of the Lifshitz formula 324
13 The Casimir interaction between real-metal plates at zero
temperature 328
13.1 Perturbation theory in the relative skin depth, and the plasma
model 328
13.2 Drude model and the Lifshitz formula at zero temperature 331
13.2.1 The Drude dielectric permittivity 331
13.2.2 Computations using the plasma and Drude models 334
13.3 Computations using tabulated optical data 335
13.4 Surface impedance approach 339
Contents xiii
13.4.1 The concept of the Leontovich impedance 339
13.4.2 The Lifshitz formula with the Leontovich impedance 341
13.5 The generalized plasma-like dielectric permittivity 343
13.5.1 Generalized plasma-like permittivity and optical data 344
13.5.2 Generalized Kramers-Kronig relations for the plasma
and plasma-like permittivities 346
13.5.3 Computations using the generalized plasma-like model 349
14 The Casimir interaction between real metals at nonzero
temperature 351
14.1 The problem associated with the zero-frequency term in the
Lifshitz formula 352
14.2 Perturbation theory for metals described by the plasma model 355
14.2.1 Casimir free energy per unit area and Casimir pressure 356
14.2.2 Agreement with the Nernst heat theorem 360
14.3 Metals described by the Drude model 361
14.3.1 Prediction of large thermal corrections below l//m 362
14.3.2 Violation of Nernst s theorem for Drude metals with
perfect crystal lattices 365
14.3.3 The role of impurities 371
14.3.4 Why the Drude model is not applicable in the Lifshitz
theory 374
14.3.5 Attempts at modifying the reflection coefficients 376
14.4 Leontovich impedance approach at nonzero temperature 380
14.4.1 Impedance in the frequency region of the normal skin
effect 381
14.4.2 Impedance in the region of the anomalous skin effect 382
14.4.3 Impedance in the region of infrared optics 383
14.4.4 Impedance using the Drude model 385
14.5 The role of evanescent and propagating waves 387
14.6 Metals described by the generalized plasma-like model 392
14.6.1 Computational results 393
14.6.2 Perturbation theory for the generalized plasma model 395
14.6.3 Agreement with the Nernst heat theorem 399
15 The Casimir interaction between a metal and a dielectric 401
15.1 An ideal-metal plate and a plate with constant permittivity 401
15.1.1 The asymptotic behavior at low and high temperature 402
15.1.2 The Casimir energy and pressure at zero temperature 405
15.2 Metal and dielectric plates with permittivities depending on
frequency 406
15.2.1 The low- and high-temperature limits 407
15.2.2 Analytical results at zero temperature 411
15.3 Computational results 413
15.4 Conductivity of a dielectric plate and the Nernst heat theorem 415
xiv Contents
16 The Lifshitz theory of atom wall interactions 419
16.1 The van der Waals and Casimir-Polder interatomic potentials 419
16.2 The Lifshitz formula for an atom above a plate 422
16.3 Interaction of atoms with a metal wall 425
16.3.1 Atom near an ideal-metal plane 425
16.3.2 A real-metal plate and an atom 429
16.3.3 Asymptotic behavior at low temperature 433
16.3.4 The case of short separations 437
16.4 Interaction of atoms with a dielectric wall 439
16.4.1 Asymptotic properties at low and high temperature for
a finite static permittivity of the wall material 439
16.4.2 Computations of the free energy 441
16.4.3 Various approaches to including the dc conductivity,
and the Nernst theorem 444
16.5 The impact of magnetic properties on atom-wall interaction 449
16.6 Atom-wall interactions in the nonequilibrium case 451
16.7 Anisotropic materials: interaction of hydrogen atoms with
graphite 453
16.7.1 Dielectric permittivity of graphite along the imaginary
frequency axis 453
16.7.2 Computational results for plates of different thickness 456
17 The Casimir force between rough surfaces and corrugated
surfaces 460
17.1 Method of pairwise summation for real bodies with rough
surfaces 461
17.1.1 Formulation of the method 461
17.1.2 Perturbation theory in the roughness amplitudes for
two parallel plates 466
17.1.3 Applications to large-scale roughness 471
17.1.4 Perturbation theory for a sphere above a plate 477
17.1.5 Stochastic roughness with large correlation length 480
17.2 The proximity force approximation for real rough bodies 482
17.2.1 Geometrical averaging for regular roughness 482
17.2.2 Geometrical averaging for stochastic roughness 485
17.3 Nonparallel plates as large-scale roughness 486
17.4 Various approaches for short-scale roughness 490
17.5 Sinusoidally corrugated surfaces 494
17.5.1 The Casimir energy and pressure 494
17.5.2 The lateral Casimir force 500
17.5.3 Application regions of approximate methods 502
17.5.4 The role of roughness and corrugations in atom-plate
interactions 506
Contents xv
III MEASUREMENTS OF THE CASIMIR FORCE AND THEIR
APPLICATIONS IN BOTH FUNDAMENTAL PHYSICS AND
NANOTECHNOLOGY
18 General requirements for Casimir force measurements 513
18.1 Primary achievements of older measurements 513
18.1.1 Experiment with parallel plates by Sparnaay 513
18.1.2 Experiments by Derjaguin et al. 515
18.1.3 Experiments by Tabor, Winterton, and Israelachvili 515
18.1.4 Experiments by van Blockland and Overbeek 516
18.1.5 Dynamical measurements by Hunklinger and Arnold
et al. 518
18.1.6 Measurements of the Casimir-Polder force by Sukenik
and Hinds et al. 518
18.2 General requirements following from the older measurements 519
18.3 Rigorous procedures for comparison of experiment and theory 520
18.3.1 Experimental errors and precision 521
18.3.2 Theoretical uncertainties for real materials 525
18.3.3 Statistical framework for the comparison of theory with
experiment 527
19 Measurements of the Casimir force between metals 530
19.1 Experiment with torsion pendulum 530
19.2 Experiments with an atomic force microscope 533
19.2.1 First AFM experiment with aluminum surfaces 533
19.2.2 Improved measurement with aluminum surfaces 537
19.2.3 Precision measurement using gold surfaces 540
19.2.4 Dynamic measurement 548
19.3 Experiments with a micromechanical torsional oscillator 549
19.3.1 Experimental setup and measurement scheme 550
19.3.2 Static and dynamic measurements 552
19.3.3 Improved dynamic measurement 556
19.3.4 More precise dynamic measurement, and conclusive
test for some models of the thermal Casimir force 563
19.3.5 Experimental test of proximity force approximation 571
19.4 Experiment using a configuration of two parallel plates 573
19.5 Related experiments 574
19.5.1 Thin metal layers 574
19.5.2 Ambient measurements 575
19.5.3 Measurements in liquids 576
19.5.4 Dynamic holography techniques 578
19.6 Prospects for future measurements 578
20 Measurements of the Casimir force with semiconductors 581
20.1 Experiment with gold-coated sphere and silicon plate 582
xvi Contents
20.1.1 Calibration of the setup 583
20.1.2 Measurement results and experimental errors 586
20.1.3 Comparison between experiment and theory 588
20.2 Experiment on the difference Casimir force for samples with
different charge carrier densities 593
20.3 Experiment on optically modulated Casimir forces 600
20.3.1 Experimental setup and sample preparation 601
20.3.2 Calibration and excited-carrier lifetime measurement 603
20.3.3 Experimental results and error analysis 606
20.3.4 Theoretical Casimir force differences and comparison
with experiment 611
20.3.5 Tests for the effect of charge carriers in dielectrics 616
20.4 Proposed experiments with semiconductor surfaces 620
20.4.1 The dielectric-metal transition 621
20.4.2 Casimir force between a sphere and a patterned plate 621
20.4.3 Pulsating Casimir force 623
21 Measurements of the Casimir force in configurations with
corrugated boundaries 625
21.1 Experiment with a sphere above a corrugated plate 625
21.2 Measurement of the lateral Casimir force 627
21.3 Calculation of the lateral Casimir force in the configuration
of a sphere above a plate 632
21.4 Control of the lateral Casimir force 636
21.5 Experiment with a sphere above rectangular trenches 638
22 Measurements of the Casimir-Polder force 643
22.1 Measurement of the thermal Casimir-Polder force 643
22.1.1 Measurement scheme and technique 643
22.1.2 Comparison with theory in thermal equilibrium 645
22.1.3 Comparison with theory out of thermal equilibrium 647
22.2 Experiments on quantum reflection 649
22.2.1 Main experimental results 649
22.2.2 Accuracy of phenomenological potential 651
23 Applications of the Casimir force in nanotechnology 655
23.1 Combined role of electrostatic and Casimir forces in MEMS
and NEMS 655
23.1.1 Modeling of the combined role of electrostatic and Casimir
forces in MEMS and NEMS 656
23.1.2 Experimental investigation of the stability of MEMS 659
23.2 Actuation of MEMS by the Casimir force 661
23.3 Nonlinear micromechanical Casimir oscillator 663
23.4 The Casimir-Polder interaction between atoms and carbon
nanostructures 666
Contents xvii
23.4.1 Lifshitz-type formulas for the interaction of an atom
with a multiwalled carbon nanotube 666
23.4.2 Lifshitz-type formulas for graphene and single-walled
carbon nanotubes 669
23.4.3 Computational results for atom-nanotube interaction 674
23.5 Prospective applications 679
24 Constraints on hypothetical interactions from the Casimir
effect 682
24.1 Long-range forces and constraints on them from gravitational
experiments 682
24.1.1 Light particles and extra-dimensional physics 682
24.1.2 Eotvos- and Cavendish-type experiments 685
24.2 Constraints from older measurements of the Casimir force 687
24.2.1 Constraints from measurements between dielectric test
bodies 688
24.2.2 Constraints from torsion pendulum experiment 689
24.2.3 Constraints from ambient experiment with two crossed
cylinders 691
24.3 Constraints from experiment with gold surfaces using an atomic
force microscope 692
24.4 Constraints from experiment using a micromachined oscillator 693
24.4.1 Constraints from Casimir pressure measurement 694
24.4.2 Constraints from Casimir-less experiment 696
25 Conclusions and outlook 698
References 703
Index 745
|
| any_adam_object | 1 |
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| id | DE-604.BV025564894 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:36:35Z |
| institution | BVB |
| isbn | 9780199238743 019923874X |
| language | English |
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| physical | XVII, 749 S. graph. Darst. |
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| series | International series of monographs on physics |
| series2 | International series of monographs on physics |
| spelling | Advances in the Casimir effect M. Bordag ... 1. publ. Oxford [u.a.] Oxford Univ. Press 2009 XVII, 749 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 145 Literaturverz. S. [703] - 743 Casimir-Effekt (DE-588)4375133-7 gnd rswk-swf Casimir-Effekt (DE-588)4375133-7 s DE-604 Bordag, Michael 1952- (DE-588)121009475 ctb International series of monographs on physics 145 (DE-604)BV000106406 145 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020163915&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Advances in the Casimir effect International series of monographs on physics Casimir-Effekt (DE-588)4375133-7 gnd |
| subject_GND | (DE-588)4375133-7 |
| title | Advances in the Casimir effect |
| title_auth | Advances in the Casimir effect |
| title_exact_search | Advances in the Casimir effect |
| title_full | Advances in the Casimir effect M. Bordag ... |
| title_fullStr | Advances in the Casimir effect M. Bordag ... |
| title_full_unstemmed | Advances in the Casimir effect M. Bordag ... |
| title_short | Advances in the Casimir effect |
| title_sort | advances in the casimir effect |
| topic | Casimir-Effekt (DE-588)4375133-7 gnd |
| topic_facet | Casimir-Effekt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020163915&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT bordagmichael advancesinthecasimireffect |