On the Relation Between Casimir Forces and Bulk Correlations

Within a microscopic approach we show that in the case of an ideal quantum gas enclosed in a slit the Casimir force can be simply expressed in terms of the bulk one-particle density matrix. The corresponding formula, which holds both for bosons and fermions, allows to relate the range of the Casimir force to the bulk correlation length. The low-temperature behavior of the Casimir forces is derived.     

Casimir forces, surface fluctuations, and thinning of superfluid film

Recent experiments on the wetting of 4He have shown that the film becomes thinner at the lambda transition and in the superfluid phase. The difference in thickness above and below the transition has been attributed to a Casimir interaction which is a consequence of a broken continuous symmetry in the bulk superfluid. However, the observed thinning of the film is larger than can be accounted by this Casimir force. We show that surface fluctuations give rise to an additional force, similar in form but larger in magnitude, which may explain the observations.     

Creep motion in a granular pile exhibiting steady surface flow

We investigate experimentally granular piles exhibiting steady surface flow. Below the surface flow, it has been believed that a "frozen" bulk region exists, but our results show no such frozen bulk. We report here that even the particles in layers deep in the bulk exhibit very slow flow and that such motion can be detected at an arbitrary depth. The mean velocity of the creep motion decays exponentially with depth, and the characteristic decay length is approximately equal to the particle size and is independent of the flow rate. It is expected that the creep motion we have seen is observable in all sheared granular systems.     

Casimir force on a surface with shallow nanoscale corrugations: geometry and finite conductivity effects

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.     

Three-dimensional Casimir piston for massive scalar fields

We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a⁴ when a→0⁺ and decays exponentially when a→∞. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case.     

Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations

In this work we investigate the influence of the combined effect from random self-affine roughness, finite conductivity, and finite temperature on the pull-in voltage in microswitches influenced by thermal and quantum vacuum fluctuations through the Casimir force and electrostatic forces. It is shown that for separations within the micron or sub-micron range the roughness influence plays a dominant role, while temperature starts to show its influence well above micron separations. Indeed, increasing the temperature leads to higher pull-in voltages since it leads to an increased Casimir force. The temperature influence is more significant for relatively large roughness exponent H ∼ 1, while its influence is significantly lower with increasing lateral roughness correlation length ξ or due to long wavelength surface smoothness.     

Haldane gap in the S = 1 Haldane-Shastry model

We present evidence that the S = 1 Haldane- Shastry model has a gap in the energy spectrum, extending to the case of a model with long-range interactions results previously obtained by Haldane and, numerically, by other authors for the case of short-range interactions. We studied the groundstate and first excited state using a modified Lanczos algorithm and obtained the low temperature behavior diagonalizing exactly small chains. The correlation functions decay exponentially with distance and the low-T susceptibility decays exponentially to zero. The gap is larger than for the Heisenberg model and the correlation functions decay faster indicating a smaller correlation length.     

Static and dynamic profile of the electric field within the bulk of fused silica glass during and after thermal poling

We use the electric-field-induced second-harmonic (EFISH) technique to characterize, for the first time to our knowledge, the profile of the electric field induced within the bulk of fused silica glass samples both during and after thermal-poling treatment. During thermal poling, the initially homogeneous electric field decays exponentially from the anodic to the cathodic surface. After the poling treatment, a permanent electric field is induced within the bulk of the sample. It also decays exponentially from a positive value on the anodic surface to a negative value on the cathodic surface. The exponential decay constant depends on the thickness of the sample, the poling time, and the temperature. The temperature evolution of this constant makes it possible to retrieve the activation energy of the rapidly moving ionic species. This ensemble of observations indicates that modifications to models previously proposed are necessary.     

Critical Casimir effect in three-dimensional Ising systems: measurements on binary wetting films

The critical Casimir force (CF) is observed in thin wetting films of a binary liquid mixture close to the liquid/vapor coexistence. X-ray reflectivity shows thickness (L) enhancement near the bulk consolute point. The extracted Casimir amplitude Delta(+-)=3+/-1 agrees with the theoretical universal value for the antisymmetric 3D Ising films. The onset of CF in the one-phase region occurs at L/xi approximately 5 regardless of whether the bulk correlation length xi is varied with temperature or composition. The shape of the Casimir scaling function depends monotonically on the dimensionality.     

Long-range magnetic interaction due to the Casimir effect

The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the Casimir effect and of the magneto-optical Kerr effect gives rise to a long-range magnetic interaction. The Casimir magnetic force is found to decay as D-1 in the limit of short distances, and as D-5 in the limit of long distances. Explicit expressions for realistic systems are given in the large- and small-distance limits. An experimental test of the Casimir magnetic interaction is proposed.     

The Bulk Correlation Length and the Range of Thermodynamic Casimir Forces at Bose-Einstein Condensation

The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas.     

Influence of surface electronic structure on the Casimir force

Recent nonlocal microscopic theory of Casimir force which expresses the interaction energy between two metallic slabs in terms of surface polariton propagators calculated from diamagnetic and paramagnetic current-current response functions, sensitive to details of the surface electron density profiles and single-particle excitations on the surfaces, is used here to calculate various contributions to the Casimir energies for a silver film described by two different models. Current-current response functions are constructed from energy levels and wave functions obtained in two different models: jellium and Chulkov one-dimensional model potential, and the results are compared with the local plasmon model results. The results show how the details of such surface electronic structure modify Casimir force.     

直流电晕充电下环氧树脂表面电位衰减特性的研究

介质材料表面电荷的积累和衰减行为是制约众多高压直流电力设备研制的关键因素. 薄片状介质试样的表面电荷密度与表面电位近似呈线性关系, 因此常通过表面电位衰减行为研究表面电荷的衰减特性. 基于电晕充电、表面电荷沉积和脱陷、介质体内单极性电荷输运等3个物理过程, 建立表面电位动态响应的物理模型. 通过计算环氧树脂的表面电位衰减行为, 得到栅极电压、相对介电常数和体电导率等对其表面电位衰减特性的影响. 栅极电压越高, 表面电位的衰减速度越快; 环氧树脂材料参数典型值(相对介电常数3.93, 体电导率10^-14 S· m^-1)下, 归一化表面电位的衰减速率随时间变化的曲线可拟合为分段幂函数, 其中, 分段幂函数的特征时间、指数系数与栅极电压分别呈幂函数和线性变化关系. 相对介电常数越大, 表面电位的衰减速度越慢; 环氧树脂相对介电常数典型范围(3–4)内, 表面电位衰减时间常数由1720 s增大到2540 s, 两者呈线性关系. 体电导率越大, 表面电位的衰减速度越快; 环氧树脂体电导率典型范围(10^-15–10^-13 S· m^-1)内, 表面电位衰减时间常数由24760 s 减小到260 s, 两者呈幂函数变化关系.     

Casimir and Surface Tension Forces on a Single Interacting Bose–Einstein Condensate in Canonical Ensemble

The forces on a single Bose–Einstein condensate confined between two parallel plates consist of two components, namely, surface tension force and Casimir force. In canonical ensemble, these forces are quite different from the one in grand canonical ensemble. In small region with distance $$\ell $$ between two parallel plates, using double parabola approximation, we find that surface tension force decreases as $${{\ell }^{{ - 3}}}$$, whereas the Casimir force, in one-loop approximation of the quantum field, is proportional to $${{\ell }^{{ - 13/2}}}$$. The total force is also considered and its veer is found.     

Diffusion with stochastic resetting

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r*. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.     

Correlation decay in quantum chaotic billiards with bulk or surface disorder

We study the decay properties of correlation functions in quantum billiards with surface or bulk disorder. The quantum system is modeled by means of a tight-binding Hamiltonian with diagonal disorder, solved on LxL clusters of the square lattice. The correlation function is calculated by launching the system at t=0 into a wave function of the regular (clean) system and following its time evolution. The results show that the correlation function decays exponentially with a characteristic correlation time (inverse of the Lyapunov exponent lambda). For small enough disorder the Lyapunov exponent is approximately given by the imaginary part of the self-energy induced by disorder. On the other hand, if the scaling of the Lyapunov exponent with L is investigated by keeping constant l/L, where l is the mean free path, the results show that lambda is proportional to 1/L.     

Effects of vacuum fluctuation suppression on atomic decay rates

The use of atomic decay rates as a probe of sub-vacuum phenomena will be studied. Because electromagnetic vacuum fluctuations are essential for radiative decay of excited atomic states, decay rates can serve as a measure of the suppression of vacuum fluctuations in non-classical states, such as squeezed vacua. In such states, the renormalized expectation value of the square of the electric field or the energy density can be periodically negative, representing suppression of vacuum fluctuations. We explore the extent to which atomic decays can be used to measure the mean squared electric field or energy density. We consider a scheme in which atoms in an excited state transit a closed cavity whose lowest mode contains photons in a non-classical state. A crucial feature of our analysis is that we do not employ the rotating wave approximation. The change in the decay probability of the atom in the cavity due to the non-classical state can, under certain circumstances, serve as a measure of the mean squared electric field or energy density in the cavity. We make some estimates of the magnitude of this effect, which indicate that an experimental test might be possible, although very challenging.     

Experimental investigation of the Casimir force beyond the proximity-force approximation

The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to the PFA by measuring the Casimir force and force gradient between a gold-coated plate and five gold-coated spheres with different radii using a microelectromechanical torsion oscillator. For separations z<300 nm, we find that the magnitude of the fractional deviation from the PFA in the force gradient measurement is, at the 95% confidence level, less than 0.4z/R, where R is the radius of the sphere.     

Aperiodic extended surface perturbations in the Ising model

We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power of the distance l from the free surface with an oscillating amplitude where follows some aperiodic sequence with an asymptotic density equal to 1/2 so that the mean amplitude vanishes. The relevance of the perturbation is discussed by combining scaling arguments of Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic perturbations. The relevance-irrelevance criterion involves the decay exponent , the wandering exponent which governs the fluctuation of the sequence and the bulk correlation length exponent . Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the -plane. The results are checked through a numerical finite-size-scaling study. They show that second-order effects must be taken into account in the discussion of the relevance-irrelevance criterion. The scaling behaviours of the first gap and the surface energy are also discussed. Received 1 December 1998