Casimir Effects for a Conducting Spherical Shell:
Between C60 and the Lamb Shift
Centre for Theoretical Physics
To calculate the total Casimir binding-energy B of a single body (as opposed to couplings between disjoint bodies), one must model at least semi-realistically not just the macroscopic electromagnetic response function of the material, but also certain microscopic correlations inside it. I extend the theory from insulators to conductors in its simplest possible form, using the archetypal example of a very thin spherical shell. For insulators, negative B is now known to follow from reasonable models allowing for the hard cores of interatomic potentials, and entails a negative (inward) pressure P on the shell. For conducting shells, positive B follows from the standard non-retarded hydrodynamic plasma model, if B is taken to denote the total zero-point energy of the plasmons. The corresponding (positive) P requires, in addition to Coulomb forces, also purely mechanical stresses due to the kinetic energy of the fluid. (The correction for the quantized nature of the Maxwell field, namely the Lamb shift, is also positive, but smaller than the leading terms of B by many orders of magnitude.) The physically expected negative B and P must stem from other effects, like the attraction between the ion cores responsible for the cohesion of metals, or the covalent bonds between the carbon atoms of C60.
On the Vacuum Energy of the Color Magnetic Vortex
Institute for Theoretical Physics
We calculate the vacuum energy in the background of a color magnetic vortex for SU(2) and SU(3). We use zeta functional regularization to obtain analytic expressions suitable for numerical treatment. The momentum integration is turned to the imaginary axis and fast converging sums/integrals are obtained. We investigate numerically a number of profiles of the background in order to find out which configuration minimizes the total energy of the system. In this problem bound states (tachyonic modes) turn out to be present for all investigated profiles making them intrinsically unstable.
Casimir Effect in Dielectrics: On the Low-Frequency Contributions
Motion Induced Radiation
Istituto Nazionale di Fisica Nucleare
We present an undergoing feasibility study for looking at the dynamical Casimir effect to a non uniform accelleration of a moving boundary. Such condition is the basis for platons production from vacuum field. Aims of our proposal is to check the possibility to detect such photons created from the moving boundary conditions. A possible experimental approach mainly bases on the fast minor switching using direct band-gap semiconductors, will be presented in connection with some possible practical configurations.
Thermodynamic Issues Related to Casimir Forces from a Classical Physics Perspective
Daniel C. Cole
Using our present knowledge of Casimir forces, it is interesting to return to early thermodynamic blackbody radiation analyses and examine how they would be modified if these ideas were taken into account. The first part of this talk dwells on the conventional analysis entering into the Wien displacement law, as often still reported in conventional textbooks in thermodynamics, statistical mechanics, and quantum mechanics. A number of subtle, but critical, assumptions are conventionally made that are clearly invalid when one takes into account the presence of Casimir-type forces. If these assumptions are not imposed, but the analysis is carried out in more generality by properly accounting for the change in the normal modes of the radiation as cavity changes are made, then a generalized Wien displacement law can be derived that holds with Casimir forces being present. In addition, however, a far more surprising result is also obtained, namely, a derivation falls out for the appropriate spectrum of classical electromagnetic zero-point radiation, in order for this analysis to hold at temperature T=0.
Dynamical Casimir Effect in 3D
Diego A. R. Dalvit
We compute the photon creation inside a perfectly conducting, three dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and (generalized) Neumann type, we analyze as a preliminary step the dynamical Casimir effect for a scalar field satisfying generalized Neumann boundary conditions. We show that particle production is enhanced with respect to the case of Dirichlet boundary conditions. Then we consider the transverse electric and transverse magnetic polarizations of the electromagnetic field. For resonant frequencies, the total number of photons grows exponentially in time for both polarizations, the rate being greater for transverse magnetic modes.
Calculations of the Casimir Effect in Cosmology
As is well known ---and most clearly explained in a recent
paper by Björken--- a non-zero cosmological constant in
Einstein's (or FRW) equations can be traded for the presence
of a vacuum
Work done in collaboration with Shin'ichi Nojiri (Kyoto), Sergei D. Odintsov (Tomsk), Sachiko Ogushi (Kyoto), and Alex Tort (Rio de Janeiro).
Isotopic Dependence of the Casimir Force: Theory and Experiment
We calculate the dependence of the Casimir force on the isotopic composition of the interacting objects. This dependence arises from a subtle influence of the nuclear masses on the electronic properties of the bodies. We discuss the relevance of these results to current experiments utilizing the isoelectronic effect to search at very short separations for new weak forces suggested by various unification theories. Preliminary results from an ongoing experiment will be presented.
Focusing Vacuum Fluctuations
L.H. Ford and N.F. Svaiter
The quantization of the electromagnetic field in the presence of a parabolic mirror is discussed in the context of a geometric optics approximation. We calculate the mean squared electric field near the focal line of a parabolic cylindrical mirror. This quantity is found to grow as an inverse power of the distance from the focus. We give a combination of analytic and numerical results for the mean squared field. In particular, we find that the mean squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean squared electric field corresponds to a repulsive Van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.
Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
Casimir Energies in Light of Quantum Field Theory
Traditional Casimir calculations are done by imposing perfect boundary conditions on surfaces. Of course, no real material creates a boundary condition at arbitrarily high energies; there is always an effective cutoff above which the material appears transparent. Although this idealization is justified in many useful problems, such the Casimir force between rigid bodies, there are situations where it can be hazardous, such as Casimir stress problems or general relativity applications. We present an efficient calculational program in which we study the Casimir energy of a background potential that approximates a Dirichlet boundary condition. We conclude that the stress on the Dirichlet sphere depends on the details of the material that implements the cutoff, and thus is infinite in the limit of an ideal boundary. This approach might also shed new light on the classic Boyer results for a conducting sphere.
Survey of Repulsive Casimir Forces
Velvel S. Hushwater
455 Grant Ave., #7
This talk will concentrate on the enigma of the repulsive Casimir effect. I survey old and recent different methods for computing repulsive Casimir forces. First I consider the repulsive force between atoms and then the force between macroscopic systems. I also discuss a few heuristic ideas for explaining such an effect.
Influence of the Optical Properties of Materials in the Casimir-Lifshitz Force
D. Iannuzzi, H. B. Chan, R. N. Kleiman, F. Capasso*
The Casimir force in MicroElectroMechanical System (MEMS) is significantly influenced by the optical properties of the materials used in their construction. To emphasize this aspect, we will present two examples. First we will describe an experimental attempt to decrease the Casimir force between a sphere and a micro-torsional device by tuning in situ the reflection coefficient of the film evaporated on the sphere. In the second example we will review a recent theoretical paper (O. Kenneth et al., Phys. Rev. Lett. 89, 033001 (2002)) and discuss its implications on MEMS.
Path Integral Formulation for Deformed Boundaries
Path integral methods are used to calculate the (normal and
transverse) Casimir forces between two deformed metallic plates,
as well as dynamic consequences of their motion. Variation of
Fermion Vacuum Energy Effects on the Higgs Sector of the Electroweak Theory
PROBLEMS WITH THE THERMAL CASIMIR FORCE BETWEEN REAL METALS
Galina L. Klimchitskaya
Physics Department, Federal University of
The energy of fluctuation electromagnetic field is investigated for the thermal Casimir force acting between parallel plates made of real metal. It is proved that for nondissipative media with temperature independent dielectric permittivity the energy at nonzero temperature comprises of the (renormalized) energies of the zero-point and thermal photons. If the dielectric permittivity depends on temperature the energy contains additional terms proportional to the derivatives of the dielectric permittivity with respect to temperature, and the quasiparticle interpretation fails. Previous computations of the Casimir energy in the framework of the Lifshitz formula at zero temperature and optical tabulated data supplemented by the Drude model at room temperature are analysed. It is demonstrated that this quantity does not serve as a good approximation neither to free energy nor to energy. The physical interpretation of this hybrid quantity is suggested. The contradictory results in the recent literature on whether or not the zero-frequency term of the Lifshitz formula for the perpendicular polarized modes contribute to physical quantities are discussed. Four main approaches to the resolution of this problem are specified. The precise expressions for entropy of the fluctuation field between plates made of real metal are obtained and this helps to decide between different approaches. The conclusion is that the Lifshitz formula supplemented by the plasma model and the surface impedance approach are best suited to describe the thermal Casimir force between real metals.
Measurements of Long-Range Atom-Surface Forces
G. P. Lafyatis
Casimir Forces in Cavities with a Finite Plasma Frequency
We extend previous calculations of the Casimir forces in perfectly conducting rectangular cavities in order to consider finite conductivity by including an exponential cutoff in the frequency. We study the renormalized stress energy tensor of the system as an explicit function of the cutoff frequency and the cavity geometry. As in the case of perfectly conducting cavities, we predict changes in the sign and magnitude of the force as the geometry of the cavity is modified. In particular, repulsive forces are predicted, even for cavities with a finite plasma frequency, but the transition from attractive to repulsive forces occurs for deeper cavities, making experiments more difficult.
Calculating Casimir Energies in Renormalizable Quantum Field Theory
Kimball A. Milton
Quantum vacuum energy has been known
to have observable consequences since 1948 when Casimir calculated
the force of attraction between parallel uncharged plates, a
phenomenon confirmed experimentally with ever increasing precision.
Casimir himself suggested that a similar attractive self-stress
existed for a conducting spherical shell, but Boyer obtained
a repulsive stress. Other geometries and higher dimensions have
been considered over the years. Local effects, and divergences
associated with surfaces and edges have been considered by several
authors. Quite recently, Graham et al. have re-examined such
calculations, using conventional techniques of perturbative quantum
field theory to remove divergences, and have suggested that previous
self-stress results may be suspect. Here we show that the examples
considered in their work are misleading; in particular, it is
Casimir Force Experiments Using the Atomic Force Microscope
Constraints on Predictions of Fundamental Physics from the Recent Casimir Corce Measurements
Departamento de Fisica, Universidade Federal
We consider Yukawa- and power-type interactions inspired by extra dimensional physics with low-energy compactification scale and by the exchange of light and massless elementary particles, such as dilaton, axion, arion, graviphoton, moduli etc, between the atoms of two closely spaced macrobodies. It is argued that within the submillimeter interaction range, where the Casimir force is the dominant background force, the gravitational experiments of the Eotvos- and Cavendish-type do not lead to strong constraints on the parameters of hypothetical interactions predicted by fundamental elementary particle physics. The constraints obtained from the recent Casimir force measurements by means of a torsion pendulum and an atomic force microscope are collected and compared. New constraints are obtained from the first observation of the lateral Casimir force. We show that the experiments with the Casimir force have already given the possibility to strengthen the previously known constraints up to several thousand times within a wide interaction range. Further strengthening is expected in near future. The conclusion is made that the Casimir force measurements have an advantage over the conventional accelerator and gravitational experiments as a search for hypothetical interactions within the submillimeter interaction range.
Casimir -Lifschitz: LESSONS from CHEMISTRY
Barry W. Ninham
1. The QED Derivation of Dzyaloshinski, Lifschitz, Pitaevski
is exactly equivalent to semiclassical theory. In the presence
of an intervening plasma the temperature dependent contribution
is exactly equivalent to the linearised version of Onsager Samaris
theory for the change of interfacial tension with dissolved salt.
A consequence is that the DLVO and Debye Huckel type theories
of molecular interactions are deeply flawed-- They violate the
gauge condition on the electromagnetic field and the Gibbs adsorption
isotherms. Electrostatic double layer forces and dispersion forces
can not be separated and have to taken together the same level.
When the theory is remedied a slew of conceptual locks that inhibited
the application of physical chemistry to biology are removed.
2. The text book retarded Casimir Polder interaction between atoms is correct only at zero temperature. At any finite temperature a different form obtains. This has consequences for interpretation of retardation which is not due to the finite velocity of light , but due to the quantisation of light.
3. A fortiori is this so for the retarded resonance ground state excited state interaction which is incorrect even at zero temperature. The correct form will be given. This probably implications for catalysis and insect pheremone recognition. As for 1 above the same comment holds for the classical Forster interaction in biophysics where the separation of electron transfer from photon transfer is routine.
4. Nuclear Forces from Casimir: The Casimir plate problem with an intervening plasma at high T or large distance is discussed. It has a Yukawa like form. The pi meson mass, lifetime, range and strength of nuclear forces seem to emerge naturally from Casimir as excitations in a virtual electron positron pair sea whose density can be predicted.
B.W. Ninham, V.A. Parsegian , Van der Waals
forces: special characteristics in lipid-water systems and a
V.A. Parsegian, B.W. Ninham, Temperature-dependent van der Waals forces, Biophysical Journal 10, no. 7 (1970) 664-674.
B.W. Ninham, V.A. Parsegian, Van der Waals interactions in multilayer systems, Journal of Chemical Physics 53, no. 9 (1970) 3398-3402.
B.W. Ninham, V.A. Parsegian, G.H. Weiss, On the macroscopic theory of temperature-dependent van der Waals forces, Journal of Statistical Physics 2, no. 4 (1970) 323-328.
B.W. Ninham, N.E. Frankel, M.L. Glasser, B.D. Hughes, Möbius, Mellin and Mathematical physics, Physica A 186 (1992) 441-481.
B.W. Ninham, V.V. Yaminsky, Ion binding and ion specificity-The Hofmeister effect, Onsager and Lifschitz theories, Langmuir 13 (1997) 2097-2108
B.W. Ninham, J. Daicic, Lifschitz theory of Casimir forces at finite temperature , Physical Review A 57 (1998) 1870-1880.
H. Wennerstrom, J. Daicic, B.W. Ninham, Temperature dependence of atom-atom interactions, Physical Review A 60 (1999) 2581-2584
Surface Tension of Electrolytes: Specific Ion Effects Explained by Dispersion Forces, M. Boström, D.R.M. Williams and B.W. Ninham, Langmuir (2001) 17, 4475
Physical Chemistry: The Loss of Certainty, B.W. Ninham,Progress in Colloid and Polymer Science 120 (2002) 1-12
Atom-atom interactions at and between metal surfaces at non-zero temperature, M. Boström, J. Longdell and B.W. Ninham, Phys Rev A 64 D622702 (2001)
Resonance Interaction between Atoms in an Excited State, M.Bostrom, J.J. Longdell D.J.Mitchell and B.W.Ninham,European Journal of Physics D, in press.
Specific Ion Effects in Colloid Interactions: Why DLVO Theory fails for Biology, M.Bostrom, D.R.M Williams and B.W.Ninham, Phys.Rev.Letts. (2001) 87, 168103
Ion Specificity of Micelles and Microemulsions Explained by Ionic Dispersion Forces , M.Bostrom D.R.Williams B.W.Ninham , Langmuir 2002, 18, 6010-6014;
Resonance Interaction in Channels, M Bostrom J Longdell B. W .Ninham, Europhys Letters 2002, 59, 21
Influence of Hofmeister effects on surface pH and binding of peptides to membranes, M Bostrom , D.R Williams B.W.Ninham Langmuir vol 018 issue 22 in press.
Why Colloid Science failed to contribute to biology, M Bostrom , D.R Williams B.W.Ninham, Progress in Colloid and Polymers Science Special ECIS 2001 Edition
Influence of ionic dispersion potentials on counterion condensation on polyelectrolytes, M. Bostrom, D.R. Williams and B.W Ninham ,J. Phys. Chem. B 2002, 106, 7908-7912.
Hofmeister Effects and the Role of Coions in pH Measurements, M. Bostrom, V.J. S. Craig, R. Albion, D.R.M .Williams and B.W.Ninham, J Phys Chem submitted
A Mechanism of Insect Pheromone Action via Photon Transfer, Barry W. Ninham*, M. Boström, J. J. Longdell, A. Carnerup and Z. Blum, Chem Evolution, submitted
Specific Ion Effects: why the properties of Lysozyme in Salt Solutions follows a Hofmeister Series, M Bostrom, D.R.W. Williams, B.W. Ninham, Biophys J. submitted.
The role of Coions in Biology;The Influence of Salts on Conformational Equilibria in Rhodopsin, M Bostrom, D.R W. Williams, B.W. Ninham European Journal of Physics D. Submitted
Specific Ion Effects: the Role of Salt & Buffer on Protonation of Cytochrome C., M Bostrom, D.R.W. Williams, B.W. Ninham J Mol. Biology submitted
Screened Casimir Forces at Finite Temperature: A possible role for Nuclear Interactions, B W Ninham and M Bostrom Phys Rev A Rapid communications submitted
New Variants and Other Results for the Casimir Effect
We discuss a new variant of the Casimir effect involving unisotropic and misaligned conductivities in the two parallel plates.
The effect is exactly computed using path integral techniques and we discuss the feasibility of its experimental measurement.
We argue that the Casimir energy of two separate conducting bodies is always negative and that the repulsive Casimir effect computed for specific geometries ( As opposed to that due to electric.magnetic polarizabilities) cannot be directly measured.
Most materials are not ideal conductors; interfaces are not step functions. The Lifshitz formulation liberated Casimir theory from its ideal-conductor assumption. This talk will consider interfaces with spatially graded dielectric response in the direction perpendicular to the parallel faces of interacting planar bodies. We have recently followed earlier work with Jim Kiefer & George Weiss to extend the Lifshitz result for any spatial variation of dielectric response normal to the faces of interacting half-spaces. Working in a macroscopic-continuum limit, we are able to include the consequences of retardation and finite temperature. Noisome contact divergences in the interaction free energy can be made to disappear. New facility emerges to formulate interactions involving spatially inhomogeneous systems.
Measurement of the Casimir force between parallel metallic surfaces
The study of macroscopic effects of quantum vacuum fluctuations is important to understand their role in macroscopic physics, gravitation and cosmology in particular. An attractive quantum pressure between two parallel and infinite planes made of conducting materials has been predicted by Casimir based on the sum of all the zero-point electromagnetic fluctuations.
We have measured the Casimir force between conducting surfaces in a parallel configuration. The force is exerted between a silicon cantilever coated with chromium and a similar rigid surface and is detected by looking at the shifts induced in the cantilever frequency when the latter is approached. The scaling of the force with the distance between the two surfaces was tested in the 0.5-3.0 µm range, and the related force coefficient was determined at the 15% precision level. Studies of a possible upgrade of the apparatus for a measurement of the finite temperature corrections to the force are also underway.
Van der Waals and Casimir Forces: Effects of Finite Temperature and Dissipation
Bo E. Sernelius
I will discuss the zero-temperature dispersion-forces in terms of changes in the zero-point energy of the electromagnetic normal-modes of the system. The van der Waals and Casimir forces are due to different types of mode. In the simplest cases the result can be found from summing the changes of each mode. In the more complex situations one may use a generalization of the Argument Principle, a well-known theorem from complex analysis, and end up with integrations or summations along the complex-frequency axis.
I will address the dispersion forces between metal plates and discuss effects from finite temperature and dissipation. Results for "perfect" metals, from simple Drude approximation, from full Drude approximation and from using the experimental dielectric function will be presented.
I will also briefly discuss the analytical properties of the dissipation correction in the dielectric function, the dynamic relaxation time.
At the end I will raise some questions or discussion topics:
The first is about thermal equilibrium. Our system consist of two parts: the interior of the metal plates and the surrounding vacuum. The interior is kept at 300 K. The vacuum in the outer space is kept at 3 K. Can we assume that the vacuum between and near the plates is at equilibrium at 300 K?
Why do the TM-modes but not the TE-modes contribute to the dominating term at high temperatures and/or large separations?
Are the boundary conditions used by us and by others O.K.?
Quantum Reflection of a Neutral Atom from Solid Surface
Quantum reflection is reflection of a matter wave that occurs when the wave encounters a steep potential slope. This reflection is equivalent to the reflection of a light wave at a boundary of refractive index, and the reflectivity is same regardless of the propagation direction of the matter wave. We report in this talk the first quantitative measurement of quantum reflection of an atomic wave by attractive potential near the solid surface. By changing the normal incident velocity from a few mm/s to several tens cm/s the reflectivity varies from several 10^-1 to less than 10^-3. Simultaneously, the distance from the surface to the reflecting plane varies form micron meters to several tens nm, where the dominant interaction is van der Waals and Casimir potentials. We will also discuss a method to increase reflection and its technical applications.
Higher-Order Poles in Electron-Hydrogen Scattering:
Who Ordered That?
Casimir Forces in Non-Homogeneous Planar and Spherical Systems
C. Villarreal, R. Esquivel-Sirvent, L. Mochan, and C. Noguez
Institute de Fisica
With the advent of new nanotechonologies and experimental techniques exact measurements of the Casimir forces are now feasible. Within that context, we calculate three-dimensional Casimir forces for non-homogeneous materials. In the case of heterogeneous slabs, we compare with experimental results obtained using atomic force microscopes. In addition, we determine the Casimir force between a spherical dielectric particle and a planar substrate in the non-retarded approximation by including multipolar couplings between the particle and the substrate. Our results generalize the dipolar approximation of Casimir and Polder. We discuss the applicability of the proximity force theorem.