*M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko*

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0014
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter begins with a discussion of the problem of the zero-frequency term in the Lifshitz formula. The thermal Casimir free energy and pressure are computed using both the plasma and the Drude ...
More

This chapter begins with a discussion of the problem of the zero-frequency term in the Lifshitz formula. The thermal Casimir free energy and pressure are computed using both the plasma and the Drude model, with the tabulated optical data for the complex refractive index extrapolated by use of the Drude model. It is shown that the plasma model combined with the Lifshitz formula agrees with thermodynamics while the Drude model does not if the metal crystal lattice is perfect. Physical arguments are presented for why the Drude model is outside the application region of the Lifshitz formula. The approximate approach, based on the Leontovich impedance, is shown to be consistent with thermodynamics. The role of evanescent and traveling waves in the Casimir effect between metals is discussed. The chapter concludes with the approach using the generalized plasma-like permittivity, which is shown to be thermodynamically consistent.Less

This chapter begins with a discussion of the problem of the zero-frequency term in the Lifshitz formula. The thermal Casimir free energy and pressure are computed using both the plasma and the Drude model, with the tabulated optical data for the complex refractive index extrapolated by use of the Drude model. It is shown that the plasma model combined with the Lifshitz formula agrees with thermodynamics while the Drude model does not if the metal crystal lattice is perfect. Physical arguments are presented for why the Drude model is outside the application region of the Lifshitz formula. The approximate approach, based on the Leontovich impedance, is shown to be consistent with thermodynamics. The role of evanescent and traveling waves in the Casimir effect between metals is discussed. The chapter concludes with the approach using the generalized plasma-like permittivity, which is shown to be thermodynamically consistent.

*Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, and Vladimir Mikhaylovich Mostepanenko*

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

The subject of this book is the Casimir effect, i.e., a manifestation of zero-point oscillations of the quantum vacuum in the form of forces acting between closely spaced bodies. It is a purely ...
More

The subject of this book is the Casimir effect, i.e., a manifestation of zero-point oscillations of the quantum vacuum in the form of forces acting between closely spaced bodies. It is a purely quantum effect. There is no force acting between neutral bodies in classical electrodynamics. The Casimir effect has become an interdisciplinary subject. It plays an important role in various fields of physics such as condensed matter physics, quantum field theory, atomic and molecular physics, gravitation and cosmology, and mathematical physics. Most recently, the Casimir effect has been applied to nanotechnology and for obtaining constraints on the predictions of unification theories beyond the Standard Model. The book assembles together the field-theoretical foundations of this phenomenon, the application of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force, including the comparison between experiment and theory. There is increasing interest in forces of vacuum origin. Numerous new results have been obtained during the last few years which are not reflected in the literature, but are very promising for fundamental science and nanotechnology. The book provides a source of information which presents a critical assessment of all of the main results and approaches contained in published journal papers. It also proposes new ideas which are not yet universally accepted but are finding increasing support from experiment.Less

The subject of this book is the Casimir effect, i.e., a manifestation of zero-point oscillations of the quantum vacuum in the form of forces acting between closely spaced bodies. It is a purely quantum effect. There is no force acting between neutral bodies in classical electrodynamics. The Casimir effect has become an interdisciplinary subject. It plays an important role in various fields of physics such as condensed matter physics, quantum field theory, atomic and molecular physics, gravitation and cosmology, and mathematical physics. Most recently, the Casimir effect has been applied to nanotechnology and for obtaining constraints on the predictions of unification theories beyond the Standard Model. The book assembles together the field-theoretical foundations of this phenomenon, the application of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force, including the comparison between experiment and theory. There is increasing interest in forces of vacuum origin. Numerous new results have been obtained during the last few years which are not reflected in the literature, but are very promising for fundamental science and nanotechnology. The book provides a source of information which presents a critical assessment of all of the main results and approaches contained in published journal papers. It also proposes new ideas which are not yet universally accepted but are finding increasing support from experiment.

*M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko*

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

This chapter demonstrates that the Casimir force inside a rectangular box can be both attractive and repulsive. A detailed investigation of the Casimir energy and force for fields of various spins, ...
More

This chapter demonstrates that the Casimir force inside a rectangular box can be both attractive and repulsive. A detailed investigation of the Casimir energy and force for fields of various spins, when it may be positive or negative, as a function of the box dimensions and the type of boundary conditions is performed. In particular, the analytical results for two- and three-dimensional boxes are obtained by repeated application of the Abel–Plana formula and using the Epstein zeta function. The problem of isolation of the divergent terms in the vacuum energy and their interpretation is discussed in connection with the problem of a rectangular box divided into two sections by a movable partition (piston). Both the old classical results and recent results related to boxes with a piston at zero and nonzero temperatures are presented. As shown in the chapter, the two sets of results are in mutual agreement.Less

This chapter demonstrates that the Casimir force inside a rectangular box can be both attractive and repulsive. A detailed investigation of the Casimir energy and force for fields of various spins, when it may be positive or negative, as a function of the box dimensions and the type of boundary conditions is performed. In particular, the analytical results for two- and three-dimensional boxes are obtained by repeated application of the Abel–Plana formula and using the Epstein zeta function. The problem of isolation of the divergent terms in the vacuum energy and their interpretation is discussed in connection with the problem of a rectangular box divided into two sections by a movable partition (piston). Both the old classical results and recent results related to boxes with a piston at zero and nonzero temperatures are presented. As shown in the chapter, the two sets of results are in mutual agreement.