Casimir Forces: Recent Developments in Experiment and Theory


































Casimir Effects for a Conducting Spherical Shell:

Between C60 and the Lamb Shift

G. Barton

Centre for Theoretical Physics
University of Sussex,
Brighton BN1 9QH, UK

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

M. Bordag

Institute for Theoretical Physics
University of Leipzig
Augustusplatz 10
04109 Leipzig, Germany

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

I. Brevik

Division of Applied Mechanics

Norwegian University of Science and Technology

N-7491 Trondheim, Norway

How to calculate the lowest-frequency contribution to the Casimir force between metallic surfaces is a delicate point. The problem is whether the zero Matsubara frequency (m=0) contributes to the transverse electric (TE) mode or not. By adopting the Drude dispersive model at low frequencies we show, by means of a limiting procedure, that the contribution from the m=0 TE mode has to be zero. Analytical work on the Casimir force is reported, both for spherical and for planar surfaces. Numerical results are given for planar surfaces, choosing gold as an example. Apparent theoretical difficulties coming from negative Casimir entropies in a restricted temperature interval are discussed. The present paper reports work done in collaboration with J. S. Høye, J. B. Aarseth, and K. A. Milton.


Motion Induced Radiation

Giovanni Carugno

Istituto Nazionale di Fisica Nucleare
Via Marzolo,
8- 35131 Padova, Italy


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

Dept. of Manufacturing Engineering

15 St. Mary's Street

Boston University

Brookline, MA 02446

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.

This talk then reviews related work where this similar analysis has been applied to other systems, including N harmonic electric dipole oscillators, and cavities of arbitrary shape that are composed of perfectly conducting walls, all bathed in blackbody radiation. There are both practical as well as purely theoretical possible consequences of this work, as will be discussed here.

Dynamical Casimir Effect in 3D

Diego A. R. Dalvit

Theoretical Division
Los Alamos National Laboratory
PO Box B210 Los Alamos NM 87545

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

Emilio Elizalde

Instituto de Ciencias del Espacio (ICE/CSIC)

Institut d'Estudis Espacials de Catalunya (IEEC/CSIC)

Departament ECM

Facultat de Física

Universitat de Barcelona

Edifici Nexus, Gran Capità, 2-4,

08034 Barcelona, Spain.

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
energy density corresponding to some fundamental field, and may have an influence down to the level of particle physics. It is thus very interesting to calculate the Casimir effect in cosmological models, as is the case of braneworld universes. This will be done for a conformal or massive scalar when the bulk represents five-dimensional AdS or dS space with two or one four-dimensional dS branes, some of which may correspond to our universe. These computations of the Casimir effect in cosmology turn out to be rather non-trivial. They will be carried out using zeta-function regularization, which advantageously yields the different mass and/or temperature expansions for the effective potential. Using these results, some basic issues as the possibility of brane stabilization using the Casimir force only, or getting the observational value of the cosmological constant in the physical brane, can be discussed.

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

Ephraim Fischbach

Physics Department
Purdue University
525 Northwestern Ave
West Lafayette,IN 47907-2036


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

Physics Department
Tufts University
Medford, MA 02155


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

S.A. Fulling

Texas A&M University

Departments of Mathematics and Physics

College Station, TX 77843-3368


Abstract PDF


Casimir Energies in Light of Quantum Field Theory

Noah Graham

Bicentennial Hall
Middlebury College
Middlebury, VT 05753

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
Palo Alto, CA 94306

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*

Bell Laboratories ­ Lucent Technologies

Murray Hill, NJ 07974, USA

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

Mehran Kardar

Physics Department, Room 12-108
77 Massachusetts Ave.
Cambridge, MA 02139

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 the static
normal force with the wavelength of deformation is an example of the non-trivial geometry dependence of the Casimir effect, and its distinction to pairwise additive forces. 


Fermion Vacuum Energy Effects on the Higgs Sector of the Electroweak Theory

Vishesh Khemani

6-106 Center for Theoretical Physics
77 Massachusetts Ave.
Cambridge, MA 0213

We calculate the fermion vacuum energy functional of the Gauge-Higgs configuration space in the Electroweak theory. We compute it exactly using phaseshifts of the Dirac wave-functions. We render it finite by using standard renormalization methods in Quantum Field Theory. We consider the effective energy obtained by adding the fermion vacuum energy to the classical energy of the background fields, for a fixed fermion number. For strong values of the Yukawa coupling, we look for the emergence of a stable, non-topological, fermionic soliton. This would maintain the cancellation of anomalies in the low energy theory and allow the heavy fermion to decouple. We find no such stable configuration. We also study the correction to the sphaleron energy barrier between topologically inequivalent vacua and the possible emergence of new barriers. These effects would modify the rate of fermion number violating processes which is crucial for baryogenesis in the early universe We find that the fermion vacuum energy correction to the sphaleron is positive and large. Moreover, as the Yukawa coupling is increased to make the fermion heavier than the sphaleron, we find the emergence of a barrier which maintains the exponential suppression of the fermion decay, in contrast to the classical picture. This barrier does not persist as the fermion is made even heavier, and in this case we demonstrate the existence of an unsuppressed decay path over the sphaleron.



Galina L. Klimchitskaya

Physics Department, Federal University of Paraiba, C.P.5008,
CEP 58059-970, Joao Pessoa, Pb-Brazil
(on leave from North-West Polytechnical University, St.Petersburg, Russia)

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

Department of Physics
Ohio State University
274 W. 18th Ave.
Columbus, OH 43210

Talk PDF


Casimir Forces in Cavities with a Finite Plasma Frequency

Jordan Maclay

Quantum Fields LLC

Richland Center WI 53581

Carlos Villarreal

Institute de Fisica

Universidad Autonoma de Mexico

Apartado Postal 20-364

Mexico, 01000, D.F.

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

Department of Physics and Astronomy

University of Oklahoma

Norman, OK 73019-0430

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 well-known
that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension $D$ not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for $D\ne1$. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in $D$ dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations.

Casimir Force Experiments Using the Atomic Force Microscope 

Umar Mohideen  

Department of Physics

University of California

Riverside, CA 92521  

After a brief discussion of the history of Casimir force measurements,  our experimental results of  Casimir force measurements using an Atomic Force Microscope will bepresented.  First, the results from our precision measurements of the normal Casimir force will be reviewed. Next our  experiments demonstrating the shape dependence of the Casimir force  using a periodic uniaxial sinusoidal corrugation will be discussed. Finally, our recent experimental results of the demonstration of  the lateral Casimir force will be presented. 


Constraints on Predictions of Fundamental Physics from the Recent Casimir Corce Measurements

V.M. Mostepanenko

Departamento de Fisica, Universidade Federal da Paraiba,
C.P.5008, CEP 58059-970, Joao Pessoa, Pb-Brazil
(on leave from A. Friedmann Laboratory for Theoretical Physics, St.Petersburg, Russia)

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

Department of Chemistry and CSGI,
University of Florence
via della Lastruccia 3, Sesto Fiorentino
50019 Florence, Italy

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.
The same is true for Casimir between metal plates.

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 across triple-layer films, Journal of Chemical Physics 52, no. 9 (1970) 4578-4587.

B.W. Ninham, V.A. Parsegian , Van der Waals forces: special characteristics in lipid-water systems and a general
method of calculation based on the Lifshitz theory , Biophysical Journal 10, no. 7 (1970) 646-663.

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

Shmuel Nussinov

Tel-Aviv University
School of Physics and Astronomy
Kaplun Bldg 404
Ramat Aviv
Tel-Aviv, Israel

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.


Adrian Parsegian


Bethesda, MD 20892 U.S.A.

Rudi Podgornik


Univ. Ljubljana, Slovenia

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

Giuseppe Ruoso

Viale dell'Universitá, 2
35020 Legnaro


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

Department of Physics and Measurement Technology

Linköping University

SE-581 83 Linköping, Sweden

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

Fujio Shimizu

University of Electro-Communications
Institute for Laser Science
Chofu-shi, 182-8585, Tokyo, Japan

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?

J. Sucher

Department of Physics

University of Maryland

College Park, MD 20742

It has long been known but little noted that the amplitude f for the elastic scattering of an electron by a hydrogen atom, as calculated in nonrelativistic quantum mechanics (NRQM) and in Born approximation, has peculiar properties when considered as an analytic function of the energy and momentum transfer. In particular, the exchange part fex of f Born has double and triple poles in the energy. Such singularities are unexpected in the context of particle physics, where only simple poles are encountered. Equally strange is the fact that the direct part fdir of f has a double and a single pole in the momentum transfer. I will show that these singularities are a manifestation of the long-range character of the interaction of the bound electron with the proton core, i.e. the Coulomb binding potential. They are not present in the analogous case of neutron-deuteron scattering.

At first sight it seems that one can easily understand (without carrying out any integrations) the existence and location of the singularities in fex and fdir on the basis of quantum field theory (QFT) and Feynman diagrams: One simply treats the H-atom as an elementary particle coupled trilinearly with a constant ge,p;H to the electron and the proton, or, more generally, as a composite particle with a vertex function GH (pe, pp) which describes the virtual transition H <--> e- + p of the H-atom into an electron and proton. However, there is no free lunch: This approach appears to yield only a simple pole for fex and only a branch point for fdir , as in the analogous case of neutron-deuteron scattering. Further analysis shows that the situation is much more complicated: In order for the NR limit of the QFT approach to agree with NRQM it seems to be necessary that GH is singular when the constituents go on the mass shell: pe2 = me2, pp2 = mp2. I will provide direct evidence that GH indeed has this property. As a consequence, the would-be (e.p;H) coupling constant ge,p;H, defined in direct analogy with the (n.p;d) coupling constant is infinite and the failures of the naïve model are explained. It seems that in this ancient problem there are lessons to be learned for both atomic and particle physics. We have here another manifestation of the sometimes hidden consequences of long-range forces, this time involving a charged and neutral particle.





Casimir Forces in Non-Homogeneous Planar and Spherical Systems

C. Villarreal, R. Esquivel-Sirvent, L. Mochan, and C. Noguez

Institute de Fisica
Universidad Autonoma de Mexico
Apartado Postal 20-364
Mexico, 01000, D.F.

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.