357 research outputs found
Temperature correction to the Casimir force in cryogenic range and anomalous skin effect
Temperature correction to the Casimir force is considered for real metals at
low temperatures. With the temperature decrease the mean free path for
electrons becomes larger than the field penetration depth. In this condition
description of metals with the impedance of anomalous skin effect is shown to
be more appropriate than with the permittivity. The effect is crucial for the
temperature correction. It is demonstrated that in the zero frequency limit the
reflection coefficients should coincide with those of ideal metal if we demand
the entropy to be zero at T=0. All the other prescriptions discussed in the
literature for the term in the Lifshitz formula give negative entropy. It
is shown that the temperature correction in the region of anomalous skin effect
is not suppressed as it happens in the plasma model. This correction will be
important in the future cryogenic measurements of the Casimir force.Comment: 12 pages, 2 figures, to be published in Phys. Rev.
Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force
We find the lateral projection of the Casimir force for a configuration of a
sphere above a corrugated plate. This force tends to change the sphere position
in the direction of a nearest corrugation maximum. The probability distribution
describing different positions of a sphere above a corrugated plate is
suggested which is fitted well with experimental data demonstrating the
nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur
Violation of the Nernst heat theorem in the theory of thermal Casimir force between Drude metals
We give a rigorous analytical derivation of low-temperature behavior of the
Casimir entropy in the framework of the Lifshitz formula combined with the
Drude dielectric function. An earlier result that the Casimir entropy at zero
temperature is not equal to zero and depends on the parameters of the system is
confirmed, i.e. the third law of thermodynamics (the Nernst heat theorem) is
violated. We illustrate the resolution of this thermodynamical puzzle in the
context of the surface impedance approach by several calculations of the
thermal Casimir force and entropy for both real metals and dielectrics.
Different representations for the impedances, which are equivalent for real
photons, are discussed. Finally, we argue in favor of the Leontovich boundary
condition which leads to results for the thermal Casimir force that are
consistent with thermodynamics.Comment: 24 pages, 3 figures, accepted for publication in Phys. Rev.
The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities
The Casimir mutual free energy F for a system of two dielectric concentric
nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The
present paper is a continuation of an earlier investigation [Phys. Rev. E {\bf
63}, 051101 (2001)], in which F was evaluated in full only for the case of
ideal metals (refractive index n=infinity). Here, analogous results are
presented for dielectrics, for some chosen values of n. Our basic calculational
method stems from quantum statistical mechanics. The Debye expansions for the
Riccati-Bessel functions when carried out to a high order are found to be very
useful in practice (thereby overflow/underflow problems are easily avoided),
and also to give accurate results even for the lowest values of l down to l=1.
Another virtue of the Debye expansions is that the limiting case of metals
becomes quite amenable to an analytical treatment in spherical geometry. We
first discuss the zero-frequency TE mode problem from a mathematical viewpoint
and then, as a physical input, invoke the actual dispersion relations. The
result of our analysis, based upon the adoption of the Drude dispersion
relation at low frequencies, is that the zero-frequency TE mode does not
contribute for a real metal. Accordingly, F turns out in this case to be only
one half of the conventional value at high temperatures. The applicability of
the Drude model in this context has however been questioned recently, and we do
not aim at a complete discussion of this issue here. Existing experiments are
low-temperature experiments, and are so far not accurate enough to distinguish
between the different predictions. We also calculate explicitly the
contribution from the zero-frequency mode for a dielectric. For a dielectric,
this zero-frequency problem is absent.Comment: 23 pages, LaTeX, 7 ps figures; expanded discussion, especially in
Sec. 5. To appear in Phys. Rev.
Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range
Using a template-stripping method, macroscopic gold surfaces with
root-mean-square (rms) roughness less than 0.4 nm have been prepared, making
them useful for studies of surface interactions in the nanometer range. The
utility of such substrates is demonstrated by measurements of the Casimir force
at surface separations between 20 and 100 nm, resulting in good agreement with
theory. The significance and quantification of this agreement is addressed, as
well as some methodological aspects regarding the measurement of the Casimir
force with high accuracy.Comment: 7 figure
Thermal correction to the Casimir force, radiative heat transfer, and an experiment
The low-temperature asymptotic expressions for the Casimir interaction
between two real metals described by Leontovich surface impedance are obtained
in the framework of thermal quantum field theory. It is shown that the Casimir
entropy computed using the impedance of infrared optics vanishes in the limit
of zero temperature. By contrast, the Casimir entropy computed using the
impedance of the Drude model attains at zero temperature a positive value which
depends on the parameters of a system, i.e., the Nernst heat theorem is
violated. Thus, the impedance of infrared optics withstands the thermodynamic
test, whereas the impedance of the Drude model does not. We also perform a
phenomenological analysis of the thermal Casimir force and of the radiative
heat transfer through a vacuum gap between real metal plates. The
characterization of a metal by means of the Leontovich impedance of the Drude
model is shown to be inconsistent with experiment at separations of a few
hundred nanometers. A modification of the impedance of infrared optics is
suggested taking into account relaxation processes. The power of radiative heat
transfer predicted from this impedance is several times less than previous
predictions due to different contributions from the transverse electric
evanescent waves. The physical meaning of low frequencies in the Lifshitz
formula is discussed. It is concluded that new measurements of radiative heat
transfer are required to find out the adequate description of a metal in the
theory of electromagnetic fluctuations.Comment: 19 pages, 4 figures. svjour.cls is used, to appear in Eur. Phys. J.
Surface-impedance approach solves problems with the thermal Casimir force between real metals
The surface impedance approach to the description of the thermal Casimir
effect in the case of real metals is elaborated starting from the free energy
of oscillators. The Lifshitz formula expressed in terms of the dielectric
permittivity depending only on frequency is shown to be inapplicable in the
frequency region where a real current may arise leading to Joule heating of the
metal. The standard concept of a fluctuating electromagnetic field on such
frequencies meets difficulties when used as a model for the zero-point
oscillations or thermal photons in the thermal equilibrium inside metals.
Instead, the surface impedance permits not to consider the electromagnetic
oscillations inside the metal but taking the realistic material properties into
account by means of the effective boundary condition. An independent derivation
of the Lifshitz-type formulas for the Casimir free energy and force between two
metal plates is presented within the impedance approach. It is shown that they
are free of the contradictions with thermodynamics which are specific to the
usual Lifshitz formula for dielectrics in combination with the Drude model. We
demonstrate that in the impedance approach the zero-frequency contribution is
uniquely fixed by the form of impedance function and does not need any of the
ad hoc prescriptions intensively discussed in the recent literature. As an
example, the computations of the Casimir free energy between two gold plates
are performed at different separations and temperatures. It is argued that the
surface impedance approach lays a reliable framework for the future
measurements of the thermal Casimir force.Comment: 21 pages, 3 figures, to appear in Phys. Rev.
Thermodynamical aspects of the Casimir force between real metals at nonzero temperature
We investigate the thermodynamical aspects of the Casimir effect in the case
of plane parallel plates made of real metals. The thermal corrections to the
Casimir force between real metals were recently computed by several authors
using different approaches based on the Lifshitz formula with diverse results.
Both the Drude and plasma models were used to describe a real metal. We
calculate the entropy density of photons between metallic plates as a function
of the surface separation and temperature. Some of these approaches are
demonstrated to lead to negative values of entropy and to nonzero entropy at
zero temperature depending on the parameters of the system. The conclusion is
that these approaches are in contradiction with the third law of thermodynamics
and must be rejected. It is shown that the plasma dielectric function in
combination with the unmodified Lifshitz formula is in perfect agreement with
the general principles of thermodynamics. As to the Drude dielectric function,
the modification of the zero-frequency term of the Lifshitz formula is outlined
that not to violate the laws of thermodynamics.Comment: 8pages, 4 figures; Phys. Rev. A, to appea
A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems
We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake
ecosystem model by augmenting the individual cognitive maps drawn by 8
scientists working in the area of shallow lake ecology. We calculated graph
theoretical indices of the individual cognitive maps and the collective
cognitive map produced by augmentation. The graph theoretical indices revealed
internal cycles showing non-linear dynamics in the shallow lake ecosystem. The
ecological processes were organized democratically without a top-down
hierarchical structure. The steady state condition of the generic model was a
characteristic turbid shallow lake ecosystem since there were no dynamic
environmental changes that could cause shifts between a turbid and a clearwater
state, and the generic model indicated that only a dynamic disturbance regime
could maintain the clearwater state. The model developed herein captured the
empirical behavior of shallow lakes, and contained the basic model of the
Alternative Stable States Theory. In addition, our model expanded the basic
model by quantifying the relative effects of connections and by extending it.
In our expanded model we ran 4 simulations: harvesting submerged plants,
nutrient reduction, fish removal without nutrient reduction, and
biomanipulation. Only biomanipulation, which included fish removal and nutrient
reduction, had the potential to shift the turbid state into clearwater state.
The structure and relationships in the generic model as well as the outcomes of
the management simulations were supported by actual field studies in shallow
lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to
understand the complex structure of shallow lake ecosystems as a whole and
obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure
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