Casimir effect

M. Krech. The Casimir Effect in Critical Systems. Singapore World Scientific, 1994, Chap. 3. 

B. Mosaic Stiffening and Temperature Evolution of the Boson Peak The Negative Griineisen Parameter An Elastic Casimir Effect ... 

VI. THE NEGATIVE GRUNEISEN PARAMETER AN ELASTIC CASIMIR EFFECT ... 

The temperature independence of this contribution to the Griineisen constant is the main difference between Eq. (84) and the original calculation by Phillips. The numerical value of the expression should be nearly the same for all substances and is about 8. This suggests that the direct coupling to phonons is a potential contributor to the elastic Casimir effect at temperatures around 1 K. Remember, however, the sign of the expression in Eq. (84) is unknown and its numerical value of lO only provides an estimate from the above. 

The term molecular crystal refers to crystals consisting of neutral atomic particles. Thus they include the rare gases He, Ne, Ar, Kr, Xe, and Rn. However, most of them consist of molecules with up to about 100 atoms bound internally by covalent bonds. The dipole interactions that bond them is discussed briefly in Chapter 3, and at length in books such as Parsegian (2006). This book also discusses the Lifshitz-Casimir effect which causes macroscopic solids to attract one another weakly as a result of fluctuating atomic dipoles. Since dipole-dipole forces are almost always positive (unlike monopole forces) they add up to create measurable attractions between macroscopic bodies. However, they decrease rapidly as any two molecules are separated. A detailed history of intermolecular forces is given by Rowlinson (2002). 

Thermofield dynamics Generalized bogoliubov transormations and applications to Casimir effect... 

A force from nothing onto nothing Casimir effect between bubbles in the Fermi sea... 

Abstract. Within the context of the Thermofield Dynamics, we introduce generalized Bogoliubov transformations which accounts simultaneously for spatial com-pactification and thermal effects. As a specific application of such a formalism, we consider the Casimir effect for Maxwell and Dirac fields at finite temperature. Particularly, we determine the temperature at which the Casimir pressure for a massless fermionic field in a cubic box changes its nature from attractive to repulsive. This critical temperature is approximately 100 MeV when the edge of the cube is of the order of the confining length ( 1 fm) for baryons. 

In this talk, we consider the TFD approach for free fields aiming to extend the Bogoliubov transformation to account also for spatial compactification effects. The main application of our general discussion is the Casimir effect for cartesian confining geometries at finite temperature. 

The main goal of this talk is to show that the Bogoliubov transformation of TFD can be generalized to account for spatial compactification and thermal effects simultaneously. These ideas are then applied to the Casimir effect in various cases. 

The Casimir effect for the electromagnetic field between parallel metallic plates can be obtained from Eq. (23) the Casimir energy and pressure are... 

Such a generalization must reproduce, for example, the known results for the Casimir effect in the case of the parallel plates geometry at finite temperatures. Since energy is an additive quantity, we expect to have L- and T-dependent contributions plus a mixed (LT-dependent) contribution representing the interference of the two effects. In the next Section, we will show that the proper extension of expressions (16) and (21), for this case, is... 

Casimir effect for parallel plates at finite temperature... 

We have shown that generalizations of the TFD Bogoliubov transformation allow a calculation, in a very direct way, of the Casimir effect at finite temperature for cartesian confining geometries. This approach is applied to both bosonic and fermionic fields, making very clear the... 

It is important to stress that use of the generalised Bogoliubov transformatin provides an elegant physical interpretation of the Casimir effect as a consequence of the condensation in the vacuum of the fermion or the boson field. The method can be extended to other geometries such as spherical or cylindrical. 

This effect resembles the traditional Casimir effect, which describes the attraction between two parallel metallic mirrors in vacuum. Here, however, the fluctuating (bosonic) electromagnetic fields are replaced by fermionic matter fields. Furthermore, the Casimir energy is inferred from the geometry-dependent part of the density of states, and its sign is not fixed, but oscillates according to the relative arrangement and distances of the cavities. 

Keywords Casimir effect, Fermi sea, scattering problem, Krein formula... 

Casimir effect and vacuum energy in quantum field... 

Under this scenario we have the following similarities with the ordinary Casimir effect In both cases, there exist modes sums Jj h k with constant... 

For more complicated geometries, the computations become more and more involved as it is the case for the ordinary electromagnetic Casimir effect. However, Casimir calculations of a finite number of immersed nonoverlapping spherical voids or rods, i.e. spheres and cylinders in 3 dimensions or disks in 2 dimensions, are still doable. In fact, these calculations simplify because of Krein s trace formula (Krein, 2004 Beth and Uhlenbeck, 1937)... 

Mostepanenko, V. M. and Trunov, N. N. The Casimir Effect and its Applications. Oxford University Press, New York, 1997. 

The vdW force is always attractive between any two materials in a vacuum. This is because there is no interaction between a dielectric material and a vacuum. However, in the Casimir effect, the spatial restriction of vacuum quantum fluctuations when two metal plates are placed in close proximity, creates an attractive pressure on them, in addition to the vdw force. 

It may be added that the difficulty reappeared later, when it appeared that each oscillator has a zero-point energy. This zero-point energy exists also in empty space and is independent of temperature, and may therefore be subtracted from the total energy without affecting the observed facts. However, the difference between the zero-point energy of the field between both mirrors and the vacuum field does not vanish and depends on L. It therefore gives rise to a force between the mirrors, which is a macroscopic version of the Van der Waals force between molecules, nowadays known as the Casimir effect. )... 

V. M. Mostepanenko, and N. N. Trunov, The Casimir effect and its Application, Claredon Press, Oxford (1997). 

---