Some surface effects in the hydrodynamic model of metals

Barton, G.

doi:10.1088/0034-4885/42/6/001

Cited by 232 publications

(168 citation statements)

References 94 publications

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“…In our case, however, the role of δ 0 is played by the layer thickness d (the influence of nonlocality effects on van der Waals force is discussed in [233,234] [235] demonstrating that for Au the bulk values of dielectric constants can only be obtained from films whose thickness is about 30 nm or more). That is why the above calculated results for the case of d = 20 nm are subject to corrections due to the influence of spatial dispersion.…”

Section: Computational Results Using the Optical Tabulated Datamentioning

confidence: 99%

New developments in the Casimir effect

2001

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We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

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Section: Computational Results Using the Optical Tabulated Datamentioning

confidence: 99%

New developments in the Casimir effect

2001

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“…14). As the traceless part π ij of the stress tensor (16) and the third moment tensor L (3) ijk vanish for the locally equilibrium distribution function, they remain small under conditions (6). In this case tensors π ij and L (3) ijk describe, respectively, viscosity and thermal conductivity in a collision dominated liquid.…”

Section: The Hierarchy Of Equations For the Momentsmentioning

confidence: 97%

Hydrodynamics beyond local equilibrium: Application to electron gas

Tokatly

Pankratov

2000

Phys. Rev. B

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Generalized hydrodynamic theory, which does not rest on the requirement of a local equilibrium, is derived in the long-wave limit of a kinetic equation. The theory bridges the whole frequency range between the quasistatic (Navier-Stokes) hydrodynamics and the high frequency (Vlasov) collisionless limit. In addition to pressure and velocity the theory includes new macroscopic tensor variables. In a linear approximation these variables describe an effective shear stress of a liquid and the generalized hydrodynamics recovers the Maxwellian theory of highly viscous fluids -the media behaving as solids on a short time scale, but as viscous fluids on long time intervals. It is shown that the generalized hydrodynamics can be applied to the Landau theory of Fermi liquid. Illustrative results for collective modes in confined systems are given, which show that nonequilibrium effects qualitatively change the collective dynamics in comparison with the predictions of the heuristic Bloch's hydrodynamics. Earlier improvements of the Bloch theory are critically reconsidered.

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“…The set of equations (continuity equation, Euler and Poisson equations) becomes complete when the equation of state is added, and in the original paper [1] Bloch identified P with the kinetic pressure of a degenerate Fermi gas. The Bloch's hydrodynamic theory (BHT) has been applied to variety of kinetic problems [2,3,4,5,6,7,8,9] with minor improvements (inclusion of exchange, correlation and quantum gradient corrections) [5,9].From the microscopic point of view BHT cannot be a fully consistent theory since it extends the collisiondominated hydrodynamics to the electron gas where the collisionless (Vlasov) limit is most common. For example, in the plasmon dispersion law ω 2 = ω 2 p + v 2 0 q 2 BHT predicts for degenerate electron gas v 2 0 = 1 3 v 2 F instead of a correct result 3 5 v 2 F (v F is the Fermi velocity) [4,6,7,8,11,12,13,14,15] .…”

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“…For example, in the plasmon dispersion law ω 2 = ω 2 p + v 2 0 q 2 BHT predicts for degenerate electron gas v 2 0 = 1 3 v 2 F instead of a correct result 3 5 v 2 F (v F is the Fermi velocity) [4,6,7,8,11,12,13,14,15] . At arbitrary degeneracy the hydrodynamics gives v 2 0 = v 2 s , where v s is velocity of sound, whereas in the kinetic theory v 2 0 equals to the mean square of the particle velocity < v 2 p > [15].…”

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Hydrodynamic theory of an electron gas

1999

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The generalised hydrodynamic theory of an electron gas, which does not rely on an assumption of a local equilibrium, is derived as the long-wave limit of a kinetic equation. Apart from the common hydrodynamics variables the theory includes the tensor fields of the higher moments of the distribution function. In contrast to the Bloch hydrodynamics, the theory leads to the correct plasmon dispersion and in the low frequency limit recovers the Navies-Stocks hydrodynamics. The linear approximation to the generalised hydrodynamics is closely related to the theory of highly viscous fluids.PACS numbers: 71.10. Ca, 05.20.Dd, 47.10.+g, 62.10.+s Hydrodynamic theory of an electron gas was heuristically introduced by Bloch in 1933 [1] as an extension of Thomas-Fermi model. Only macroscopic variableselectron density n(r, t), velocity v(r, t), pressure P , and electrostatic potential ϕ(r, t), enter the theory. The set of equations (continuity equation, Euler and Poisson equations) becomes complete when the equation of state is added, and in the original paper [1] Bloch identified P with the kinetic pressure of a degenerate Fermi gas. The Bloch's hydrodynamic theory (BHT) has been applied to variety of kinetic problems [2,3,4,5,6,7,8,9] with minor improvements (inclusion of exchange, correlation and quantum gradient corrections) [5,9].From the microscopic point of view BHT cannot be a fully consistent theory since it extends the collisiondominated hydrodynamics to the electron gas where the collisionless (Vlasov) limit is most common. For example, in the plasmon dispersion law ω 2 = ω 2 p + v 2 0 q 2 BHT predicts for degenerate electron gas v 2 0 = 1 3 v 2 F instead of a correct result 3 5 v 2 F (v F is the Fermi velocity) [4,6,7,8,11,12,13,14,15] . At arbitrary degeneracy the hydrodynamics gives v 2 0 = v 2 s , where v s is velocity of sound, whereas in the kinetic theory v 2 0 equals to the mean square of the particle velocity < v 2 p > [15]. It has been realized [11,12,13] that this discrepancy originates from the assumption of a local equilibrium , which underlies the common hydrodynamic theory [16]. The assumption allows to reduce the kinetic equation for the distribution function f p (r, t)to equations for macroscopic variables n(r, t),v(r, t) and, in general case, temperature T (r, t). The requirement of the local equilibrium is fulfilled if the characteristic time of the process τ ∼ 1/ω is much longer than the inverse collision frequency 1/ν and the typical length L is greater than the mean free path l ∼ u/ν (u is the average particleIn a zero oder with respect to parameters (2) Eq. (1) reduces to I p [f p ] = 0 which means that f p must have a locally equilibrium form. The stress tensor in the comoving (Lagrange) framebecomes diagonal P ij = P δ ij with P being the local pressure. As a result, the equations for the first three moments of the distribution function i.e. density n, current j = nv and stress tensor P ij , form the closed set of hydrodynamics equations for an ideal liquid. Due to the high frequency of ...

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Some surface effects in the hydrodynamic model of metals

Cited by 232 publications

References 94 publications

New developments in the Casimir effect

New developments in the Casimir effect

Hydrodynamics beyond local equilibrium: Application to electron gas

Hydrodynamic theory of an electron gas

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