Tse, Wang-Kong; MacDonald, A H
2012-12-07
We investigate the Casimir effect between two-dimensional electron systems driven to the quantum Hall regime by a strong perpendicular magnetic field. In the large-separation (d) limit where retardation effects are essential, we find (i) that the Casimir force is quantized in units of 3ħcα(2)/8π(2)d(4) and (ii) that the force is repulsive for mirrors with the same type of carrier and attractive for mirrors with opposite types of carrier. The sign of the Casimir force is therefore electrically tunable in ambipolar materials such as graphene. The Casimir force is suppressed when one mirror is a charge-neutral graphene system in a filling factor ν=0 quantum Hall state.
NASA Astrophysics Data System (ADS)
Tomaš, M. S.
2005-06-01
We demonstrate that a very recently obtained formula for the force on a slab in a material planar cavity based on the calculation of the vacuum Lorentz force [C. Raabe and D.-G. Welsch, Phys. Rev. A 71, 013814 (2005)] describes a (medium) modified Casimir force and, in addition to it, a medium-assisted force. The latter force also describes the force on the cavity medium. For dilute media, it implies the atom-mirror interaction of the Casimir-Polder type at large and of the Coulomb type at small atom-mirror distances of which the sign is insensitive to the polarizability type (electric or magnetic) of the atom.
Casimir force between hyperbolic metamaterials
NASA Astrophysics Data System (ADS)
Song, Ge; Xu, Jingping; Zhu, Chengjie; He, Pengfei; Yang, Yaping; Zhu, Shi-Yao
2017-02-01
The Casimir force between two hyperbolic metamaterials (HMMs) constructed by alternative metal-dielectric layers is investigated. Due to the existence of the hyperbolic dispersion, the electromagnetic response of HMMs becomes extremely dramatic, which is embodied by the nearly total reflection in such frequency region. As a result, the Casimir force between HMMs is much greater than that between ordinary dielectrics. In addition, it is shown that the Casimir force is proportional to the bandwidth of this hyperbolic dispersion, which is dependent on the filling factor as well as the characteristic frequencies of ingredient materials. Therefore, the relations between the force and these parameters are discussed. We show that the Casimir force can be controlled by tuning the bandwidth possessing hyperbolic dispersion of the structures. This work provides promising applications of HMMs on microelectromechanical systems and nanoelectromechanical systems.
Repulsive Casimir force: Sufficient conditions
Rosa, Luigi; Lambrecht, Astrid
2010-09-15
In this paper the Casimir energy of two parallel plates made by materials of different penetration depth and no medium in between is derived. We study the Casimir force density and derive analytical constraints on the two penetration depths which are sufficient conditions to ensure repulsion. Compared to other methods our approach needs no specific model for dielectric or magnetic material properties and constitutes a complementary analysis.
Casimir force in absorbing multilayers
Tomas, M.S.
2002-11-01
The Casimir effect in a dispersive and absorbing multilayered system is considered adopting the (net) vacuum-field pressure point of view to the Casimir force. Using the properties of the macroscopic field operators appropriate for absorbing systems and a convenient compact form of the Green function for a multilayer, a straightforward and transparent derivation of the Casimir force in a lossless layer of an otherwise absorbing multilayer is presented. The resulting expression, in terms of the reflection coefficients of the surrounding stacks of layers, is of the same form as that obtained by Zhou and Spruch for a purely dispersive multilayer using the (surface) mode summation method [Phys. Rev. A 52, 297 (1995)]. Owing to the recursion relations that the generalized Fresnel coefficients satisfy, this result can be applied to more complex systems with planar symmetry. This is illustrated by calculating the Casimir force on a dielectric (metallic) slab in a planar cavity with realistic mirrors. Also, a relationship between the Casimir force and energy in two different layers is established.
Casimir forces and graphene sheets
Drosdoff, D.; Woods, Lilia M.
2010-10-15
The Casimir force between two infinitely thin parallel sheets in a setting of N such sheets is found. The finite two-dimensional conductivities, which describe the dispersive and absorptive properties of each sheet, are taken into account, whereupon the theory is applied to interacting graphenes. By exploring similarities with in-plane optical spectra for graphite, the conductivity of graphene is modeled as a combination of Lorentz-type oscillators. We find that the graphene transparency and the existence of a universal constant conductivity e{sup 2}/(4({h_bar}/2{pi})) result in the graphene/graphene Casimir interaction at large separations to have the same distance dependence as the one for perfect conductors but with much smaller magnitude. The Casimir force is also studied when the graphene system is above a substrate or immersed in a medium. It is found that the response properties of the environmental materials can strongly affect the graphene interaction.
Nonadditivity of critical Casimir forces
Paladugu, Sathyanarayana; Callegari, Agnese; Tuna, Yazgan; Barth, Lukas; Dietrich, Siegfried; Gambassi, Andrea; Volpe, Giovanni
2016-01-01
In soft condensed matter physics, effective interactions often emerge due to the spatial confinement of fluctuating fields. For instance, microscopic particles dissolved in a binary liquid mixture are subject to critical Casimir forces whenever their surfaces confine the thermal fluctuations of the order parameter of the solvent close to its critical demixing point. These forces are theoretically predicted to be nonadditive on the scale set by the bulk correlation length of the fluctuations. Here we provide direct experimental evidence of this fact by reporting the measurement of the associated many-body forces. We consider three colloidal particles in optical traps and observe that the critical Casimir force exerted on one of them by the other two differs from the sum of the forces they exert separately. This three-body effect depends sensitively on the distance from the critical point and on the chemical functionalisation of the colloid surfaces. PMID:27097797
Nonadditivity of critical Casimir forces.
Paladugu, Sathyanarayana; Callegari, Agnese; Tuna, Yazgan; Barth, Lukas; Dietrich, Siegfried; Gambassi, Andrea; Volpe, Giovanni
2016-04-21
In soft condensed matter physics, effective interactions often emerge due to the spatial confinement of fluctuating fields. For instance, microscopic particles dissolved in a binary liquid mixture are subject to critical Casimir forces whenever their surfaces confine the thermal fluctuations of the order parameter of the solvent close to its critical demixing point. These forces are theoretically predicted to be nonadditive on the scale set by the bulk correlation length of the fluctuations. Here we provide direct experimental evidence of this fact by reporting the measurement of the associated many-body forces. We consider three colloidal particles in optical traps and observe that the critical Casimir force exerted on one of them by the other two differs from the sum of the forces they exert separately. This three-body effect depends sensitively on the distance from the critical point and on the chemical functionalisation of the colloid surfaces.
Electrostatic patch potentials in Casimir force measurements
NASA Astrophysics Data System (ADS)
Garrett, Joseph; Somers, David; Munday, Jeremy
2015-03-01
Measurements of the Casimir force require the elimination of the electrostatic force between interacting surfaces. The force can be minimized by applying a potential to one of the two surfaces. However, electrostatic patch potentials remain and contribute an additional force which can obscure the Casimir force signal. We will discuss recent measurements of patch potentials made with Heterodyne Amplitude-Modulated Kelvin Probe Force Microscopy that suggest patches could be responsible for >1% of the signal in some Casimir force measurements, and thus make the distinction between different theoretical models of the Casimir force (e.g. a Drude-model or a plasma-model for the dielectric response) difficult to discern.
Archimedes force on Casimir apparatus
NASA Astrophysics Data System (ADS)
Shevchenko, Vladimir; Shevrin, Efim
2016-08-01
This paper addresses a problem of Casimir apparatus in dense medium, put in weak gravitational field. The falling of the apparatus has to be governed by the equivalence principle with proper account for contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general expression for the corresponding force in metric with cylindrical symmetry. By way of example, we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.
Archimedes force on Casimir apparatus
NASA Astrophysics Data System (ADS)
Shevchenko, V.; Shevrin, E.
2016-11-01
The talk addresses a problem of Casimir apparatus in weak gravitational field, surrounded by a dense medium. The falling of the apparatus has to be governed by the equivalence principle, taking into account proper contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general ex pression for the corresponding force in terms of the effective action. By way of example we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.
NASA Astrophysics Data System (ADS)
Herdegen, A.
2001-01-01
Two thin conducting, electrically neutral, parallel plates forming an isolated system in vacuum exert attracting force on each other, whose origin is the quantum electrodynamical interaction. This theoretical hypothesis, known as Casimir effect, has been also confirmed experimentally. Despite long history of the subject, no completely convincing theoretical analysis of this effect appears in the literature. Here we discuss the effect (for the scalar field) anew, on a revised physical and mathematical basis. Standard, but advanced methods of relativistic quantum theory are used. No anomalous features of the conventional approaches appear. The Casimir quantitative prediction for the force is shown to constitute the leading asymptotic term, for large separation of the plates, of the full, model-dependent expression.
Halving the Casimir force with conductive oxides.
de Man, S; Heeck, K; Wijngaarden, R J; Iannuzzi, D
2009-07-24
The possibility to modify the strength of the Casimir effect by tailoring the dielectric functions of the interacting surfaces is regarded as a unique opportunity in the development of micro- and nanoelectromechanical systems. In air, however, one expects that, unless noble metals are used, the electrostatic force arising from trapped charges overcomes the Casimir attraction, leaving no room for exploitation of Casimir force engineering at ambient conditions. Here we show that, in the presence of a conductive oxide, the Casimir force can be the dominant interaction even in air, and that the use of conductive oxides allows one to reduce the Casimir force up to a factor of 2 when compared to noble metals.
Casimir Forces On A Silicon Micromechanical Chip
Zou, J.; Marset, zsolt; Rodriguez, A.W.; Reid, M. T.H.; McCauley, A. P.; Kravchenko, Ivan I; Bao, Y.; Johnson, S. G.; Chan, Ho Bun
2013-01-01
Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro- and nano-mechanical devices. Nevertheless, so far the Casimir force has been experimentally observed only in situations involving an external object manually positioned close to a micromechanical element on a silicon chip. Here, we demonstrate the Casimir effect between two silicon components on the same substrate. In addition to providing an integrated and compact platform for Casimir force measurements, this scheme also opens the possibility of tailoring the Casimir force using lithographically defined components of non-conventional shapes on a single micromechanical chip.
Halving the Casimir force with Conductive Oxides
NASA Astrophysics Data System (ADS)
de Man, S.; Heeck, K.; Wijngaarden, R. J.; Iannuzzi, D.
2009-07-01
The possibility to modify the strength of the Casimir effect by tailoring the dielectric functions of the interacting surfaces is regarded as a unique opportunity in the development of micro- and nanoelectromechanical systems. In air, however, one expects that, unless noble metals are used, the electrostatic force arising from trapped charges overcomes the Casimir attraction, leaving no room for exploitation of Casimir force engineering at ambient conditions. Here we show that, in the presence of a conductive oxide, the Casimir force can be the dominant interaction even in air, and that the use of conductive oxides allows one to reduce the Casimir force up to a factor of 2 when compared to noble metals.
Resource Letter CF-1: Casimir Force
Lamoreaux, S.K.
1999-10-01
This resource letter provides an introductory guide to the literature on the Casimir force. Journal articles and books are cited for the following topics: introductory articles and books, calculations, dynamical Casimir effect, mechanical analogs, applications, and experiments. {copyright} {ital 1999 American Association of Physics Teachers.}
Casimir force between integrable and chaotic pistons
Alvarez, Ezequiel; Mazzitelli, Francisco D.; Wisniacki, Diego A.; Monastra, Alejandro G.
2010-11-15
We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, could be qualitatively different for classically integrable or chaotic systems. We have performed a detailed numerical analysis of the corresponding Casimir force for pistons with regular and chaotic classical dynamics. For a family of stadium billiards, we have found that the correcting part of the Casimir force presents a sudden change in the transition from regular to chaotic geometries. This suggests that there could be signatures of quantum chaos in the Casimir effect.
Diamagnetic effect on the Casimir force
Inui, Norio
2011-03-15
The Casimir force between a diamagnetic plate and a magnetodielectric plate at finite temperature is considered. Under the condition that the permittivity of the magnetodielectric plate is sufficiently small, we show that the diamagnetic property dominantly determines the asymptotic behavior of the repulsive Casimir force for large separations. On the basis of this simple property, we present numerical results showing that if an effective permeability of a superconductor is much less than one, its diamagnetic response can be indirectly detected by measuring the Casimir force.
Casimir forces of metallic microstructures into cavities
NASA Astrophysics Data System (ADS)
Kenanakis, George; Soukoulis, Costas M.; Economou, Eleftherios N.
2015-08-01
A theoretical estimate of the Casimir force of a metallic structure embedded into a cubic cavity is proposed. We demonstrate that by calculating the eigenmodes of the system we can determine the Casimir force, which can be either attractive or repulsive, by simply changing the geometry of the structures relative to the walls of the cavity. In this analysis, several cases of structures are taken into account, from rectangular slabs to chiral "omega" particles, and the predicted data are consistent with recent literature. We demonstrate that the sidewalls of the studied cavity contribute decisively to the repulsive Casimir force between the system and the nearby top surface of the cavity. Finally, we provide evidence that the medium embedded into the studied cavity (and especially its permittivity) can change the intensity of the Casimir force, while its repulsive nature, once established (owing to favorable geometrical features), remains quite robust.
Stability of suspended graphene under Casimir force
NASA Astrophysics Data System (ADS)
Chudnovsky, E. M.; Zarzuela, R.
2016-08-01
We consider a graphene sheet suspended above a conducting surface. Treating graphene as an elastic membrane subjected to Casimir force, we study its stability against sagging towards the conductor. There exists a critical elevation at the edges below which the central part of the suspended graphene nucleates a trunk that sinks under the action of the Casimir force. The dependence of the critical elevation on temperature, dimensions, and the elastic stress applied to the graphene sheet is computed.
Detecting chameleons through Casimir force measurements
Brax, Philippe; Davis, Anne-Christine; Shaw, Douglas; Mota, David F.
2007-12-15
The best laboratory constraints on strongly coupled chameleon fields come not from tests of gravity per se but from precision measurements of the Casimir force. The chameleonic force between two nearby bodies is more akin to a Casimir-like force than a gravitational one: The chameleon force behaves as an inverse power of the distance of separation between the surfaces of two bodies, just as the Casimir force does. Additionally, experimental tests of gravity often employ a thin metallic sheet to shield electrostatic forces; however, this sheet masks any detectable signal due to the presence of a strongly coupled chameleon field. As a result of this shielding, experiments that are designed to specifically test the behavior of gravity are often unable to place any constraint on chameleon fields with a strong coupling to matter. Casimir force measurements do not employ a physical electrostatic shield and as such are able to put tighter constraints on the properties of chameleons fields with a strong matter coupling than tests of gravity. Motivated by this, we perform a full investigation on the possibility of testing chameleon models with both present and future Casimir experiments. We find that present-day measurements are not able to detect the chameleon. However, future experiments have a strong possibility of detecting or rule out a whole class of chameleon models.
Casimir forces on a silicon micromechanical chip.
Zou, J; Marcet, Z; Rodriguez, A W; Reid, M T H; McCauley, A P; Kravchenko, I I; Lu, T; Bao, Y; Johnson, S G; Chan, H B
2013-01-01
Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro- and nano-mechanical devices. Nevertheless, utilization of Casimir forces on the chip level remains a major challenge because all experiments so far require an external object to be manually positioned close to the mechanical element. Here by integrating a force-sensing micromechanical beam and an electrostatic actuator on a single chip, we demonstrate the Casimir effect between two micromachined silicon components on the same substrate. A high degree of parallelism between the two near-planar interacting surfaces can be achieved because they are defined in a single lithographic step. Apart from providing a compact platform for Casimir force measurements, this scheme also opens the possibility of tailoring the Casimir force using lithographically defined components of non-conventional shapes.
Casimir force in noncommutative Randall-Sundrum models revisited
Teo, L. P.
2010-07-15
We propose another method to compute the Casimir force in noncommutative Randall-Sundrum braneworld model considered by K. Nouicer and Y. Sabri, Phys. Rev. D 80, 086013 (2009). recently. Our method can be used to compute the Casimir force to any order in the noncommutative parameter. Contrary to the claim made by K. Nouicer and Y. Sabri that repulsive Casimir force can appear in the first order approximation, we show that the Casimir force is always attractive at any order of approximation.
Casimir forces in the time domain: Theory
Rodriguez, Alejandro W.; McCauley, Alexander P.; Joannopoulos, John D.; Johnson, Steven G.
2009-07-15
We present a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain (FDTD) scheme. The method involves the time evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this paper, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, both considered analytically and illustrated in the simplest parallel-plate geometry.
Direct measurement of critical Casimir forces
NASA Astrophysics Data System (ADS)
Hertlein, C.; Helden, L.; Gambassi, A.; Dietrich, S.; Bechinger, C.
2008-01-01
When fluctuating fields are confined between two surfaces, long-range forces arise. A famous example is the quantum-electrodynamical Casimir force that results from zero-point vacuum fluctuations confined between two conducting metal plates. A thermodynamic analogue is the critical Casimir force: it acts between surfaces immersed in a binary liquid mixture close to its critical point and arises from the confinement of concentration fluctuations within the thin film of fluid separating the surfaces. So far, all experimental evidence for the existence of this effect has been indirect. Here we report the direct measurement of critical Casimir force between a single colloidal sphere and a flat silica surface immersed in a mixture of water and 2,6-lutidine near its critical point. We use total internal reflection microscopy to determine in situ the forces between the sphere and the surface, with femtonewton resolution. Depending on whether the adsorption preferences of the sphere and the surface for water and 2,6-lutidine are identical or opposite, we measure attractive and repulsive forces, respectively, that agree quantitatively with theoretical predictions and exhibit exquisite dependence on the temperature of the system. We expect that these features of critical Casimir forces may result in novel uses of colloids as model systems.
Direct measurement of critical Casimir forces.
Hertlein, C; Helden, L; Gambassi, A; Dietrich, S; Bechinger, C
2008-01-10
When fluctuating fields are confined between two surfaces, long-range forces arise. A famous example is the quantum-electrodynamical Casimir force that results from zero-point vacuum fluctuations confined between two conducting metal plates. A thermodynamic analogue is the critical Casimir force: it acts between surfaces immersed in a binary liquid mixture close to its critical point and arises from the confinement of concentration fluctuations within the thin film of fluid separating the surfaces. So far, all experimental evidence for the existence of this effect has been indirect. Here we report the direct measurement of critical Casimir force between a single colloidal sphere and a flat silica surface immersed in a mixture of water and 2,6-lutidine near its critical point. We use total internal reflection microscopy to determine in situ the forces between the sphere and the surface, with femtonewton resolution. Depending on whether the adsorption preferences of the sphere and the surface for water and 2,6-lutidine are identical or opposite, we measure attractive and repulsive forces, respectively, that agree quantitatively with theoretical predictions and exhibit exquisite dependence on the temperature of the system. We expect that these features of critical Casimir forces may result in novel uses of colloids as model systems.
Critical Casimir forces along the isofields.
Zubaszewska, M; Maciołek, A; Drzewiński, A
2013-11-01
Using quasiexact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h≠0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two disks. We find that varying the temperature along the isofields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.
Critical Casimir forces along the isofields
NASA Astrophysics Data System (ADS)
Zubaszewska, M.; Maciołek, A.; Drzewiński, A.
2013-11-01
Using quasiexact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h≠0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two disks. We find that varying the temperature along the isofields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.
Matter-screened Casimir force and Casimir Polder force in planar structures
NASA Astrophysics Data System (ADS)
Raabe, Christian; Welsch, Dirk-Gunnar
2005-12-01
Using a recently developed theory of the Casimir force (Raabe and Welsch 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened, Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by the surrounding matter.
Critical Casimir forces for colloidal assembly.
Nguyen, V D; Dang, M T; Nguyen, T A; Schall, P
2016-02-03
Critical Casimir forces attract increasing interest due to their opportunities for reversible particle assembly in soft matter and nano science. These forces provide a thermodynamic analogue of the celebrated quantum mechanical Casimir force that arises from the confinement of vacuum fluctuations of the electromagnetic field. In its thermodynamic analogue, solvent fluctuations, confined between suspended particles, give rise to an attractive or repulsive force between the particles. Due to its unique temperature dependence, this effect allows in situ control of reversible assembly. Both the force magnitude and range vary with the solvent correlation length in a universal manner, adjusting with temperature from fractions of the thermal energy, k B T, and nanometre range to several ten kT and micrometer length scale. Combined with recent breakthroughs in the synthesis of complex particles, critical Casimir forces promise the design and assembly of complex colloidal structures, for fundamental studies of equilibrium and out-of-equilibrium phase behaviour. This review highlights recent developments in this evolving field, with special emphasis on the dynamic interaction control to assemble colloidal structures, in and out of equilibrium.
Finite difference computation of Casimir forces
NASA Astrophysics Data System (ADS)
Pinto, Fabrizio
2016-09-01
In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing
Scattering theory approach to electrodynamic Casimir forces
Rahi, Sahand Jamal; Kardar, Mehran; Emig, Thorsten; Graham, Noah; Jaffe, Robert L.
2009-10-15
We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.
Optical detection of the Casimir force between macroscopic objects.
Petrov, Victor; Petrov, Mikhail; Bryksin, Valeriy; Petter, Juergen; Tschudi, Theo
2006-11-01
We report the optical detection of mechanical deformation of a macroscopic object induced by the Casimir force. An adaptive holographic interferometer based on a photorefractive BaTiO3:Co crystal was used to measure periodical nonlinear deformations of a thin pellicle caused by an oscillating Casimir force. A reasonable agreement between the experimental and calculated values of the first and second harmonics of the Casimir force oscillations has been obtained.
Microstructure Effects for Casimir Forces in Chiral Metamaterials
2010-10-06
Microstructure effects for Casimir forces in chiral metamaterials Alexander P. McCauley,1 Rongkuo Zhao,2 M. T. Homer Reid,1 Alejandro W. Rodriguez,1...02139, USA Received 13 September 2010; published 6 October 2010 We examine a recent prediction for the chirality dependence of the Casimir force in...metamaterials might exhibit repulsive Casimir forces in vacuum where planar structures have only attraction.1–3 However, these predictions used
Theory of Casimir Forces without the Proximity-Force Approximation.
Lapas, Luciano C; Pérez-Madrid, Agustín; Rubí, J Miguel
2016-03-18
We analyze both the attractive and repulsive Casimir-Lifshitz forces recently reported in experimental investigations. By using a kinetic approach, we obtain the Casimir forces from the power absorbed by the materials. We consider collective material excitations through a set of relaxation times distributed in frequency according to a log-normal function. A generalized expression for these forces for arbitrary values of temperature is obtained. We compare our results with experimental measurements and conclude that the model goes beyond the proximity-force approximation.
Casimir forces in the time domain: Applications
McCauley, Alexander P.; Rodriguez, Alejandro W.; Joannopoulos, John D.; Johnson, Steven G.
2010-01-15
Our previous article [Phys. Rev. A 80, 012115 (2009)] introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this article, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir pistonlike problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of perfectly matched layer (PML) absorbing boundaries and/or periodic boundaries. In addition, we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.
Three-body critical Casimir forces.
Mattos, T G; Harnau, L; Dietrich, S
2015-04-01
Within mean-field theory we calculate universal scaling functions associated with critical Casimir forces for a system consisting of three parallel cylindrical colloids immersed in a near-critical binary liquid mixture. For several geometrical arrangements and boundary conditions at the surfaces of the colloids we study the force between two colloidal particles in the direction normal to their axes, analyzing the influence of the presence of a third particle on that force. Upon changing temperature or the relative positions of the particles we observe interesting features such as a change of sign of this force caused by the presence of the third particle. We determine the three-body component of the forces acting on one of the colloids by subtracting the pairwise forces from the total force. The three-body contribution to the total critical Casimir force turns out to be more pronounced for small surface-to-surface distances between the colloids as well as for temperatures close to criticality. Moreover, we compare our results with similar ones for other physical systems such as three atoms interacting via van der Waals forces.
Measurement of non-monotonic Casimir forces between silicon nanostructures
NASA Astrophysics Data System (ADS)
Tang, L.; Wang, M.; Ng, C. Y.; Nikolic, M.; Chan, C. T.; Rodriguez, A. W.; Chan, H. B.
2017-01-01
Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field. Apart from controlling this force via the optical properties of materials, a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps. Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators, we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.
Casimir force in the presence of a medium
Kheirandish, Fardin; Soltani, Morteza; Sarabadani, Jalal
2010-05-15
We investigate the Casimir effect in the presence of a medium by quantizing the electromagnetic field in the presence of a magnetodielectric medium using the path-integral technique. For a given medium with definite electric and magnetic susceptibilities, explicit expressions for the Casimir force are obtained. The Lifshitz formula is recovered and in the absence of a medium the results tend to the original Casimir force between two conducting parallel plates immersed in the quantum electromagnetic vacuum.
NASA Astrophysics Data System (ADS)
Chen, Feng
The Casimir effect has recently become important because of its central role in modern physics. Despite its exclusively quantum nature, associated with the zero-point energy of a quantized field, the Casimir force between neutral metallic surfaces is a macroscopic phenomenon. Because the Casimir force increases rapidly with the distance between surfaces and strongly depends on the shape of the boundary, it plays a very important role in micro-electromechanical systems. The precision measurement of the Casimir force has also been advanced as a new powerful test for hypothetical long-range interactions, including corrections to the Newtonian gravitational law at small distances predicted by the unified gauge theories, supersymmetry, supergravity and string theory. This work develops new techniques to measure the Casimir force between a Au coated sphere and plate under different boundary conditions. At the heart of these techniques is the precision force measurement adapted to the Atomic Force Microscope. Calibrations of the necessary parameters have been developed. Here we report an improved precision measurement of the normal Casimir force. The experimental data are compared with a theory that has no adjustable parameters. Combined random and systematic error of order 2.5% of the Casimir force at the closest separation is achieved. We made the first demonstration of the lateral Casimir force between two sinusoidally corrugated surfaces. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems. We also developed a sensitive differential force measurement technique for measuring the temperature correction. A preliminary experiment investigating the temperature correction to the Casimir force is reported. With further improvement, this may be able to
Membrane actuation by Casimir force manipulation
NASA Astrophysics Data System (ADS)
Pinto, Fabrizio
2008-04-01
In our laboratory, we have been developing a practical demonstration of actuation by means of the Casimir force inspired by the capacitive detection approach originally described by Arnold, Hunklinger and Dransfeld (1972 Rev. Sci. Instrum. 43 584-7). In this paper, we first describe the mathematical challenges pertaining to the electrostatic calibration of our measuring device, which has been enhanced by our recently published results regarding the computation of electrostatic fields in axial systems, such as the long-standing classical circular capacitor problem. We also discuss our computational approach to the calculation of the Casimir force in our system, including our adoption of analytical descriptions of the dielectric functions of semiconductors extended to the case of axial geometries. We will illustrate how the original AHD apparatus has been drastically improved upon, for instance by means of modern nanopositioner technology, and we shall discuss our published experimental results on the dynamics of a vibrating membrane with a central disc, which have provided the first direct verification of the mechanical resonances of such a system. The emphasis of our effort is not exclusively directed to fundamental physics research but is focused on, and ultimately motivated by, our goal of identifying viable industrial applications leading to commercially marketable products based on Casimir force actuation. Therefore we conclude this paper by briefly discussing the contribution we believe these results will offer to some current technological problems, in particular in nanotechnology, including some thoughts on the possibility that dispersion forces may enable a new and rapidly expanding industry to develop in the near future.
Normal and lateral Casimir force: Advances and prospects
NASA Astrophysics Data System (ADS)
Klimchitskaya, G. L.
2010-11-01
We discuss recent experimental and theoretical results on the Casimir force between real material bodies made of different materials. Special attention is paid to calculations of the normal Casimir force acting perpendicular to the surface with the help of the Lifshitz theory taking into account the role of free charge carriers. Theoretical results for the thermal Casimir force acting between metallic, dielectric and semiconductor materials are presented and compared with available experimental data. Main attention is concentrated on the possibility to control the magnitude and sign of the Casimir force for applications in nanotechnology. In this respect we consider experiments on the optical modulation of the Casimir force between metal and semiconductor test bodies with laser light. Another option is the use of ferromagnetic materials, specifically, ferromagnetic dielectrics. Under some conditions this allows to get Casimir repulsion. The lateral Casimir force acting between sinusoidally corrugated surfaces can be considered as some kind of noncontact friction caused by zero-point oscillations of the electromagnetic field. Recent experiments and computations using the exact theory have demonstrated the role of diffraction-type effects in this phenomenon and the possibility to get asymmetric force profiles. Conclusion is made that the Casimir force may play important role in the operation of different devices on the nanoscale.
Intermolecular Casimir-Polder forces in water and near surfaces.
Thiyam, Priyadarshini; Persson, Clas; Sernelius, Bo E; Parsons, Drew F; Malthe-Sørenssen, Anders; Boström, Mathias
2014-09-01
The Casimir-Polder force is an important long-range interaction involved in adsorption and desorption of molecules in fluids. We explore Casimir-Polder interactions between methane molecules in water, and between a molecule in water near SiO(2) and hexane surfaces. Inclusion of the finite molecular size in the expression for the Casimir-Polder energy leads to estimates of the dispersion contribution to the binding energies between molecules and between one molecule and a planar surface.
Controlling the Casimir force via the electromagnetic properties of materials
Yang Yaping; Chen Hong; Zeng Ran; Zhu Shiyao; Zubairy, M. Suhail
2010-02-15
The control of the Casimir force between two parallel plates can be achieved through adjusting the frequency-dependent electromagnetic properties of materials of the two plates. We show that, for different plate separations, the main contribution to the Casimir force comes from different frequency regions: For smaller (larger) separation, it comes from the higher (lower) frequency region. When the separation of the plates increases, the Casimir force can vary from attractive to repulsive and/or vice versa, by selecting the two plates with suitable electromagnetic properties. We discuss how a restoring Casimir force, which varies from repulsive to attractive by increasing the separation, can be realized and that the stable equilibrium is formed at zero Casimir force.
Tunable polarity of the Casimir force based on saturated ferrites
Zeng Ran; Yang Yaping
2011-01-15
We study the polarity of the Casimir force between two different parallel slabs separated by vacuum when the saturated ferrite materials under the influence of an external magnetic field are taken into consideration. Between the ordinary dielectric slab and the ferrite slab, repulsive Casimir force may be observed by adjusting the applied magnetic field. For the ferrite material, we consider the frequency dependence of the permeability modified by the external magnetic field to analyze the formation of the repulsive Casimir force. The restoring force, which means the transition of the force polarity from repulsion to attraction with the increasing slab separation, can also be obtained between two different ferrite slabs.
Casimir force at a knife's edge
Graham, Noah; Shpunt, Alexander; Rahi, Sahand Jamal; Kardar, Mehran; Emig, Thorsten; Jaffe, Robert L.
2010-03-15
The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, H and {theta}, and the cylinder's parabolic radius R. As H/R{yields}0, the proximity force approximation becomes exact. The opposite limit of R/H{yields}0 corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.
Thickness dependence of the Casimir force between a magnetodielectric plate and a diamagnetic plate
Inui, Norio
2011-11-15
This paper examines the repulsive Casimir force between a magnetodielectric plate, with static permeability greater than static permittivity, and a diamagnetic plate. As the thickness of the magnetodielectric plate is decreased, the attractive component of the Casimir force decreases more than the repulsive one. This effect makes the net Casimir force repulsive, and a larger repulsive Casimir force is generated compared to the Casimir force between the plates with infinite thickness.
Temperature dependence of the Casimir force
NASA Astrophysics Data System (ADS)
Brevik, Iver; Høye, Johan S.
2014-01-01
The Casimir force—at first, a rather unexpected consequence of quantum electrodynamics—was discovered by Hendrik Casimir in Eindhoven in 1948. It predicts that two uncharged metal plates experience an attractive force because of the zero-point fluctuations of the electromagnetic field. The idea was tested experimentally in the 1950s and 1960s, but the results were not so accurate that one could make a definite conclusion regarding the existence of the effect. Evgeny Lifshitz expanded the theory in 1955 so as to deal with general dielectric media. Much experimental work was later done to test the theory’s predictions, especially with regards to the temperature dependence of the effect. The existence of the effect itself was verified beyond doubt by Sabisky and Anderson in 1973. Another quarter century had to pass before Lamoreaux and collaborators were able to confirm—or at least make plausible—the temperature dependence predicted by Lifshitz formula in combination with reasonable input data for the material’s dispersive properties. The situation is not yet clear-cut, however, there are recent experiments indicating results in disagreement with those of Lamoreaux. In this paper, a brief review is given of the status of this research field.
Critical Casimir forces between planar and crenellated surfaces.
Tröndle, M; Harnau, L; Dietrich, S
2015-06-03
We study critical Casimir forces between planar walls and geometrically structured substrates within mean-field theory. As substrate structures, crenellated surfaces consisting of periodic arrays of rectangular crenels and merlons are considered. Within the widely used proximity force approximation, both the top surfaces of the merlons and the bottom surfaces of the crenels contribute to the critical Casimir force. However, for such systems the full, numerically determined critical Casimir forces deviate significantly from the pairwise addition formalism underlying the proximity force approximation. A first-order correction to the proximity force approximation is presented in terms of a step contribution arising from the critical Casimir interaction between a planar substrate and the right-angled steps of the merlons consisting of their upper and lower edges as well as their sidewalls.
Modal approach to Casimir forces in periodic structures
Davids, P. S.; Intravaia, F.; Rosa, F. S. S.; Dalvit, D. A. R.
2010-12-15
We present a modal approach to calculate finite-temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated by decomposing the electromagnetic field into the natural modes of the structures. The Casimir force gradient from a deeply etched silicon grating is evaluated using the modal approach and compared to experiment for validation. The Casimir force involving a two-dimensional periodic structure is computed and deviations from the proximity force approximation are examined.
Strong Casimir force reduction through metallic surface nanostructuring
Intravaia, Francesco; Koev, Stephan; Jung, Il Woong; Talin, A. Alec; Davids, Paul S.; Decca, Ricardo S.; Aksyuk, Vladimir A.; Dalvit, Diego A. R.; López, Daniel
2013-01-01
The Casimir force between bodies in vacuum can be understood as arising from their interaction with an infinite number of fluctuating electromagnetic quantum vacuum modes, resulting in a complex dependence on the shape and material of the interacting objects. Becoming dominant at small separations, the force has a significant role in nanomechanics and object manipulation at the nanoscale, leading to a considerable interest in identifying structures where the Casimir interaction behaves significantly different from the well-known attractive force between parallel plates. Here we experimentally demonstrate that by nanostructuring one of the interacting metal surfaces at scales below the plasma wavelength, an unexpected regime in the Casimir force can be observed. Replacing a flat surface with a deep metallic lamellar grating with sub-100 nm features strongly suppresses the Casimir force and for large inter-surfaces separations reduces it beyond what would be expected by any existing theoretical prediction. PMID:24071657
Strong Casimir force reduction through metallic surface nanostructuring.
Intravaia, Francesco; Koev, Stephan; Jung, Il Woong; Talin, A Alec; Davids, Paul S; Decca, Ricardo S; Aksyuk, Vladimir A; Dalvit, Diego A R; López, Daniel
2013-01-01
The Casimir force between bodies in vacuum can be understood as arising from their interaction with an infinite number of fluctuating electromagnetic quantum vacuum modes, resulting in a complex dependence on the shape and material of the interacting objects. Becoming dominant at small separations, the force has a significant role in nanomechanics and object manipulation at the nanoscale, leading to a considerable interest in identifying structures where the Casimir interaction behaves significantly different from the well-known attractive force between parallel plates. Here we experimentally demonstrate that by nanostructuring one of the interacting metal surfaces at scales below the plasma wavelength, an unexpected regime in the Casimir force can be observed. Replacing a flat surface with a deep metallic lamellar grating with sub-100 nm features strongly suppresses the Casimir force and for large inter-surfaces separations reduces it beyond what would be expected by any existing theoretical prediction.
Effect of hydrogen-switchable mirrors on the Casimir force
Iannuzzi, Davide; Lisanti, Mariangela; Capasso, Federico
2004-01-01
We present systematic measurements of the Casimir force between a gold-coated plate and a sphere coated with a hydrogen-switchable mirror. Hydrogen-switchable mirrors are shiny metals that can become transparent upon hydrogenation. Despite such a dramatic change of the optical properties of the sphere, we did not observe any significant decrease of the Casimir force after filling the experimental apparatus with hydrogen. This counterintuitive result can be explained by the Lifshitz theory that describes the Casimir attraction between metallic and dielectric materials. PMID:15024111
Collective behaviors of the Casimir force in microelectromechanical systems
Chan, H. B.; Yelton, J.
2013-01-23
Our goal was to explore the strong dependence of the Casimir force on the shape of the interacting bodies. We made significant progress and measured the Casimir force on silicon surface with rectangular corrugation and showed that the results agree with theoretical calculations, provided that the optical properties of silicon are taken into account. Furthermore, we performed measurement of the Casimir force within a single chip for the first time, between a doubly clamped beam and a movable, on-chip electrode at liquid helium temperature. This experiment represents a new way of studying the Casimir effect, a significant advance from the conventional approach of placing an external surface close to a force transducer.
Crossover of critical Casimir forces between different surface universality classes.
Mohry, T F; Maciołek, A; Dietrich, S
2010-06-01
In confined systems near a continuous phase transition the long-ranged fluctuations of the corresponding order parameter are subject to boundary conditions. These constraints result in so-called critical Casimir forces acting as effective forces on the confining surfaces. For systems belonging to the Ising bulk universality class corresponding to a scalar order parameter the critical Casimir force is studied for the film geometry in the crossover regime characterized by different surface fields at the two surfaces. The scaling function of the critical Casimir force is calculated within mean-field theory. Within our approach, the scaling functions of the critical Casimir force and of the order parameter profile for finite surface fields can be mapped by rescaling, except for a narrow crossover regime, onto the corresponding scaling function of the so-called normal fixed point of strong surface fields. In the crossover regime, the critical Casimir force as function of temperature exhibits more than one extremum and for certain ranges of surface field strengths it changes sign twice upon varying temperature. Monte Carlo simulation data obtained for a three-dimensional Ising film show similar trends. The sign of the critical Casimir force can be inferred from the comparison of the order parameter profiles in the film and in the semi-infinite geometry.
Casimir forces at the threshold of the Cherenkov effect
Maslovski, Stanislav I.; Silveirinha, Mario G.
2011-12-15
We study the Casimir-Lifshitz forces in a strongly nonreciprocal system: a waveguide filled with a medium moving at a relativistic velocity. In such a waveguide the waves propagate dominantly along a single direction that coincides with the direction of the velocity. Our theory shows that the Casimir forces acting on a piston in such a quasi-one-way waveguide vanish when the velocity approaches the Cherenkov threshold.
Thermal Casimir versus Casimir-Polder Forces: Equilibrium and Nonequilibrium Forces
Buhmann, Stefan Yoshi; Scheel, Stefan
2008-06-27
We critically discuss whether and under what conditions Lifshitz theory may be used to describe thermal Casimir-Polder forces on atoms or molecules. An exact treatment of the atom-field coupling reveals that for a ground-state atom (molecule), terms associated with virtual-photon absorption lead to a deviation from the traditional Lifshitz result; they are identified as a signature of nonequilibrium dynamics. Even the equilibrium force on a thermalized atom (molecule) may be overestimated when using the ground-state polarizability instead of its thermal counterpart.
Temperature dependence of the Casimir force for bulk lossy media
Yampol'skii, V. A.; Maizelis, Z. A.; Apostolov, S. S.; Savel'ev, Sergey; Nori, Franco
2010-09-15
We discuss the limitations for the applicability of the Lifshitz theory to describe the temperature dependence of the Casimir force between bulk lossy metal slabs of finite sizes. We pay attention to the important fact that Lifshitz's theory is not applicable when the characteristic wavelength of the fluctuating field, responsible for the temperature-dependent terms in the Casimir force, are longer than the size of the sample. As a result, the widely discussed linearly decreasing temperature dependence of the Casimir force can be observed only for dirty and large metal samples at high enough temperatures. Moreover, for the correct description of the Casimir effect at low enough temperatures, a careful consideration of the concrete geometry of the interacting samples is essential.
Tunable Casimir forces by means of the external magnetic field
Wang Jing; Zhang Xiangdong; Pei Shouyong; Liu Dahe
2006-04-15
We have theoretically investigated the tuning of Casimir forces by means of an external magnetic field. We have found that the Casimir force between two homogeneous slabs can be tuned by the external field in two ways. One is to add cap layers to the two dielectric slabs. The other is to insert a new dielectric layer into the cavity made of the two slabs. Since the dielectric constants of the materials used as the cap layers or the inserted layers depend on the external magnetic field, the Casimir force can be modified significantly by the external magnetic field. Our results show that it is possible to control the Casimir interaction in the fabrication of materials by an external field.
Controlling colloidal phase transitions with critical Casimir forces.
Nguyen, Van Duc; Faber, Suzanne; Hu, Zhibing; Wegdam, Gerard H; Schall, Peter
2013-01-01
The critical Casimir force provides a thermodynamic analogue of the quantum mechanical Casimir force that arises from the confinement of electromagnetic field fluctuations. In its thermodynamic analogue, two surfaces immersed in a critical solvent mixture attract each other due to confinement of solvent concentration fluctuations. Here, we demonstrate the active assembly control of colloidal equilibrium phases using critical Casimir forces. We guide colloidal particles into analogues of molecular liquid and solid phases via exquisite control over their interactions. By measuring the critical Casimir pair potential directly from density fluctuations in the colloidal gas, we obtain insight into liquefaction at small scales. We apply the van der Waals model of molecular liquefaction and show that the colloidal gas-liquid condensation is accurately described by the van der Waals theory, even on the scale of a few particles. These results open up new possibilities in the active assembly control of micro and nanostructures.
Fluctuations of the Casimir-like force between two membrane inclusions.
Bitbol, Anne-Florence; Dommersnes, Paul G; Fournier, Jean-Baptiste
2010-05-01
Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance d between the inclusions is decreased from infinity, the variance of the Casimir force decreases as -1/d2. This distance dependence shares a common physical origin with the Casimir force itself.
Switching Colloidal Superstructures by Critical Casimir Forces.
Nguyen, Truc A; Newton, Arthur; Veen, Sandra J; Kraft, Daniela J; Bolhuis, Peter G; Schall, Peter
2017-09-01
Recent breakthroughs in colloidal synthesis promise the bottom-up assembly of superstructures on nano- and micrometer length scales, offering molecular analogues on the colloidal scale. However, a structural control similar to that in supramolecular chemistry remains very challenging. Here, colloidal superstructures are built and controlled using critical Casimir forces on patchy colloidal particles. These solvent-mediated forces offer direct analogues of molecular bonds, allowing patch-to-patch binding with exquisite temperature control of bond strength and stiffness. Particles with two patches are shown to form linear chains undergoing morphological changes with temperature, resembling a polymer collapse under poor-solvent conditions. This reversible temperature switching carries over to particles with higher valency, exhibiting a variety of patch-to-patch bonded structures. Using Monte Carlo simulations, it is shown that the collapse results from the growing interaction range favoring close-packed configurations. These results offer new opportunities for the active control of complex structures at the nano and micrometer scale, paving the way to novel temperature-switchable materials. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Transient Casimir Forces from Quenches in Thermal and Active Matter.
Rohwer, Christian M; Kardar, Mehran; Krüger, Matthias
2017-01-06
We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.
Transient Casimir Forces from Quenches in Thermal and Active Matter
NASA Astrophysics Data System (ADS)
Rohwer, Christian M.; Kardar, Mehran; Krüger, Matthias
2017-01-01
We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.
A design manual for micromachines using Casimir forces: Preliminary considerations
NASA Astrophysics Data System (ADS)
Maclay, G. Jordan
2000-01-01
General properties of the Casimir force are reviewed, with particular attention to the effects of geometry. Using the conservation of energy, the forces in several simple idealized structures are derived, including the lateral forces on partially overlapping parallel plates, the force in a Casimir ``comb'' drive with several interleaved surfaces, and the average force when a plate is inserted into a rectangular cavity. The properties of rectangular cavities with a moveable piston are discussed, and illustrated with numerical computations. An oscillating structure is proposed. .
CasimirSim - A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries
Sedmik, Rene; Tajmar, Martin
2007-01-30
The so-called Casimir effect is one of the most interesting macro-quantum effects. Being negligible on the macro-scale it becomes a governing factor below structure sizes of 1 {mu}m where it accounts for typically 100 kN m-2. The force does not depend on gravity, or electric charge but solely on the materials properties, and geometrical shape. This makes the effect a strong candidate for micro(nano)-mechanical devices M(N)EMS. Despite a long history of research the theory lacks a uniform description valid for arbitrary geometries which retards technical application. We present an advanced state-of-the-art numerical tool overcoming all the usual geometrical restrictions, capable of calculating arbitrary 3D geometries by utilizing the Casimir Polder approximation for the Casimir force.
CasimirSim — A Tool to Compute Casimir Polder Forces for Nontrivial 3D Geometries
NASA Astrophysics Data System (ADS)
Sedmik, René; Tajmar, Martin
2007-01-01
The so-called Casimir effect is one of the most interesting macro-quantum effects. Being negligible on the macro-scale it becomes a governing factor below structure sizes of 1 μm where it accounts for typically 100 kN m-2. The force does not depend on gravity, or electric charge but solely on the materials properties, and geometrical shape. This makes the effect a strong candidate for micro(nano)-mechanical devices M(N)EMS. Despite a long history of research the theory lacks a uniform description valid for arbitrary geometries which retards technical application. We present an advanced state-of-the-art numerical tool overcoming all the usual geometrical restrictions, capable of calculating arbitrary 3D geometries by utilizing the Casimir Polder approximation for the Casimir force.
Dynamics of thermal Casimir-Polder forces on polar molecules
Ellingsen, Simen Aadnoey; Buhmann, Stefan Yoshi; Scheel, Stefan
2009-05-15
We study the influence of thermal Casimir-Polder forces on the near-surface trapping of cold polar molecules, with emphasis on LiH and YbF near a Au surface at room temperature. We show that even for a molecule initially prepared in its electronic and rovibrational ground state, the Casimir-Polder force oscillates with the molecule-wall separation. The nonresonant force and the evanescent part of the resonant force almost exactly cancel at high temperature which results in a saturation of the (attractive) force in this limit. This implies that the Casimir-Polder force on a fully thermalized molecule can differ dramatically from that obtained using a naive perturbative expansion of the Lifshitz formula based on the molecular ground-state polarizability. A dynamical calculation reveals how the spatial oscillations die out on a typical time scale of several seconds as thermalization of the molecule with its environment sets in.
Demonstration of angle-dependent Casimir force between corrugations.
Banishev, A A; Wagner, J; Emig, T; Zandi, R; Mohideen, U
2013-06-21
The normal Casimir force between a sinusoidally corrugated gold coated plate and a sphere was measured at various angles between the corrugations using an atomic force microscope. A strong dependence on the orientation angle of the corrugation is found. The measured forces were found to deviate from the proximity force approximation and are in agreement with the theory based on the gradient expansion including correlation effects of geometry and material properties. We analyze the role of temperature. The obtained results open new opportunities for control of the Casimir effect in micromechanical systems.
Casimir force and in situ surface potential measurements on nanomembranes.
Garcia-Sanchez, Daniel; Fong, King Yan; Bhaskaran, Harish; Lamoreaux, Steve; Tang, Hong X
2012-07-13
We present Casimir force measurements in a sphere-plate configuration that consists of a high quality nanomembrane resonator and a millimeter sized gold coated sphere. The nanomembrane is fabricated from stoichiometric silicon nitride metallized with gold. A Kelvin probe method is used in situ to image the surface potentials to minimize the distance-dependent residual force. Resonance-enhanced frequency-domain measurements of the nanomembrane motion allow for very high resolution measurements of the Casimir force gradient (down to a force gradient sensitivity of 3 μN/m). Using this technique, the Casimir force in the range of 100 nm to 2 μm is accurately measured. Experimental data thus obtained indicate that the device system in the measured range is best described with the Drude model.
The Casimir force between real materials: Experiment and theory
Klimchitskaya, G. L.; Mohideen, U.; Mostepanenko, V. M.
2009-10-15
The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has been achieved in the last few years. It includes a critical assessment of the proposed approaches to the resolution of the puzzles arising in the applications of the Lifshitz theory of the van der Waals and Casimir forces to real materials. All the primary experiments on the measurement of the Casimir force between macroscopic bodies and the Casimir-Polder force between an atom and a wall that have been performed in the last decade are reviewed, including the theory needed for their interpretation. The methodology for the comparison between experiment and theory in the force-distance measurements is presented. The experimental and theoretical results described here provide a deeper understanding of the phenomenon of dispersion forces in real materials and offer guidance for the application of the Lifshitz theory to the interpretation of the measurement results.
Apparatus for measuring the thermal Casimir force at large distances.
Bimonte, Giuseppe
2014-12-12
We describe a Casimir apparatus based on a differential force measurement between a Au-coated sphere and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer, covering both regions. The setup offers two important advantages over existing Casimir setups. On one hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.
Apparatus for Measuring the Thermal Casimir Force at Large Distances
NASA Astrophysics Data System (ADS)
Bimonte, Giuseppe
2014-12-01
We describe a Casimir apparatus based on a differential force measurement between a Au-coated sphere and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer, covering both regions. The setup offers two important advantages over existing Casimir setups. On one hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.
Casimir switch: steering optical transparency with vacuum forces.
Liu, Xi-Fang; Li, Yong; Jing, H
2016-06-03
The Casimir force, originating from vacuum zero-point energy, is one of the most intriguing purely quantum effects. It has attracted renewed interests in current field of nanomechanics, due to the rapid size decrease of on-chip devices. Here we study the optomechanically-induced transparency (OMIT) with a tunable Casimir force. We find that the optical output rate can be significantly altered by the vacuum force, even terminated and then restored, indicating a highly-controlled optical switch. Our result addresses the possibility of designing exotic optical nano-devices by harnessing the power of vacuum.
Nonequilibrium Casimir-like Forces in Liquid Mixtures.
Kirkpatrick, T R; Ortiz de Zárate, J M; Sengers, J V
2015-07-17
In this Letter, we consider a liquid mixture confined between two thermally conducting walls subjected to a stationary temperature gradient. While in a one-component liquid nonequilibrium fluctuation forces appear inside the liquid layer, nonequilibrium fluctuations in a mixture induce a Casimir-like force on the walls. The physical reason is that the temperature gradient induces large concentration fluctuations through the Soret effect. Unlike temperature fluctuations, nonequilibrium concentration fluctuations are also present near a perfectly thermally conducting wall. The magnitude of the fluctuation-induced Casimir force is proportional to the square of the Soret coefficient and is related to the concentration dependence of the heat and volume of mixing.
Casimir switch: steering optical transparency with vacuum forces
Liu, Xi-fang; Li, Yong; Jing, H.
2016-01-01
The Casimir force, originating from vacuum zero-point energy, is one of the most intriguing purely quantum effects. It has attracted renewed interests in current field of nanomechanics, due to the rapid size decrease of on-chip devices. Here we study the optomechanically-induced transparency (OMIT) with a tunable Casimir force. We find that the optical output rate can be significantly altered by the vacuum force, even terminated and then restored, indicating a highly-controlled optical switch. Our result addresses the possibility of designing exotic optical nano-devices by harnessing the power of vacuum. PMID:27256630
Casimir force in noncommutative Randall-Sundrum models
Nouicer, Khireddine; Sabri, Youssef
2009-10-15
In this paper we study the effect of spacetime noncommutativity in the five-dimensional Randall-Sundrum braneworlds on the Casimir force acting on a pair of parallel plates. We show that the presence of a noncommutative scale length affects the nature of the Casimir force for small plate separation. Using accurate experimental bounds for the Casimir force in parallel plate geometry, we find an upper bound for the noncommutative cutoff of the order of 10{sup 3} TeV; we also find that the size of the interbrane distance in the first Randall-Sundrum model is approximately given by kR < or approx. 20.5 and kR < or approx. 18.4 for k=10{sup 19} GeV and k=10{sup 16} GeV, respectively.
Casimir force induced by an imperfect Bose gas.
Napiórkowski, Marek; Piasecki, Jarosław
2011-12-01
We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand-canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region, the force decays exponentially fast when distance D between the walls tends to infinity. When the Bose-Einstein condensation point is approached, the decay length in the exponential law diverges with critical exponent ν(IMP) = 1, which differs from the perfect gas case where ν(P) = 1/2. In the two-phase region, the Casimir force is long range and decays following the power law D(-3), with the same amplitude as in the perfect gas.
Aspect-ratio dependence of thermodynamic Casimir forces.
Hucht, Alfred; Grüneberg, Daniel; Schmidt, Felix M
2011-05-01
We consider the three-dimensional Ising model in a L(⊥)×L(∥)×L(∥) cuboid geometry with a finite aspect ratio ρ=L(⊥)/L(∥) and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature T(c). Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary ρ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for ρ=1 and becomes repulsive in periodic systems for ρ>1.
Casimir forces in multilayer magnetodielectrics with both gain and loss
Amooghorban, Ehsan; Wubs, Martijn; Mortensen, N. Asger; Kheirandish, Fardin
2011-07-15
A path-integral approach to the quantization of the electromagnetic field in a linearly amplifying magnetodielectric medium is presented. Two continua of inverted harmonic oscillators are used to describe the polarizability and magnetizability of the amplifying medium. The causal susceptibilities of the amplifying medium, with negative imaginary parts in finite frequency intervals, are identified and their relationships to microscopic coupling functions are determined. By carefully relating the two-point functions of the field theory to the optical Green functions, we calculate the Casimir energy and Casimir forces for a multilayer magnetodielectric medium with both gain and loss. We point out the essential differences with a purely passive layered medium. For a single layer, we find different bounds on the Casimir force for fully amplifying and for lossy media. The force is attractive in both cases, even if the medium exhibits negative refraction. From our Lagrangian we also derive by canonical quantization the postulates of the phenomenological theory of amplifying magnetodielectrics.
Casimir force in presence of multi layer magnetodielectric slabs
Kheirandish, Fardin; Soltani, Morteza; Sarabadani, Jalal
2011-03-15
Research Highlights: > The Casimir force has been obtained in the presence of some dielectrics. > The approach is based on a Lagrangian. > It can be generalized to include the rough surfaces. > Finite temperature correction can be easily obtained. - Abstract: By using the path-integral formalism, electromagnetic field in the presence of some linear, isotropic magnetodielectric slabs is quantized and related correlation functions are found. In the framework of path-integral techniques, Casimir force between two infinitely large, parallel and ideal conductors, with a different number of magnetodielectric slabs in between, is obtained by calculating the Green's function corresponding to each geometry.
Sign Flip in the Casimir Force for Interacting Fermion Systems.
Flachi, Antonino; Nitta, Muneto; Takada, Satoshi; Yoshii, Ryosuke
2017-07-21
In this work we consider a fermionic chain of finite length ℓ. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate.
Critical Casimir forces in colloidal suspensions on chemically patterned surfaces.
Soyka, Florian; Zvyagolskaya, Olga; Hertlein, Christopher; Helden, Laurent; Bechinger, Clemens
2008-11-14
We investigate the behavior of colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine in the presence of a chemically patterned substrate. Close to the critical point of the mixture, the particles are subjected to critical Casimir interactions with force components normal and parallel to the surface. Because the strength and sign of these interactions can be tuned by variations in the surface properties and the mixtures temperature, critical Casimir forces allow the formation of highly ordered monolayers but also extend the use of colloids as model systems.
Critical Casimir Forces in Colloidal Suspensions on Chemically Patterned Surfaces
NASA Astrophysics Data System (ADS)
Soyka, Florian; Zvyagolskaya, Olga; Hertlein, Christopher; Helden, Laurent; Bechinger, Clemens
2008-11-01
We investigate the behavior of colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine in the presence of a chemically patterned substrate. Close to the critical point of the mixture, the particles are subjected to critical Casimir interactions with force components normal and parallel to the surface. Because the strength and sign of these interactions can be tuned by variations in the surface properties and the mixtures temperature, critical Casimir forces allow the formation of highly ordered monolayers but also extend the use of colloids as model systems.
Casimir force phase transitions in the graphene family
Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; ...
2017-03-15
The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. We found that the expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. Here, we discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. Particularly, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences onmore » characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.« less
Casimir force phase transitions in the graphene family.
Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J M; Dalvit, Diego A R; Woods, Lilia M
2017-03-15
The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.
Electromagnetic energy, absorption, and Casimir forces. II. Inhomogeneous dielectric media
Rosa, F. S. S.; Dalvit, D. A. R.; Milonni, P. W.
2011-11-15
A general, exact formula is derived for the expectation value of the electromagnetic energy density of an inhomogeneous absorbing and dispersive dielectric medium in thermal equilibrium, assuming that the medium is well approximated as a continuum. From this formula we obtain the formal expression for the Casimir force density. Unlike most previous approaches to Casimir effects in which absorption is either ignored or admitted implicitly through the required analytic properties of the permittivity, we include dissipation explicitly via the coupling of each dipole oscillator of the medium to a reservoir of harmonic oscillators. We obtain the energy density and the Casimir force density as a consequence of the van der Waals interactions of the oscillators and also from Poynting's theorem.
Casimir force phase transitions in the graphene family
Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; Woods, Lilia M.
2017-01-01
The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible. PMID:28294111
Casimir force phase transitions in the graphene family
NASA Astrophysics Data System (ADS)
Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; Woods, Lilia M.
2017-03-01
The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.
Controlling and Harnessing Critical Casimir Forces
NASA Astrophysics Data System (ADS)
Gambassi, A.
2010-04-01
This contribution provides a brief overview of recent advances in the theoretical and experimental study of the critical Casimir effect originating from the confinement of the enhanced thermal fluctuations which occur close to a critical point. The resulting effect turns out to be highly tunable, it influences the behavior of soft matter, from wetting films of fluids to colloidal dispersions, and therefore might find applications for the manipulation of matter at the micrometer and sub-micrometer scale.
Three-dimensional Casimir force between absorbing multilayer dielectrics
NASA Astrophysics Data System (ADS)
Raabe, Christian; Knöll, Ludwig; Welsch, Dirk-Gunnar
2003-09-01
Recently the influence of dielectric and geometrical properties on the Casimir force between dispersing and absorbing multilayered plates in the zero-temperature limit has been studied within a one-dimensional (1D) quantization scheme for the electromagnetic field in the presence of causal media [R. Esquivel-Sirvent, C. Villarreal, and G.H. Cocoletzi, Phys. Rev. Lett. 64, 052108 (2001)]. In the present paper a rigorous 3D analysis is given, which shows that for complex heterostructures the 1D theory only roughly reflects the dependence of the Casimir force on the plate separation in general. Further, an extension of the very recently derived formula for the Casimir force at zero temperature [M.S. Tomaš, Phys. Rev. A 66, 052103 (2002)] to finite temperatures is given, and analytical expressions for specific distance laws in the zero-temperature limit are derived. In particular, it is shown that the Casimir force between two single-slab plates behaves asymptotically like d-6 instead of d-4 (d, plate separation).
Casimir force between a microfabricated elliptic cylinder and a plate
Decca, R. S.; Fischbach, E.; Klimchitskaya, G. L.; Krause, D. E.; Lopez, D.; Mostepanenko, V. M.
2011-10-15
We investigate the Casimir force between a microfabricated elliptic cylinder (cylindrical lens) and a plate made of real materials. After a brief discussion of the fabrication procedure, which typically results in elliptic rather than circular cylinders, the Lifshitz-type formulas for the Casimir force and for its gradient are derived. In the specific case of equal semiaxes, the resulting formulas coincide with those derived previously for circular cylinders. The nanofabrication procedure may also result in asymmetric cylindrical lenses obtained from parts of two different cylinders, or rotated through some angle about the axis of the cylinder. In these cases, the Lifshitz-type formulas for the Casimir force between a lens and a plate and for its gradient are also derived, and the influence of lens asymmetry is determined. Additionally, we obtain an expression for the shift of the natural frequency of a micromachined oscillator with an attached elliptic cylindrical lens interacting with a plate via the Casimir force in a nonlinear regime.
Non-Equilibrium Casimir Force between Vibrating Plates
Hanke, Andreas
2013-01-01
We study the fluctuation-induced, time-dependent force between two plates confining a correlated fluid which is driven out of equilibrium mechanically by harmonic vibrations of one of the plates. For a purely relaxational dynamics of the fluid we calculate the fluctuation-induced force generated by the vibrating plate on the plate at rest. The time-dependence of this force is characterized by a positive lag time with respect to the driving. We obtain two distinctive contributions to the force, one generated by diffusion of stress in the fluid and another related to resonant dissipation in the cavity. The relation to the dynamic Casimir effect of the electromagnetic field and possible experiments to measure the time-dependent Casimir force are discussed. PMID:23326401
Numerical calculation of the Casimir forces between a gold sphere and a nanocomposite sheet
NASA Astrophysics Data System (ADS)
Inui, Norio; Miura, Kouji; Akamatsu, Kensuke; Ishikawa, Makoto
2010-11-01
The repulsive Casimir force is expected as a force which enables to levitate small objects such as machine parts used in Micro Electro Mechanical Systems (MEMS), and superlubricity in MEMS may be realized by this levitation. We study the Casimir force between a gold sphere and a nanocomposite sheet containing many nickel nanoparticles. In particular, we focus on the dependence of the Casimir force on the separation between the gold sphere and the surface of the nanocomposite sheet. The Casimir force changes from the attractive force to the repulsive force as the separation increases. The strength of the repulsive force is, however, too small to levitate MEMS parts.
Many-body effects for critical Casimir forces.
Mattos, T G; Harnau, L; Dietrich, S
2013-02-21
Within mean-field theory we calculate the scaling functions associated with critical Casimir forces for a system consisting of two spherical colloids immersed in a binary liquid mixture near its consolute point and facing a planar, homogeneous substrate. For several geometrical arrangements and boundary conditions we analyze the normal and the lateral critical Casimir forces acting on one of the two colloids. We find interesting features such as a change of sign of these forces upon varying either the position of one of the colloids or the temperature. By subtracting the pairwise forces from the total force we are able to determine the many-body forces acting on one of the colloids. We have found that the many-body contribution to the total critical Casimir force is more pronounced for small colloid-colloid and colloid-substrate distances, as well as for temperatures close to criticality, where the many-body contribution to the total force can reach up to 25%.
Nonequilibrium Casimir Force with a Nonzero Chemical Potential for Photons
NASA Astrophysics Data System (ADS)
Chen, Kaifeng; Fan, Shanhui
2016-12-01
We introduce a new class of nonequilibrium Casimir forces, where the deviation from equilibrium is achieved through the use of a nonzero chemical potential of photons. Such a force can be observed when two semiconductors are brought in close proximity to each other, and when at least one of the semiconductors is subject to an external voltage. By exact numerical calculations of a sphere-plate configuration, we show that in the total force the non-equilibrium component can dominate over its equilibrium counterpart with a relatively modest external voltage, even when the sphere-plate separation is in the nanoscale. As a result, repulsion can be achieved at the nanoscale even with a relatively modest applied voltage. The results here point to a pathway that can significantly advance the quest for observing and harnessing nonequilibrium Casimir forces in solid-state systems.
Casimir-like forces at the percolation transition.
Gnan, Nicoletta; Zaccarelli, Emanuela; Sciortino, Francesco
2014-01-01
Percolation and critical phenomena show common features such as scaling and universality. Colloidal particles, immersed in a solvent close to criticality, experience long-range effective forces named critical Casimir forces. Building on the analogy between critical phenomena and percolation, here we explore the possibility of observing long-range forces near a percolation threshold. To this aim, we numerically evaluate the effective potential between two colloidal particles dispersed in a chemical sol, and we show that it becomes attractive and long-ranged on approaching the sol percolation transition. We develop a theoretical description based on a polydisperse Asakura-Oosawa model that captures the divergence of the interaction range, allowing us to interpret such effect in terms of depletion interactions in a structured solvent. Our results provide the geometric analogue of the critical Casimir force, suggesting a novel way for tuning colloidal interactions by controlling the clustering properties of the solvent.
Nonequilibrium Casimir Force with a Nonzero Chemical Potential for Photons.
Chen, Kaifeng; Fan, Shanhui
2016-12-23
We introduce a new class of nonequilibrium Casimir forces, where the deviation from equilibrium is achieved through the use of a nonzero chemical potential of photons. Such a force can be observed when two semiconductors are brought in close proximity to each other, and when at least one of the semiconductors is subject to an external voltage. By exact numerical calculations of a sphere-plate configuration, we show that in the total force the non-equilibrium component can dominate over its equilibrium counterpart with a relatively modest external voltage, even when the sphere-plate separation is in the nanoscale. As a result, repulsion can be achieved at the nanoscale even with a relatively modest applied voltage. The results here point to a pathway that can significantly advance the quest for observing and harnessing nonequilibrium Casimir forces in solid-state systems.
Finite-temperature Casimir force between perfectly metallic corrugated surfaces
Sarabadani, Jalal; Miri, MirFaez
2011-09-15
We study the Casimir force between two corrugated plates due to thermal fluctuations of a scalar field. For arbitrary corrugations and temperature T, we provide an analytical expression for the Casimir force, which is exact to second order in the corrugation amplitude. We study the specific case of two sinusoidally corrugated plates with corrugation wavelength {lambda}, lateral displacement b, and mean separation H. We find that the lateral Casimir force is F{sub l}(T,H)sin(2{pi}b/{lambda}). In other words, at all temperatures, the lateral force is a sinusoidal function of the lateral shift. In the limit {lambda}>>H, F{sub l}(T{yields}{infinity},H){proportional_to}k{sub B}TH{sup -4}{lambda}{sup -1}. In the opposite limit {lambda}<
La force de Casimir et les plasmons de surface
NASA Astrophysics Data System (ADS)
Intravaia, F.; Lambrecht, A.; Reynaud, S.
2004-11-01
La présence de fluctuations irréductibles de champ dans le vide est une prédiction importante de la théorie quantique. Ces fluctuations ont de nombreux effets bien connus, dont l'archétype est la force de Casimir apparaîssant entre deux miroirs placés dans le vide par suite de la pression de radiation du vide. Elle a été récemment mesurée avec une précision de l'ordre du %. De nombreux travaux sont consacrés à l'évaluation théorique de cette force en visant une précision du même ordre. Ici nous étudions la force de Casimir dans la configuration de deux miroirs métalliques plans parallèles à température nulle. En supposant les miroirs décrits par un modèle plasma nous interprétons la force de Casimir comme le résultat de l'interaction entre les plasmons de surface des deux miroirs.
Critical Casimir forces between homogeneous and chemically striped surfaces.
Parisen Toldin, Francesco; Tröndle, Matthias; Dietrich, S
2013-11-01
Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a homogeneous adsorption preference or homogeneous Dirichlet boundary conditions, which within a lattice model are realized by open boundary conditions. By means of mean-field theory, Monte Carlo simulations, and finite-size scaling analysis we determine the critical Casimir force acting on the two parallel walls and its corresponding universal scaling function. We show that in the limit of stripe widths small compared with the film thickness, on the striped surface the system effectively realizes Dirichlet boundary conditions, which generically do not hold for actual fluids. Moreover, the critical Casimir force is found to be attractive or repulsive, depending on the width of the stripes of the chemically patterned surface and on the boundary condition applied to the opposing surface.
Casimir force in the rotor model with twisted boundary conditions.
Bergknoff, Jonathan; Dantchev, Daniel; Rudnick, Joseph
2011-10-01
We investigate the three-dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is α where 0≤α≤π. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film--and the Casimir force it generates--as a function of the temperature T, the angle α, and the thickness L of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter α and the temperature and that can be attractive or repulsive. In particular, by varying α and/or T one controls both the sign and the magnitude of the Casimir force in a reversible way. Furthermore, for the case α=π, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.
Halving the Casimir force with conductive oxides: Experimental details
Man, S. de; Heeck, K.; Iannuzzi, D.
2010-12-15
This work is an extended version of a paper published previously [S. de Man et al., Phys. Rev. Lett. 103, 040402 (2009)], where we presented measurements of the Casimir force between a gold-coated sphere and a plate coated with either gold or an indium tin oxide (I TO) layer. The experiment, which was performed in air, showed that I TO conducts sufficiently to prevent charge accumulation but is still transparent enough to halve the Casimir attraction when compared to gold. Here we report all the experimental details that, owing to the limited space available, were omitted in the previous article. We discuss the performance of our setup in terms of stability of the calibration procedure and reproducibility of the Casimir force measurement. We also introduce and demonstrate a technique to obtain the spring constant of our force sensor. Furthermore, we present a thorough description of the experimental method, a comprehensive explanation of data elaboration and error analysis, and a complete characterization of the dielectric function and of the surface roughness of the samples used in the actual experiment.
Garrett, Joseph L; Somers, David; Munday, Jeremy N
2015-06-03
Measurements of the Casimir force require the elimination of the electrostatic force between the surfaces. However, due to electrostatic patch potentials, the voltage required to minimize the total force may not be sufficient to completely nullify the electrostatic interaction. Thus, these surface potential variations cause an additional force, which can obscure the Casimir force signal. In this paper, we inspect the spatially varying surface potential of e-beamed, sputtered, sputtered and annealed, and template stripped gold surfaces with Heterodyne amplitude modulated Kelvin probe force microscopy (HAM-KPFM). It is demonstrated that HAM-KPFM improves the spatial resolution of surface potential measurements compared to amplitude modulated Kelvin probe force microscopy. We find that patch potentials vary depending on sample preparation, and that the calculated pressure can be similar to the pressure difference between Casimir force calculations employing the plasma and Drude models.
NASA Astrophysics Data System (ADS)
Garrett, Joseph L.; Somers, David; Munday, Jeremy N.
2015-06-01
Measurements of the Casimir force require the elimination of the electrostatic force between the surfaces. However, due to electrostatic patch potentials, the voltage required to minimize the total force may not be sufficient to completely nullify the electrostatic interaction. Thus, these surface potential variations cause an additional force, which can obscure the Casimir force signal. In this paper, we inspect the spatially varying surface potential of e-beamed, sputtered, sputtered and annealed, and template stripped gold surfaces with Heterodyne amplitude modulated Kelvin probe force microscopy (HAM-KPFM). It is demonstrated that HAM-KPFM improves the spatial resolution of surface potential measurements compared to amplitude modulated Kelvin probe force microscopy. We find that patch potentials vary depending on sample preparation, and that the calculated pressure can be similar to the pressure difference between Casimir force calculations employing the plasma and Drude models.
Convergent conductivity corrections to the Casimir force via exponential basis functions
Cui, Song; Soh, Yeng Chai
2010-12-15
A closed-form finite conductivity correction factor for the ideal Casimir force is proposed, based on exponential basis functions. Our method can facilitate experimental verifications of theories in the study of the Casimir force. A theoretical analysis is given to explain why our method is accurate at both large and small separation gaps. Numerical computations have been performed to confirm that our method is accurate in various experimental configurations. Our approach is widely applicable to various Casimir force interactions between metals and dielectrics. Our study can be extended to the study of the repulsive Casimir force as well.
Casimir force between dielectric media with free charges.
Høye, Johan S; Brevik, Iver
2009-07-01
The statistical mechanical approach to Casimir problems for dielectrics separated by a vacuum gap turns out to be compact and effective. A central ingredient of this method is the effect of interacting fluctuating dipole moments of the polarizable particles. At arbitrary temperature the path-integral formulation of quantized particles, developed by Høye-Stell and others, is needed. At high temperature-the limit considered in the present paper-the classical theory is, however, sufficient. Our present theory is related to an idea put forward earlier by Jancovici and Samaj (2004), namely, to evaluate the Casimir force between parallel plates invoking an electronic plasma model and the Debye-Hückel theory for electrolytes. Their result was recently recovered by Høye (2008), using a related statistical mechanical method. In the present paper we generalize this by including a constant permittivity in the description. The present paper generalizes our earlier theory for parallel plates (1998), as well as for spherical dielectrics (2001). We also consider the Casimir force between a polarizable particle and a conductor with a small density of charges, finding agreement with the result recently derived by Pitaevskii (2008).
Casimir force and its relation to surface tension
NASA Astrophysics Data System (ADS)
Høye, J. S.; Brevik, I.
2017-05-01
From energy considerations there is reason to expect that the work done by Casimir forces during a slow displacement of the parallel plates reflects the free energy of the surface tension of the adjacent surfaces. We show this explicitly, for a one-component ionic fluid or plasma with qc as ionic charge, where the particles are neutralized by a uniform continuous oppositely charged background. For two equal half-planes, the surface-associated free energy for one half-plane turns out to be just one half of the total Casimir energy for the conventional Casimir setup. We also comment, from a wider perspective, on the intriguing possibility that knowledge about the magnitude of the surface tension coefficient obtained from statistical mechanics or experiments may give insight into the value of the conventional cutoff time-splitting parameter τ =t -t' occurring in quantum field theory. A simple analysis suggests that the minimal distance τ c is of the order of atomic dimensions, which is a physically natural result.
Virtual photons in imaginary time: Computing Casimir forces in new geometries
NASA Astrophysics Data System (ADS)
Johnson, Steven G.
2009-03-01
One of the most dramatic manifestations of the quantum nature of light in the past half-century has been the Casimir force: a force between neutral objects at close separations caused by quantum vacuum fluctuations in the electromagnetic fields. In classical photonics, wavelength-scale structures can be designed to dramatically alter the behavior of light, so it is natural to consider whether analogous geometry-based effects occur for Casimir forces. However, this problem turns out to be surprisingly difficult for all but the simplest planar geometries. (The deceptively simple case of an infinite plate and infinite cylinder, for perfect metals, was first solved in 2006.) Many formulations of the Casimir force, indeed, correspond to impossibly hard numerical problems. We will describe how the availability of large-scale computing resources in NSF's Teragrid, combined with reformulations of the Casimir-force problem oriented towards numerical computation, are enabling the exploration of Casimir forces in new regimes of geometry and materials.
Possibility of measuring thermal effects in the Casimir force
Geyer, B.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2010-09-15
We analyze the possibility of measuring small thermal effects in the Casimir force between metal test bodies in configurations of a sphere above a plate and two parallel plates. For the sphere-plate geometry used in many experiments, we investigate the applicability of the proximity force approximation (PFA) to calculation of thermal effects in the Casimir force and its gradient. It is shown that for real metals the two formulations of the PFA used in the literature lead to relative differences in the results obtained being less than a small parameter equal to the ratio of separation distance to sphere radius. For ideal metals, PFA results for the thermal correction are obtained and compared with available exact results. It is emphasized that in the experimental region in the zeroth order of the small parameter already mentioned, the thermal Casimir force and its gradient calculated using the PFA (and thermal corrections in their own right) coincide with the respective exact results. For real metals, available exact results are outside the application region of the PFA. However, the exact results are shown to converge with the PFA results when the small parameter goes down to experimental values. We arrive at the conclusion that the large thermal effects predicted by the Drude-model approach, if they exist, could be measured in both static and dynamic experiments in sphere-plate and plate-plate configurations. As for the small thermal effects predicted by the plasma-model approach, the static experiment in the configuration of two parallel plates is found to be the best for their observation.
Casimir force between δ -δ' mirrors transparent at high frequencies
NASA Astrophysics Data System (ADS)
Braga, Alessandra N.; Silva, Jeferson Danilo L.; Alves, Danilo T.
2016-12-01
We investigate, in the context of a real massless scalar field in 1 +1 dimensions, models of partially reflecting mirrors simulated by Dirac δ -δ' point interactions. In the literature, these models do not exhibit full transparency at high frequencies. In order to provide a more realistic feature for these models, we propose a modified δ -δ' point interaction that enables full transparency in the limit of high frequencies. Taking this modified δ -δ' model into account, we investigate the Casimir force, comparing our results with those found in the literature.
Casimir force for a scalar field in warped brane worlds
Linares, Roman; Morales-Tecotl, Hugo A.; Pedraza, Omar
2008-03-15
In looking for imprints of extra dimensions in braneworld models one usually builds these so that they are compatible with known low energy physics and thus focuses on high energy effects. Nevertheless, just as submillimeter Newton's law tests probe the mode structure of gravity other low energy tests might apply to matter. As a model example, in this work we determine the 4D Casimir force corresponding to a scalar field subject to Dirichlet boundary conditions on two parallel planes lying within the single brane of a Randall-Sundrum scenario extended by one compact extra dimension. Using the Green's function method such a force picks the contribution of each field mode as if it acted individually but with a weight given by the square of the mode wave functions on the brane. In the low energy regime one regains the standard 4D Casimir force that is associated to a zero mode in the massless case or to a quasilocalized or resonant mode in the massive one while the effect of the extra dimensions gets encoded as an additional term.
Optical Modification of Casimir Forces for Improved Function of Micro-and Nano-Scale Devices
NASA Technical Reports Server (NTRS)
Strekalov, Dmitry V.; Yu, Nan
2010-01-01
Recently, there has been a considerable effort to study the Casimir and van der Waals forces, enabled by the improved ability to measure small forces near surfaces. Because of the continuously growing role of micro- and nanomechanical devices, the focus of this activity has shifted towards the ability to control these forces. Possible approaches to manipulating the Casimir force include development of composite materials, engineered nanostructures, mixed-phase materials, or active elements. So far, practical success has been limited. The role of geometrical factors in the Casimir force is significant. It is known, for example, that the Casimir force between two spherical shells enclosed one into the other is repulsive instead of normal attractive. Unfortunately, nanosurfaces with this topology are very difficult to make. A more direct approach to manipulating and neutralizing the Casimir force is using external mechanical or electromagnetic forces. Unfortunately, the technological overhead of such an approach is quite large. Using electromagnetic compensation instead of mechanical will considerably reduce this overhead and at the same time provide the degree of control over the Casimir force that mechanical springs cannot provide. A mechanical analog behind Casimir forces is shown.
Rudnick, Joseph; Zandi, Roya; Shackell, Aviva; Abraham, Douglas
2010-10-01
Finite-size effects in certain critical systems can be understood as universal Casimir forces. Here, we compare the Casimir force for free, fixed, periodic, and antiperiodic boundary conditions in the exactly calculable case of the ferromagnetic Ising model in one and two dimensions. We employ a procedure which allows us to calculate the Casimir force with the aforementioned boundary conditions analytically in a transparent manner. Among other results, we find an attractive Casimir force for the case of periodic boundary conditions and a repulsive Casimir force in the antiperiodic case.
Crossover from attractive to repulsive Casimir forces and vice versa.
Schmidt, Felix M; Diehl, H W
2008-09-05
Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.
The role of the "Casimir force analogue" at the microscopic processes of crystallization and melting
NASA Astrophysics Data System (ADS)
Chuvildeev, V. N.; Semenycheva, A. V.
2016-10-01
Melting (crystallization), a phase transition from a crystalline solid to a liquid state, is a common phenomenon in nature. We suggest a new factor, "the Casimir force analogue", to describe mechanisms of melting and crystallization. The Casimir force analogue is a force occurring between the surfaces of solid and liquid phases of metals caused by different energy density of phonons of these phases. It explains abrupt changes in geometry and thermodynamic parameters at a melting point. "The Casimir force analogue" helps to estimate latent melting heat and to gain an insight into a solid-liquid transition problem.
Drastic change of the Casimir force at the metal-insulator transition
Galkina, E. G.; Ivanov, B. A.; Savel'ev, Sergey; Yampol'skii, V. A.; Nori, Franco
2009-09-15
The dependence of the Casimir force on material properties is important for both future applications and to gain further insight on its fundamental aspects. Here we apply the general Lifshitz theory of the Casimir force to low-conducting compounds, or poor metals. For distances in the micrometer range, the Casimir force for a large variety of such materials is described by universal equations containing a few parameters: the effective plasma frequency {omega}{sub p}, dissipation rate {gamma} of the free carriers, and electric permittivity {epsilon}{sub {infinity}} for {omega}{>=}{omega}{sub p} (in the infrared range). This theory of the Casimir force for poor metals can also describe inhomogeneous composite materials containing small regions with different conductivity. The Casimir force for systems involving samples made with compounds that have a metal-insulator transition shows a drastic change of the Casimir force within the transition region, where the metallic and dielectric phases coexist. Indeed, the Casimir force can increase by a factor of 2 near this transition.
Constraints on Stable Equilibria with Fluctuation-Induced (Casimir) Forces
Rahi, Sahand Jamal; Kardar, Mehran; Emig, Thorsten
2010-08-13
We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir or van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also unstable if the permittivities of all objects are higher or lower than that of the enveloping medium, the former being the generic case for ordinary materials in vacuum.
Measurement of the Casimir force between dissimilar metals.
Decca, R S; López, D; Fischbach, E; Krause, D E
2003-08-01
The first precise measurement of the Casimir force between dissimilar metals is reported. The attractive force, between a Cu layer evaporated on a microelectromechanical torsional oscillator and an Au layer deposited on an Al2O3 sphere, was measured dynamically with a noise level of 6 fN/sqrt[Hz]. Measurements were performed for separations in the 0.2-2 micro m range. The results agree to better than 1% in the 0.2-0.5 micro m range with a theoretical model that takes into account the finite conductivity and roughness of the two metals. The observed discrepancies, which are much larger than the experimental precision, can be attributed to a lack of a complete characterization of the optical properties of the specific samples used in the experiment.
Direct calculation of the critical Casimir force in a binary fluid.
Puosi, Francesco; Cardozo, David Lopes; Ciliberto, Sergio; Holdsworth, Peter C W
2016-10-01
We show that critical Casimir effects can be accessed through direct simulation of a model binary fluid passing through the demixing transition. We work in the semi-grand-canonical ensemble, in slab geometry, in which the Casimir force appears as the excess of the generalized pressure, P_{⊥}-nμ. The excesses of the perpendicular pressure, P_{⊥}, and of nμ, are individually of much larger amplitude. A critical pressure anisotropy is observed between forces parallel and perpendicular to the confinement direction, which collapses onto a universal scaling function closely related to that of the critical Casimir force.
Mohideen, Umar
2015-04-14
Duration of award was from 4/15/10-4/14/15. In this grant period our contributions to the field of VdW/Casimir forces are 24 refereed publications in journals such as Physical Review Letters (4) [1-4], Physical Review B (10) [5-14], Physical Review D (2) [15,16], Applied Physics Letters (1) [17], Review of Scientific Instruments (1) [18] and the International Journal of Modern Physics A (5) [19-23] and B(1) (invited review article [24]). We presented 2 plenary conference talks, 3 lectures at the Pan American School on Frontiers in Casimir Physics, 2 conferences, 1 colloquium and 11 APS talks. If publications are restricted to only those with direct connection to the aims proposed in the prior grant period, then it will be a total of 12: Physical Review Letters (3) [2-4], Physical Review B (6) [6-8,12,13,25], Review of Scientific Instruments (1) [18], International Journal of Modern Physics A (1) [19] and B(1) [169]. A brief aggregated description of the directly connected accomplishments is below. The following topics are detailed: dispersion force measurements with graphene, dispersion force from ferromagnetic metals, conclusion on role of electrostatic patches, UV radiation induced modification of the Casimir force, low temperature measurement of the Casimir force, and Casimir force from thin fluctuating membranes.
Thermal fluctuations and stability of a particle levitated by a repulsive Casimir force in a liquid.
Inui, Norio; Goto, Kosuke
2013-11-01
We study the vertical Brownian motion of a gold particle levitated by a repulsive Casimir force to a silica plate immersed in bromobenzene. The time evolution of the particle distribution starting from an equilibrium position, where the Casimir force and gravitational force are balanced, is considered by solving the Langevin equation using the Monte Carlo method. When the gold particle is very close to the silica plate, the Casimir force changes from repulsive to attractive, and the particle eventually sticks to the surface. The escape rate from a metastable position is calculated by solving the Fokker-Plank equation; it agrees with the value obtained by Kramers' escape theory. The duration of levitation increases as the particle radius increases up to around 2.3 μm. As an example, we show that a 1-μm-diameter gold particle can be levitated for a significantly long time by the repulsive Casimir force at room temperature.
Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii
Bezerra, V. B.; Romero, C.; Klimchitskaya, G. L.; Mohideen, U.; Mostepanenko, V. M.
2011-02-15
The impact of imperfections, which are always present on surfaces of lenses with centimeter-size curvature radii, on the Casimir force in the lens-plate geometry is investigated. It is shown that the commonly used formulation of the proximity force approximation is inapplicable for spherical lenses with surface imperfections, such as bubbles and pits. More general expressions for the Casimir force are derived that take surface imperfections into account. Using these expressions, we show that surface imperfections can both increase and decrease the magnitude of the Casimir force up to a few tens percent when compared with the case of a perfectly spherical lens. We demonstrate that the Casimir force between a perfectly spherical lens and a plate described by the Drude model can be made approximately equal to the force between a sphere with some surface imperfection and a plate described by the plasma model, and vice versa. In the case of a metallic sphere and a semiconductor plate, approximately the same Casimir forces are obtained for four different descriptions of charge carriers in the semiconductor if appropriate surface imperfections on the lens surface are present. The conclusion is made that there is a fundamental problem in the interpretation of measurement data for the Casimir force using spherical lenses of centimeter-size radii.
Critical Casimir forces from the equation of state of quantum critical systems
NASA Astrophysics Data System (ADS)
Rançon, Adam; Henry, Louis-Paul; Rose, Félix; Cardozo, David Lopes; Dupuis, Nicolas; Holdsworth, Peter C. W.; Roscilde, Tommaso
2016-10-01
The mapping between a classical length and inverse temperature as imaginary time provides a direct equivalence between the Casimir force of a classical system in D dimensions and internal energy of a quantum system in d =D -1 dimensions. The scaling functions of the critical Casimir force of the classical system with periodic boundaries thus emerge from the analysis of the symmetry related quantum critical point. We show that both nonperturbative renormalization group and quantum Monte Carlo analysis of quantum critical points provide quantitative estimates for the critical Casimir force in the corresponding classical model, giving access to widely different aspect ratios for the geometry of confined systems. In light of these results, we propose protocols for the realization of critical Casimir forces for periodic boundaries through state-of-the-art cold-atom and solid-state experiments.
Casimir force for absorbing media in an open quantum system framework: Scalar model
Lombardo, Fernando C.; Rubio Lopez, Adrian E.; Mazzitelli, Francisco D.
2011-11-15
In this article we compute the Casimir force between two finite-width mirrors at finite temperature, working in a simplified model in 1+1 dimensions. The mirrors, considered as dissipative media, are modeled by a continuous set of harmonic oscillators which in turn are coupled to an external environment at thermal equilibrium. The calculation of the Casimir force is performed in the framework of the theory of open quantum systems. It is shown that the Casimir interaction has two different contributions: the usual radiation pressure from the vacuum, which is obtained for ideal mirrors without dissipation or losses, and a Langevin force associated with the noise induced by the interaction between dielectric atoms in the slabs and the thermal bath. Both contributions to the Casimir force are needed in order to reproduce the analogous Lifshitz formula in 1+1 dimensions. We also discuss the relationship between the electromagnetic properties of the mirrors and the spectral density of the environment.
Reply to 'Comment on 'Temperature dependence of the Casimir force for lossy bulk media''
Yampol'skii, V. A.; Maizelis, Z. A.; Apostolov, S. S.; Savel'ev, Sergey; Nori, Franco
2011-09-15
Here, we present an estimate of the characteristic wavelengths of the evanescent modes, which define the main contribution to the thermal part of the Casimir force. This estimate is more precise than the one in the preceding Comment by Bimonte et al.[Phys. Rev. A 84, 036501 (2011)]. The wavelengths we derive are indeed smaller than the sizes of the interacting bodies. We also discuss the results of several experiments on the thermal effects in the Casimir force.
Chen, F.; Mohideen, U.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2006-10-27
A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology.
Fluctuations of the Casimir-Polder force between an atom and a conducting wall
Messina, R.; Passante, R.
2007-09-15
We consider quantum fluctuations of the Casimir-Polder force between a neutral atom and a perfectly conducting wall in the ground state of the system. In order to obtain the atom-wall force fluctuation we first define an operator directly associated with the force experienced by the atom considered as a polarizable body in an electromagnetic field and we use a time-averaged force operator in order to avoid ultraviolet divergences appearing in the fluctuation of the force. This time-averaged force operator takes into account that any measurement involves a finite time. We also calculate the Casimir-Polder force fluctuation for an atom between two conducting walls. Experimental observability of these Casimir-Polder force fluctuations is also discussed, as well as the dependence of the relative force fluctuation on the duration of the measurement.
Toldin, Francesco Parisen; Tröndle, Matthias; Dietrich, S
2015-06-03
Recent experimental realizations of the critical Casimir effect have been implemented by monitoring colloidal particles immersed in a binary liquid mixture near demixing and exposed to a chemically structured substrate. In particular, critical Casimir forces have been measured for surfaces consisting of stripes with periodically alternating adsorption preferences, forming chemical steps between them. Motivated by these experiments, we analyze the contribution of such chemical steps to the critical Casimir force for the film geometry and within the Ising universality class. By means of Monte Carlo simulations, mean-field theory and finite-size scaling analysis we determine the universal scaling function associated with the contribution to the critical Casimir force due to individual, isolated chemical steps facing a surface with homogeneous adsorption preference or with Dirichlet boundary condition. In line with previous findings, these results allow one to compute the critical Casimir force for the film geometry and in the presence of arbitrarily shaped, but wide stripes. In this latter limit the force decomposes into a sum of the contributions due to the two homogeneous parts of the surface and due to the chemical steps between the stripes. We assess this decomposition by comparing the resulting sum with actual simulation data for the critical Casimir force in the presence of a chemically striped substrate.
Casimir force in brane worlds: Coinciding results from Green's and zeta function approaches
Linares, Roman; Morales-Tecotl, Hugo A.; Pedraza, Omar
2010-06-15
Casimir force encodes the structure of the field modes as vacuum fluctuations and so it is sensitive to the extra dimensions of brane worlds. Now, in flat spacetimes of arbitrary dimension the two standard approaches to the Casimir force, Green's function, and zeta function yield the same result, but for brane world models this was only assumed. In this work we show that both approaches yield the same Casimir force in the case of universal extra dimensions and Randall-Sundrum scenarios with one and two branes added by p compact dimensions. Essentially, the details of the mode eigenfunctions that enter the Casimir force in the Green's function approach get removed due to their orthogonality relations with a measure involving the right hypervolume of the plates, and this leaves just the contribution coming from the zeta function approach. The present analysis corrects previous results showing a difference between the two approaches for the single brane Randall-Sundrum; this was due to an erroneous hypervolume of the plates introduced by the authors when using the Green's function. For all the models we discuss here, the resulting Casimir force can be neatly expressed in terms of two four-dimensional Casimir force contributions: one for the massless mode and the other for a tower of massive modes associated with the extra dimensions.
Casimir force in O(n) systems with a diffuse interface.
Dantchev, Daniel; Grüneberg, Daniel
2009-04-01
We study the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry infinity;{d-1}xL , where 2
Efficient evaluation of Casimir force in z-invariant geometries by integral equation methods
Xiong, Jie L.; Chew, Weng Cho
2009-10-12
We introduce an efficient and accurate way to evaluate the Casimir force [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between arbitrary z-invariant structures using integral equation method. It casts the evaluation of mean Maxwell stress tensor to a series of traditional two-dimensional electromagnetic scattering problems. The number of times that the scattering problem needs to be solved is independent of the number of unknowns.
Bao, Y.; Guerout, R.; Lussange, J.; Lambrecht, A.; Cirelli, R. A.; Klemens, F.; Mansfield, W. M.; Pai, C. S.; Chan, H. B.
2010-12-17
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.
Critical Casimir force in the presence of random local adsorption preference.
Parisen Toldin, Francesco
2015-03-01
We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p, the system exhibits a crossover between an attractive and a repulsive force. At p=1/2, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.
Wei, Q.; Dalvit, D. A. R.; Lombardo, F. C.; Mazzitelli, F. D.; Onofrio, R.
2010-05-15
We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurements performed in the parallel-plane configuration, showing that the dependence on distance of the minimizing potential, if present at all, is milder than in the sphere-plane or cylinder-plane geometries. General considerations on the interplay between the distance-dependent minimizing potential and the precision of Casimir force measurements in the range relevant to detect the thermal corrections for all geometries are finally reported.
Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls.
Nowakowski, Piotr; Napiórkowski, Marek
2014-08-14
We analyze the lateral critical Casimir force acting between two planar, chemically inhomogeneous walls confining an infinite 2D Ising strip of width M. The inhomogeneity of each of the walls has size N1; they are shifted by the distance L along the strip. Using the exact diagonalization of the transfer matrix, we calculate the lateral critical Casimir force and discuss its properties, in particular its scaling close to the 2D bulk critical point, as a function of temperature, surface magnetic field, and the geometric parameters M, N1, L. We determine the magnetization profiles which display the formation of the bridge joining the inhomogeneities on the walls and establish the relation between the characteristic properties of the lateral Casimir force and magnetization morphologies. We check numerically that breaking of the bridge is related to the inflection point of the lateral force.
How to observe the giant thermal effect in the Casimir force for graphene systems
NASA Astrophysics Data System (ADS)
Bimonte, G.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2017-07-01
A differential measurement scheme is proposed which allows for clear observation of the giant thermal effect for the Casimir force, which was recently predicted to occur in graphene systems at short separation distances. The difference among the Casimir forces acting between a metal-coated sphere and the two halves of a dielectric plate, one uncoated and the other coated with graphene, is calculated in the framework of the Dirac model using the rigorous formalism of the polarization tensor. It is shown that in the proposed configuration both the difference among the Casimir forces and its thermal contribution can be easily measured using existing experimental setups. An observation of the giant thermal effect should open opportunities for modulation and control of dispersion forces in micromechanical systems based on graphene and other novel two-dimensional (2D) materials.
Chen, F.; Mohideen, U.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2006-08-15
The experimental investigation of the Casimir force between a large metallized sphere and semiconductor plate is performed using an atomic force microscope. Improved calibration and measurement procedures permitted a reduction in the role of different uncertainties. Rigorous statistical procedures are applied for the analysis of random, systematic, and total experimental errors at 95% confidence. The theoretical Casimir force is computed for semiconductor plates with different conductivity properties, taking into account all theoretical uncertainties discussed in the literature. The comparison between experiment and theory is done at both 95% and 70% confidence. It is demonstrated that the theoretical results computed for the semiconductor plate used in experiment are consistent with the data. At the same time, the theory describing a dielectric plate is excluded by experiment at 70% confidence. Thus, the Casimir force is proved to be sensitive to the conductivity properties of semiconductors.
Repulsive Casimir forces between solid materials with high-refractive-index intervening liquids
Zwol, P. J. van; Palasantzas, G.
2010-06-15
In order to explore repulsive Casimir or van der Waals forces between solid materials with liquid as the intervening medium, we analyze dielectric data for a wide range of materials as, for example, (p)olytetrafluoroethylene, polystyrene, silica, and more than 20 liquids. Although significant variation in the dielectric data from different sources exists, we provide a scheme based on measured static dielectric constants, refractive indices, and applying Kramers-Kronig consistency to dielectric data to create accurate dielectric functions at imaginary frequencies. The latter is necessary for more accurate force calculations via the Lifshitz theory, thereby allowing reliable predictions of repulsive Casimir forces.
Influence of materials' optical response on actuation dynamics by Casimir forces.
Sedighi, M; Broer, W H; Van der Veeke, S; Svetovoy, V B; Palasantzas, G
2015-06-03
The dependence of the Casimir force on the frequency-dependent dielectric functions of interacting materials makes it possible to tailor the actuation dynamics of microactuators. The Casimir force is largest for metallic interacting systems due to the high absorption of conduction electrons in the far-infrared range. For less conductive systems, such as phase change materials or conductive silicon carbide, the reduced force offers the advantage of increased stable operation of MEMS devices against pull-in instabilities that lead to unwanted stiction. Bifurcation analysis with phase portraits has been used to compare the sensitivity of a model actuator when the optical properties are altered.
Dynamic measurement and modeling of the Casimir force at the nanometer scale
Kohoutek, John; Wan, Ivy Yoke Leng; Mohseni, Hooman
2010-02-08
We present a dynamic method for measurement of the Casimir force with an atomic force microscope (AFM) with a conventional AFM tip. With this method, originally based on the phase of vibration of the AFM tip, we are able to verify the Casimir force at distances of nearly 6 nm with an AFM tip that has a radius of curvature of nearly 100 nm. Until now dynamic methods have been done using large metal spheres at greater distances. Also presented is a theoretical model based on the harmonic oscillator, including nonidealities. This model accurately predicts the experimental data.
Casimir force in the Gödel space-time and its possible induced cosmological inhomogeneity
NASA Astrophysics Data System (ADS)
Khodabakhshi, Sh.; Shojai, A.
2017-07-01
The Casimir force between two parallel plates in the Gödel universe is computed for a scalar field at finite temperature. It is observed that when the plates' separation is comparable with the scale given by the rotation of the space-time, the force becomes repulsive and then approaches zero. Since it has been shown previously that the universe may experience a Gödel phase for a small period of time, the induced inhomogeneities from the Casimir force are also studied.
A Light Sail Inspired Model to Harness Casimir Forces for Propellantless Propulsion
DeBiase, R. L.
2010-01-28
The model used to calculate Casimir forces for variously shaped conducting plates in this paper assumes the vacuum energy pervades all space and that photons randomly pop into and out of existence. While they exist, they possess energy and momentum that can be transferred by reflection as in a light sail. Quantum mechanics in the model is entirely bound up in the Casimir equation of force per unit area. This model is compared with two different experiments: that of Chen and Mohideen demonstrating lateral Casimir forces for sinusoidally corrugated spherical and flat plates and Lamoreaux demonstrating normal Casimir forces between a conducting sphere and flat plate. The calculated forces using this model were compared to the forces obtained in these experiments as well as with calculations using the proximity force approximation. In both cases the results (when compared to the actual plates measured and calculated using non-corrected equations) were less than a few parts per thousand different for the range of separation distances used. When the model was used to calculate forces on the opposite plates, different force magnitudes were obtained seemingly indicating prospects for propellentless propulsion but requiring skeptical verification.
Modelling critical Casimir force induced self-assembly experiments on patchy colloidal dumbbells.
Newton, Arthur C; Nguyen, T Anh; Veen, Sandra J; Kraft, Daniela J; Schall, Peter; Bolhuis, Peter G
2017-07-19
Colloidal particles suspended in a binary liquid mixture can interact via solvent mediated interactions, known as critical Casimir forces. For anisotropic colloids this interaction becomes directional, which leads to rich phase behavior. While experimental imaging and particle tracking techniques allow determination of isotropic effective potentials via Boltzmann inversion, the modeling of effective interaction in anisotropic systems is non-trivial precisely because of this directionality. Here we extract effective interaction potentials for non-spherical dumbbell particles from observed radial and angular distributions, by employing reference interaction site model (RISM) theory and direct Monte Carlo simulations. For colloidal dumbbell particles dispersed in a binary liquid mixture and interacting via induced critical Casimir forces, we determine the effective site-site potentials for a range of experimental temperatures. Using these potentials to simulate the system for strong Casimir forces, we reproduce the experimentally observed collapse, and provide a qualitative explanation for this behavior.
Critical adsorption and critical Casimir forces in the canonical ensemble.
Gross, Markus; Vasilyev, Oleg; Gambassi, Andrea; Dietrich, S
2016-08-01
Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.
Critical adsorption and critical Casimir forces in the canonical ensemble
NASA Astrophysics Data System (ADS)
Gross, Markus; Vasilyev, Oleg; Gambassi, Andrea; Dietrich, S.
2016-08-01
Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.
Reduction of the Casimir Force from Indium Tin Oxide Film by UV Treatment
Chang, C.-C.; Banishev, A. A.; Mohideen, U.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2011-08-26
A significant decrease in the magnitude of the Casimir force (from 21% to 35%) was observed after an indium tin oxide sample interacting with an Au sphere was subjected to the UV treatment. Measurements were performed by using an atomic force microscope in high vacuum. The experimental results are compared with theory and a hypothetical explanation for the observed phenomenon is proposed.
Rectification of the lateral Casimir force in a vibrating noncontact rack and pinion.
Ashourvan, Arash; Miri, Mirfaez; Golestanian, Ramin
2007-04-01
The nonlinear dynamics of a cylindrical pinion that is kept at a distance from a vibrating rack is studied, and it is shown that the lateral Casimir force between the two corrugated surfaces can be rectified. The effects of friction and external load are taken into account, and it is shown that the pinion can do work against loads of up to a critical value, which is set by the amplitude of the lateral Casimir force. We present a phase diagram for the rectified motion that could help its experimental investigations, as the system exhibits a chaotic behavior in a large part of the parameter space.
Noncontact racK and pinion powered by the lateral Casimir force.
Ashourvan, Arash; Miri, MirFaez; Golestanian, Ramin
2007-04-06
The lateral Casimir force is employed to propose a design for a potentially wear-proof rack and pinion with no contact, which can be miniaturized to the nanoscale. The robustness of the design is studied by exploring the relation between the pinion velocity and the rack velocity in the different domains of the parameter space. The effects of friction and added external load are also examined. It is shown that the device can hold up extremely high velocities, unlike what the general perception of the Casimir force as a weak interaction might suggest.
Computational Considerations in the Calculation of the Casimir Force Between Multilayered Systems
NASA Astrophysics Data System (ADS)
Pinto, Fabrizio
It is shown that, in contrast to the case of two semi-infinite slabs, the Casimir force between two periodic multilayer stacks cannot be computed by means of the typical Lifshitz integration along the imaginary frequency axis because both the integrand and the reflectivity coefficients display multiple poles on such axis. Consequently, all objections to the possibility of radically engineering the magnitude, gap width dependence, and sign of the Casimir force, which were based upon such invalid expressions, are removed. Some experimental and computational implications of these results are discussed.
Tricritical Casimir forces and order parameter profiles in wetting films of ^{3}He-^{4}He mixtures.
Farahmand Bafi, N; Maciołek, A; Dietrich, S
2017-03-01
Tricritical Casimir forces in ^{3}He-^{4}He wetting films are studied, within mean field theory, in terms of a suitable lattice gas model for binary liquid mixtures with short-ranged surface fields. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with ^{4}He and it allows, inter alia, for the occurrence of a vapor phase. As a result, the model facilitates the formation of wetting films, which provides a strengthened theoretical framework to describe available experimental data for tricritical Casimir forces acting in ^{3}He-^{4}He wetting films.
Tricritical Casimir forces and order parameter profiles in wetting films of 3He-4He mixtures
NASA Astrophysics Data System (ADS)
Farahmand Bafi, N.; Maciołek, A.; Dietrich, S.
2017-03-01
Tricritical Casimir forces in 3He-4He wetting films are studied, within mean field theory, in terms of a suitable lattice gas model for binary liquid mixtures with short-ranged surface fields. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with 4He and it allows, inter alia, for the occurrence of a vapor phase. As a result, the model facilitates the formation of wetting films, which provides a strengthened theoretical framework to describe available experimental data for tricritical Casimir forces acting in 3He-4He wetting films.
Plasma versus Drude Modeling of the Casimir Force: Beyond the Proximity Force Approximation
NASA Astrophysics Data System (ADS)
Hartmann, Michael; Ingold, Gert-Ludwig; Neto, Paulo A. Maia
2017-07-01
We calculate the Casimir force and its gradient between a spherical and a planar gold surface. Significant numerical improvements allow us to extend the range of accessible parameters into the experimental regime. We compare our numerically exact results with those obtained within the proximity force approximation (PFA) employed in the analysis of all Casimir force experiments reported in the literature so far. Special attention is paid to the difference between the Drude model and the dissipationless plasma model at zero frequency. It is found that the correction to PFA is too small to explain the discrepancy between the experimental data and the PFA result based on the Drude model. However, it turns out that for the plasma model, the corrections to PFA lie well outside the experimental bound obtained by probing the variation of the force gradient with the sphere radius [D. E. Krause et al., Phys. Rev. Lett. 98, 050403 (2007), 10.1103/PhysRevLett.98.050403]. The corresponding corrections based on the Drude model are significantly smaller but still in violation of the experimental bound for small distances between plane and sphere.
Using the Casimir Force to Measure the Gravitational Constant
NASA Technical Reports Server (NTRS)
Pinto, F.
1998-01-01
I show that the dynamics of two coupled torsion pendulums is drastically affected by their mutual Casimir surface interaction if the masses involved are relatively close to each other. The effect is directly related to the ratio of the masses used to the Planck mass.
Casimir friction force between a SiO2 probe and a graphene-coated SiO2 substrate
NASA Astrophysics Data System (ADS)
Volokitin, A. I.
2016-10-01
The possibility of mechanical detection of Casimir friction with the use of a noncontact atomic force microscope is discussed. A SiO2 probe tip located above a graphene-coated SiO2 substrate is subjected to the frictional force caused by a fluctuating electromagnetic field produced by a current in graphene. This frictional force will create the bend of a cantilever, which can be measured by a modern noncontact atomic force microscope. Both the quantum and thermal contributions to the Casimir frictional force can be measured using this experimental setup. This result can also be used to mechanically detect Casimir friction in micro- and nanoelectromechanical systems.
NASA Astrophysics Data System (ADS)
Liang, Binbin; Zhang, Long; Wang, Binglei; Zhou, Shenjie
2015-07-01
A size-dependent model for the electrostatically actuated Nano-Electro-Mechanical Systems (NEMS) incorporating nonlinearities and Casimir force is presented by using a variational method. The governing equation and boundary conditions are derived with the help of strain gradient elasticity theory and Hamilton principle. Generalized differential quadrature (GDQ) method is employed to solve the problem numerically. The pull-in instability with Casimir force included is then studied. The results reveal that Casimir force, which is a spontaneous force between the two electrodes, can reduce the external applied voltage. With Casimir force incorporated, the pull-in instability occurs without voltage applied when the beam size is in nanoscale. The minimum gap and detachment length can be calculated from the present model for different beam size, which is important for NEMS design. Finally, discussions of size effect induced by the strain gradient terms reveal that the present model is more accurate since size effect play an important role when beam in nanoscale.
The role of the “Casimir force analogue” at the microscopic processes of crystallization and melting
Chuvildeev, V.N. Semenycheva, A.V.
2016-10-15
Melting (crystallization), a phase transition from a crystalline solid to a liquid state, is a common phenomenon in nature. We suggest a new factor, “the Casimir force analogue”, to describe mechanisms of melting and crystallization. The Casimir force analogue is a force occurring between the surfaces of solid and liquid phases of metals caused by different energy density of phonons of these phases. It explains abrupt changes in geometry and thermodynamic parameters at a melting point. “The Casimir force analogue” helps to estimate latent melting heat and to gain an insight into a solid–liquid transition problem.
Bimonte, Giuseppe
2009-10-15
We develop an exact method for computing Casimir forces and the power of radiative heat transfer between two arbitrary nanostructured surfaces out of thermal equilibrium. The method is based on a generalization of the scattering approach recently used in investigations on the Casimir effect. Analogously to the equilibrium case, we find that also out of thermal equilibrium the shape and composition of the surfaces enter only through their scattering matrices. The expressions derived provide exact results in terms of the scattering matrices of the intervening surfaces.
NASA Astrophysics Data System (ADS)
Banishev, Alexandr; Chang, Chia-Cheng; Mohideen, Umar
2012-02-01
The Casimir effect is important in various fields from atomic physics to nanotechnology. According to the Lifshitz theory of the Casimir force, the interaction between two objects depends both on their dielectric permittivity and magenetic permeability. Thus the role of magnetic properties on the Casimir force is interesting particularly due to the possibility of a reduction the Casimir force. In this report we will present the results of a Casimir force measurement between a magnetic material such as nickel coated on SiO2 plate and a Au-coated sphere.
Edge effects in electrostatic calibrations for the measurement of the Casimir force
NASA Astrophysics Data System (ADS)
Wei, Qun; Onofrio, Roberto
2010-05-01
We have performed numerical simulations to evaluate the effect on the capacitance of finite size boundaries realistically present in the parallel plane, sphere-plane, and cylinder-plane geometries. The potential impact of edge effects in assessing the accuracy of the parameters obtained in the electrostatic calibrations of Casimir force experiments is then discussed.
Gross, Markus; Gambassi, Andrea; Dietrich, S
2017-08-01
The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.
NASA Astrophysics Data System (ADS)
Gross, Markus; Gambassi, Andrea; Dietrich, S.
2017-08-01
The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ɛ =4 -d , where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ɛ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two
Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes
Tian, T.; Zheng, T. Y.; Wang, Z. H.; Zhang, X.
2010-07-15
In this article, we consider the dynamic Casimir-Polder force between an atom and a conducting wall in a one-dimensional cavity. Using quasimode theory to describe the dissipation of the electromagnetic fields in the cavity, our investigation shows that the force oscillations are damped in a short time, and tend to a final, steady, negative value. We discuss in detail the effects on the force of the quasimode decay rate, the cavity size, and the atom-wall distance.
Casimir forces in transmission-line circuits: QED and fluctuation-dissipation formalisms
NASA Astrophysics Data System (ADS)
Shahmoon, Ephraim
2017-06-01
It was recently shown that transmission-line waveguides can mediate long-range fluctuation forces between neutral objects, potentially leading to novel Casimir forces in electric circuits. Here we present two approaches for the general description of these forces between electric components embedded in transmission-line circuits. The first, following ordinary quantum electrodynamics (QED), consists of the quantization and scattering theory of voltage and current waves inside transmission lines. The second approach relies on a simple circuit analysis with additional noisy current sources due to resistors in the circuit, as per the fluctuation-dissipation theorem (FDT). We apply the latter approach to derive a general formula for the Casimir force induced by circuit fluctuations between any two impedances. The application of this formula, considering the sign of the resulting force, is discussed. While both QED and FDT approaches are equivalent, we conclude that the latter is simpler to generalize and solve.
Lateral Casimir Force on a Rotating Particle near a Planar Surface.
Manjavacas, Alejandro; Rodríguez-Fortuño, Francisco J; García de Abajo, F Javier; Zayats, Anatoly V
2017-03-31
We study the lateral Casimir force experienced by a particle that rotates near a planar surface. The origin of this force lies in the symmetry breaking induced by the particle rotation in the vacuum and thermal fluctuations of its dipole moment, and therefore, in contrast to lateral Casimir forces previously described in the literature for corrugated surfaces, it exists despite the translational invariance of the planar surface. Working within the framework of fluctuational electrodynamics, we derive analytical expressions for the lateral force and analyze its dependence on the geometrical and material properties of the system. In particular, we show that the direction of the force can be controlled by adjusting the particle-surface distance, which may be exploited as a new mechanism to manipulate nanoscale objects.
How to modify the van der Waals and Casimir forces without change of the dielectric permittivity.
Klimchitskaya, G L; Mohideen, U; Mostepanenko, V M
2012-10-24
We propose a new experiment on the measurement of the Casimir force and its gradient between a Au-coated sphere and two different plates made of doped semiconductors. The concentrations of charge carriers in the plates are chosen slightly below and above the critical density at which the Mott-Anderson insulator-metal transition occurs. We calculate changes in the Casimir force and the Casimir pressure due to the insulator-metal transition using the standard Lifshitz theory and the phenomenological approach neglecting the contribution of free charge carriers in the dielectric permittivity of insulator materials (this approach was recently supported by the measurement data of several experiments). It is demonstrated that for the special selection of semiconductor materials (S- or Se-doped Si, B-doped diamond) the calculation results using the two theoretical approaches differ significantly and the predicted effects are easily detectable using the existing laboratory setups. In the case that the prediction of the phenomenological approach is confirmed, this would open opportunities to modify the van der Waals and Casimir forces with almost no change of room temperature dielectric permittivity.
Nonlocal microscopic theory of Casimir forces at finite temperature
Despoja, V.; Marusic, L.
2011-04-15
The interaction energy between two metallic slabs in the retarded limit at finite temperature is expressed in terms of surface polariton propagators for separate slabs, avoiding the usual matching procedure, with both diamagnetic and paramagnetic excitations included correctly. This enables appropriate treatment of arbitrary electron density profiles and fully nonlocal electronic response, including both collective and single-particle excitations. The results are verified by performing the nonretarded and long-wavelength (local) limits and showing that they reduce to the previously obtained expressions. Possibilities for practical use of the theory are explored by applying it to calculation of various contributions to the Casimir energy between two silver slabs.
Comment on ``Casimir force acting on magnetodielectric bodies embedded in media''
NASA Astrophysics Data System (ADS)
Pitaevskii, L. P.
2006-04-01
It is shown that the Raabe and Welsch [Phys. Rev. A 71, 013814 (2005)] criticism of the Dzyaloshinskii-Lifshitz-Pitaevskii theory of the van der Waals Casimir forces inside a medium is based on misunderstandings. It is explained why and at which conditions one can use the “Minkowski-like” stress tensor for calculations of the forces. The reason why, in my opinion, the approach of Raabe and Welsch is incorrect is discussed.
Nonlinear dynamics of a rack-pinion-rack device powered by the Casimir force.
Miri, MirFaez; Nekouie, Vahid; Golestanian, Ramin
2010-01-01
Using the lateral Casimir force-a manifestation of the quantum fluctuations of the electromagnetic field between objects with corrugated surfaces-as the main force transduction mechanism, a nanomechanical device with rich dynamical behaviors is proposed. The device is made of two parallel racks that are moving in the same direction and a pinion in the middle that couples with both racks via the noncontact lateral Casimir force. The built-in frustration in the device causes it to be very sensitive and react dramatically to minute changes in the geometrical parameters and initial conditions of the system. The noncontact nature of the proposed device could help with the ubiquitous wear problem in nanoscale mechanical systems.
Measurement of the Temperature Dependence of the Casimir-Polder Force
Obrecht, J. M.; Wild, R. J.; Cornell, E. A.; Antezza, M.; Stringari, S.; Pitaevskii, L. P.
2007-02-09
We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure {sup 87}Rb Bose-Einstein condensate a few microns from a dielectric substrate and exciting its dipole oscillation. Changes in the collective oscillation frequency of the magnetically trapped atoms result from spatial variations in the surface-atom force. In our experiment, the dielectric substrate is heated up to 605 K, while the surrounding environment is kept near room temperature (310 K). The effect of the Casimir-Polder force is measured to be nearly 3 times larger for a 605 K substrate than for a room-temperature substrate, showing a clear temperature dependence in agreement with theory.
Rabi interferometry and sensitive measurement of the Casimir-Polder force with ultracold gases
Chwedenczuk, Jan; Piazza, Francesco; Smerzi, Augusto; Pezze, Luca
2010-09-15
We show that Rabi oscillations of a degenerate fermionic or bosonic gas trapped in a double-well potential can be exploited for the interferometric measurement of external forces at micrometer length scales. The Rabi interferometer is less sensitive but easier to implement than the Mach-Zehnder, since it does not require dynamical beam-splitting or recombination processes. As an application we propose a measurement of the Casimir-Polder force acting between the atoms and a dielectric surface. We find that even if the interferometer is fed with a coherent state of relatively small number of atoms, and in the presence of realistic experimental noise, the force might be measured with a sensitivity sufficient to discriminate between thermal and zero-temperature regimes of the Casimir-Polder potential. Higher sensitivities can be reached with bosonic spin squeezed states.
Ultralong-range Casimir-Lifshitz forces mediated by nanowire materials
Maslovski, Stanislav I.; Silveirinha, Mario G.
2010-08-15
Here, we show that the Casimir-Lifshitz force (either attractive or repulsive) between two planar material slabs embedded in a dense array of silver nanowires is an ultralong-range force that decays with the separation of the bodies, a, as 1/a{sup 2}, whereas in an isotropic background it decays as 1/a{sup 4}. It is demonstrated that the nanowires effectively channel the quantum fluctuations of the electromagnetic field through the region between the bodies, boosting in this manner the intensity of the Casimir force at long distances. Moreover, in a configuration involving a stationary planar slab and a spherical object able to slide within the nanowire background (e.g., an air bubble) the dependence of the force on the separation is shown to be 1/a as compared to 1/a{sup 3} in an isotropic background. Our theoretical calculations suggest that a significant repulsive Casimir force can be measured for distances up to 10 {mu}m in such a scenario.
Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results.
Nowakowski, Piotr; Napiórkowski, Marek
2016-06-07
We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to +h1 except for a group of N1 neighboring surface spins where it is equal to -h1. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance L. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for different temperature regimes: below the wetting temperature, between the wetting and the critical temperature, and above the critical temperature. The lateral critical Casimir force acts in the direction opposite to the shift L, and the excess normal force is always attractive. Upon increasing the shift L we observe, depending on the temperature regime, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on L. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for different models of the strip with the same type of inhomogeneity.
Critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results.
Dantchev, Daniel; Krech, Michael
2004-04-01
We present general arguments and construct a stress tensor operator for finite lattice spin models. The average value of this operator gives the Casimir force of the system close to the bulk critical temperature T(c). We verify our arguments via exact results for the force in the two-dimensional Ising model, d -dimensional Gaussian, and mean spherical model with 2
Temperature-independent Casimir-Polder forces in arbitrary geometries
Ellingsen, Simen A.; Buhmann, Stefan Yoshi; Scheel, Stefan
2011-12-15
We prove that the nonretarded Casimir-Polder potential of a particle in an energy eigenstate (hence in thermal nonequilibrium) is independent of the environment temperature for a well-conducting body of arbitrary shape. This is true even when the thermal photon numbers at the relevant atomic transition energies are large. A compact expression is obtained for the temperature-independent potential, which can greatly simplify calculations in nontrivial geometries for experimentally relevant systems such as Rydberg atoms and polar molecules. We give criteria for the validity of our temperature-independent result and derive general expressions for its leading corrections. They are illustrated by numerical studies of a particle near a gold sphere or inside a gold cylindrical cavity.
NASA Astrophysics Data System (ADS)
Dubail, J.; Santachiara, R.; Emig, T.
2017-03-01
Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szegö formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface renormalization group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.
Analytical results on Casimir forces for conductors with edges and tips
Maghrebi, Mohammad F.; Rahi, Sahand Jamal; Emig, Thorsten; Graham, Noah; Jaffe, Robert L.; Kardar, Mehran
2011-01-01
Casimir forces between conductors at the submicron scale are paramount to the design and operation of microelectromechanical devices. However, these forces depend nontrivially on geometry, and existing analytical formulae and approximations cannot deal with realistic micromachinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically wedges and cones. The Casimir interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of microelectromechanical devices. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe. We find an unexpectedly large temperature dependence of the force in the cone tip which is of immediate relevance to experiments.
Comment on ``Casimir force acting on magnetodielectric bodies embedded in media''
NASA Astrophysics Data System (ADS)
Brevik, Iver; Ellingsen, Simen A.
2009-02-01
In a recent paper [Raabe and Welsch, Phys. Rev. A 71, 013814 (2005)] an electromagnetic energy-momentum tensor is suggested as an alternative to the Abraham-Minkowski tensor and is applied to calculations of Casimir forces in planar geometries. We argue that the universality of the suggested tensor is doubtful; application of the Raabe-Welsch theory to a simple example in classical electrodynamics shows that their proposed tensor is unable to describe the situation in a simple way. We also show that modified Casimir forces acting on the cavity medium as prescribed by these authors suffer from problems of definiteness and peculiar properties which call for experimental support before this theory can be regarded as acceptable.
Critical Casimir forces between defects in the 2D Ising model
NASA Astrophysics Data System (ADS)
Nowakowski, P.; Maciołek, A.; Dietrich, S.
2016-12-01
An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a finite group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.
Temperature control of colloidal phases by Critical Casimir forces -- a simulation study
NASA Astrophysics Data System (ADS)
Triet Dang, Minh; Nguyen, Van Duc; Vila Verde, Ana; Bolhuis, Peter; Schall, Peter
2012-02-01
Critical Casimir forces arising from the confinement of critical solvent fluctuations between the surfaces of colloidal particles have recently been shown a promising route to control colloidal assembly. Such forces are strongly temperature dependent, and thus allow for direct temperature control of colloidal interactions. However, colloidal phase transitions controlled by this highly temperature-dependent potential are still poorly understood. Here, we report Monte Carlo simulations of critical Casimir-driven colloidal phase behavior using input potentials directly measured in experiments. We map the gas-liquid coexistence region using Gibbs ensemble simulations and the solid-fluid coexistence boundaries using Gibbs-Duhem integration, and determine the gas-liquid critical point by applying scaling theory. The constructed gas-liquid-solid phase diagram agrees quantitatively with that observed in experiments. Remarkably, the simulated gas-liquid coexistence curve exhibits 3D Ising scaling despite the strong temperature dependence of the pair potentials.
NASA Astrophysics Data System (ADS)
Esteso, Victoria; Carretero-Palacios, Sol; Míguez, Hernán
2016-04-01
We study at thermal equilibrium the effect of temperature deviations around room temperature on the equilibrium distance (deq) at which thin films made of Teflon, silica, or polystyrene immersed in glycerol levitate over a silicon substrate due to the balance of Casimir, gravity, and buoyancy forces. We find that the equilibrium nature (stable or unstable) of deq is preserved under temperature changes, and provide simple rules to predict whether the new equilibrium position will occur closer to or further from the substrate at the new temperature. These rules depend on the static permittivities of all materials comprised in the system ( ɛ0 ( m ) ) and the equilibrium nature of deq. Our designed dielectric configuration is excellent for experimental observation of thermal effects on the Casimir force indirectly detected through the tunable equilibrium distances (with slab thickness and material properties) in levitation mode.
Reanalysis of Casimir force measurements in the 0.6-to-6-{mu}m range
Lamoreaux, S. K.
2010-08-15
A systematic correction for Casimir force measurements is proposed and applied to the results of an experiment that was performed more than a decade ago. This correction brings the experimental results into good agreement with the Drude model of the metallic plates' permittivity. The systematic is due to time-dependent fluctuations in the distance between the plates caused by mechanical vibrations, tilt, or position measurement uncertainty and is similar to the correction for plate roughness.
Manipulation and amplification of the Casimir force through surface fields using helicity.
Dantchev, Daniel; Rudnick, Joseph
2017-04-01
We present both exact and numerical results for the behavior of the Casimir force in O(n) systems with a finite extension L in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems, the Casimir force in certain temperature ranges is of the order of L^{-2}, both above and below the critical temperature, T_{c}, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one-dimensional XY and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle, and the three-dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean-field version of the three-dimensional O(2) model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite-size scaling.
Stable Levitation and Alignment of Compact Objects by Casimir Spring Forces
Rahi, Sahand Jamal; Zaheer, Saad
2010-02-19
We investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium--unlike the direction of the torque--can be predicted based on the sign of the force between two slabs of the same material.
Precision Measurement of the Casimir Force for Au Using a Dynamic Afm
NASA Astrophysics Data System (ADS)
Chang, C.-C.; Banishev, A. A.; Castillo-Garza, R.; Klimchitskaya, G. L.; Mostepanenko, V. M.; Mohideen, U.
2012-07-01
The gradient of the Casimir force between carefully cleaned Au surfaces of a sphere and a plate is measured using a dynamic atomic force microscope in the frequency modulation regime in high vacuum. The electrostatic calibration of the setup did not reveal any effect of patches or surface contaminants. The experimental data for the force gradient are found to be consistent with theory using the plasma model approach over the entire measurement range. The Drude model approach is excluded by the data at separations from 235 to 400 nm at a 67% confidence level.
Thermal and nonthermal signatures of the Unruh effect in Casimir-Polder forces.
Marino, Jamir; Noto, Antonio; Passante, Roberto
2014-07-11
We show that Casimir-Polder forces between two relativistic uniformly accelerated atoms exhibit a transition from the short distance thermal-like behavior predicted by the Unruh effect to a long distance nonthermal behavior, associated with the breakdown of a local inertial description of the system. This phenomenology extends the Unruh thermal response detected by a single accelerated observer to an accelerated spatially extended system of two particles, and we identify the characteristic length scale for this crossover with the inverse of the proper acceleration of the two atoms. Our results are derived separating at fourth order in perturbation theory the contributions of vacuum fluctuations and radiation reaction field to the Casimir-Polder interaction between two atoms moving in two generic stationary trajectories separated by a constant distance and linearly coupled to a scalar field. The field can be assumed in its vacuum state or at finite temperature, resulting in a general method for the computation of Casimir-Polder forces in stationary regimes.
Lamoreaux, S.K.; Buttler, W.T.
2005-03-01
A general analysis of thermal noise in torsion pendulums is presented. The specific case where the torsion angle is kept fixed by electronic feedback is analyzed. This analysis is applied to a recent experiment that employed a torsion pendulum to measure the Casimir force. The ultimate limit to the distance at which the Casimir force can be measured to high accuracy is discussed, and in particular we elaborate on the prospects for measuring the thermal correction.
Casimir-Polder force fluctuations as spatial probes of dissipation in metals
NASA Astrophysics Data System (ADS)
Cherroret, Nicolas; Crépin, Pierre-Philippe; Guérout, Romain; Lambrecht, Astrid; Reynaud, Serge
2017-03-01
We study the spatial fluctuations of the Casimir-Polder force experienced by an atom or a small sphere moved above a metallic plate at fixed separation distance. We demonstrate that unlike the mean force, the magnitude of these fluctuations crucially relies on the relaxation of conduction electron in the metallic bulk, and even achieves values that differ by orders of magnitude depending on the amount of dissipation. We also discover that fluctuations suffer a spectacular decrease at large distances in the case of nonzero temperature.
Cavero-Pelaez, Ines; Milton, Kimball A.; Parashar, Prachi; Shajesh, K. V.
2008-09-15
We calculate the lateral Casimir force between corrugated parallel plates, described by {delta}-function potentials, interacting through a scalar field, using the multiple scattering formalism. The contributions to the Casimir energy due to uncorrugated parallel plates is treated as a background from the outset. We derive the leading- and next-to-leading-order contribution to the lateral Casimir force for the case when the corrugation amplitudes are small in comparison to corrugation wavelengths. We present explicit results in terms of finite integrals for the case of the Dirichlet limit, and exact results for the weak-coupling limit, for the leading- and next-to-leading-orders. The correction due to the next-to-leading contribution is significant. In the weak coupling limit we calculate the lateral Casimir force exactly in terms of a single integral which we evaluate numerically. Exact results for the case of the weak limit allows us to estimate the error in the perturbative results. We show that the error in the lateral Casimir force, in the weak coupling limit, when the next-to-leading order contribution is included is remarkably low when the corrugation amplitudes are small in comparison to corrugation wavelengths. We expect similar conclusions to hold for the Dirichlet case. The analogous calculation for the electromagnetic case should reduce the theoretical error sufficiently for comparison with the experiments.
Global consequences of a local Casimir force: Adhered cantilever
NASA Astrophysics Data System (ADS)
Svetovoy, V. B.; Melenev, A. E.; Lokhanin, M. V.; Palasantzas, G.
2017-07-01
Although stiction is a cumbersome problem for microsystems, it stimulates investigations of surface adhesion. In fact, the shape of an adhered cantilever carries information of the adhesion energy that locks one end to the substrate. We demonstrate here that the system is also sensitive to the dispersion forces that are operative very close to the point of contact, but their contribution to the shape is maximum at about one third of the unadhered length. When the force exceeds a critical value, the cantilever does not lose stability but settles at a smaller unadhered length, whose relation to adhesion energy is only slightly affected by the force. Our calculations suggest the use of adhered cantilevers to measure the dispersion forces at short separations, where other methods suffer from jump-to-contact instability. Simultaneous measurement of the force and adhesion energy allows the separation of the dispersion contribution to the surface adhesion.
Casimir-Polder-like force on an atom outside a Schwarzschild black hole
Zhang Jialin; Yu Hongwei
2011-10-15
We calculate, in the framework of open quantum systems, the ground state energy-level shift for a static two-level atom outside a spherically symmetric black hole in interaction with fluctuating massless scalar fields in the Boulware and Unruh vacuums. We find that the energy-level shift is position dependent and thus gives rise to a force on the atom besides the classical gravitational force. For the case of the Boulware vacuum that represents a star which has not collapsed through its event horizon, this force is attractive near the horizon and is repulsive far away from the black hole with a behavior of r{sup -3}. For the case of the Unruh vacuum which represents a radiating black hole, we find that the contribution to the Casimir-Polder-like force due to the presence of Hawking radiation is always attractive and, remarkably, this attractive force diverges at the event horizon.
Measurement of the Casimir force between Germanium plates using a torsion balance
Dalvit, Diego; Kim, W J; Sushkov, A O; Lamoreaux, S K
2008-01-01
We report the measurement of the Casimir force between Ge plates in a sphere-plane configuration using a torsion balance. We observe that the effective contact potential between the plates varies with their separation distance, resulting in a systematic force. In addition, an unexpected 1/d force is also found in our data that persists even when the electrostatic force between the plates is experimentally minimized by applying a compensating potential. After applying corrections due to these systematic forces, likely of electrostatic origin, our result can be described by the bare permittivity of Ge without conduction, the Drude and the diffusion models for electrical and optical properties of Ge, but not by the plasma model.
Strong Thermal and Electrostatic Manipulation of the Casimir Force in Graphene Multilayers.
Abbas, Chahine; Guizal, Brahim; Antezza, Mauro
2017-03-24
We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage of the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also achieve the anomalous nonmonotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi level. In addition to a strong thermal modulation occurring at short separations, in a region where the force is orders of magnitude larger than the one occurring at large distances, the force can be also adjusted by varying the number of graphene layers as well as their Fermi levels, allowing for relevant force amplifications which can be tuned, very rapidly and in situ, by simply applying an electric potential. Our predictions can be relevant for both Casimir experiments and micro- or nanoelectromechanical systems and in new devices for technological applications.
Strong Thermal and Electrostatic Manipulation of the Casimir Force in Graphene Multilayers
NASA Astrophysics Data System (ADS)
Abbas, Chahine; Guizal, Brahim; Antezza, Mauro
2017-03-01
We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage of the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also achieve the anomalous nonmonotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi level. In addition to a strong thermal modulation occurring at short separations, in a region where the force is orders of magnitude larger than the one occurring at large distances, the force can be also adjusted by varying the number of graphene layers as well as their Fermi levels, allowing for relevant force amplifications which can be tuned, very rapidly and in situ, by simply applying an electric potential. Our predictions can be relevant for both Casimir experiments and micro- or nanoelectromechanical systems and in new devices for technological applications.
Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space
NASA Astrophysics Data System (ADS)
Setare, M. R.
2006-02-01
The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.
Calculation of nonzero-temperature Casimir forces in the time domain
Pan, Kai; Reid, M. T. Homer; McCauley, Alexander P.; Rodriguez, Alejandro W.; White, Jacob K.; Johnson, Steven G.
2011-04-15
We show how to compute Casimir forces at nonzero temperatures with time-domain electromagnetic simulations, for example, using a finite-difference time-domain (FDTD) method. Compared to our previous zero-temperature time-domain method, only a small modification is required, but we explain that some care is required to properly capture the zero-frequency contribution. We validate the method against analytical and numerical frequency-domain calculations, and show a surprising high-temperature disappearance of a nonmonotonic behavior previously demonstrated in a pistonlike geometry.
Dependence of the Direction of the Casimir Force on the Shape of the Boundary
Schaden, Martin
2009-02-13
The Casimir force due to a massless scalar field satisfying Dirichlet boundary conditions may draw a piston into the neck or toward the bulb of a flasklike container. In the worldline formalism this is due to competing contributions to the interaction energy from two types of Brownian bridges. Geometrical subtractions define a finite interaction energy. The procedure does not require regularization and appears well suited for numerical studies. The worldline analysis is robust with respect to variations in the shape of both piston and flask.
Comment on ''Temperature dependence of the Casimir force for lossy bulk media''
Bimonte, G.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2011-09-15
Recently Yampol'skii et al.[Phys. Rev. A 82, 032511 (2010)] advocated that Lifshitz theory is not applicable when the characteristic wavelength of the fluctuating electromagnetic field, responsible for the thermal correction to the Casimir force, is larger than the size of the metal test bodies. It was claimed that this is the case in experiments which exclude Lifshitz theory combined with the Drude model. We calculate the wavelengths of the evanescent waves making the dominant contribution to the thermal correction and we find that they are much smaller than the sizes of the test bodies. The opposite conclusion obtained by the authors arose from confusion between propagating and evanescent waves.
Messina, Riccardo; Antezza, Mauro
2011-10-15
We study the radiative heat transfer and the Casimir-Lifshitz force occurring between two bodies in a system out of thermal equilibrium. We consider bodies of arbitrary shape and dielectric properties, held at two different temperatures and immersed in environmental radiation at a third different temperature. We derive explicit closed-form analytic expressions for the correlations of the electromagnetic field and for the heat transfer and Casimir-Lifshitz force in terms of the bodies' scattering matrices. We then consider some particular cases which we investigate in detail: the atom-surface and the slab-slab configurations.
Rodriguez, Alejandro; Ibanescu, Mihai; Joannopoulos, J. D.; Johnson, Steven G.; Iannuzzi, Davide
2007-09-15
We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising nonmonotonic ''lateral'' force from the walls.
Van der Waals, Casimir, and Lifshitz forces in soft matter
NASA Astrophysics Data System (ADS)
Kats, E. I.
2015-09-01
E M Lifshitz's theory of fluctuation molecular forces (Zh. Eksp. Teor. Fiz., Vol. 29, p. 94, 1955 [Sov. Phys. JETP, Vol. 2, 73, 1956]) and related problems are introduced from a historical perspective. Applications of the theory to soft matter physics are discussed, together with some new predictions (for example, the stability of smectic or cholesteric liquid crystal films).
Casimir Forces and Quantum Friction from Ginzburg Radiation in Atomic Bose-Einstein Condensates.
Marino, Jamir; Recati, Alessio; Carusotto, Iacopo
2017-01-27
We theoretically propose an experimentally viable scheme to use an impurity atom in an atomic Bose-Einstein condensate, in order to realize condensed-matter analogs of quantum vacuum effects. In a suitable atomic level configuration, the collisional interaction between the impurity atom and the density fluctuations in the condensate can be tailored to closely reproduce the electric-dipole coupling of quantum electrodynamics. By virtue of this analogy, we recover and extend the paradigm of electromagnetic vacuum forces to the domain of cold atoms, showing in particular the emergence, at supersonic atomic speeds, of a novel power-law scaling of the Casimir force felt by the atomic impurity, as well as the occurrence of a quantum frictional force, accompanied by the Ginzburg emission of Bogoliubov quanta. Observable consequences of these quantum vacuum effects in realistic spectroscopic experiments are discussed.
Casimir Forces and Quantum Friction from Ginzburg Radiation in Atomic Bose-Einstein Condensates
NASA Astrophysics Data System (ADS)
Marino, Jamir; Recati, Alessio; Carusotto, Iacopo
2017-01-01
We theoretically propose an experimentally viable scheme to use an impurity atom in an atomic Bose-Einstein condensate, in order to realize condensed-matter analogs of quantum vacuum effects. In a suitable atomic level configuration, the collisional interaction between the impurity atom and the density fluctuations in the condensate can be tailored to closely reproduce the electric-dipole coupling of quantum electrodynamics. By virtue of this analogy, we recover and extend the paradigm of electromagnetic vacuum forces to the domain of cold atoms, showing in particular the emergence, at supersonic atomic speeds, of a novel power-law scaling of the Casimir force felt by the atomic impurity, as well as the occurrence of a quantum frictional force, accompanied by the Ginzburg emission of Bogoliubov quanta. Observable consequences of these quantum vacuum effects in realistic spectroscopic experiments are discussed.
A microscopic approach to Casimir and Casimir–Polder forces between metallic bodies
Barcellona, Pablo Passante, Roberto
2015-04-15
We consider the Casimir–Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate the overall two- and three-body contributions to the macroscopic Casimir–Polder and Casimir force, and to compare them with each other, for the two following geometries: metal nanoparticle/half-space and half-space/half-space, where all the materials are assumed perfect conductors. The above evaluation is obtained by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticles). In the case of nanoparticle/half-space, our results fully agree with those that can be extracted from the corresponding macroscopic results, and explicitly show the non-applicability of the pairwise approximation for the geometry considered. In both cases, we find that, while the overall two-body contribution yields an attractive force, the overall three-body contribution is repulsive. Also, they turn out to be of the same order, consistently with the known non applicability of the pairwise approximation. The issue of the rapidity of convergence of the many-body expansion is also briefly discussed.
NASA Astrophysics Data System (ADS)
Farrokhabadi, Amin; Abadian, Naeime; Rach, Randolph; Abadyan, Mohamadreza
2014-09-01
The Casimir force can induce instability and adhesion in freestanding nanostructures. Previous research efforts in this area have exclusively focused on modeling the instability in structures with planar or rectangular cross-section, while, to the best knowledge of the authors, no attention has been paid to investigate this phenomenon for nanowires with circular cross-section. In this study, effects of the Casimir force on the instability and adhesion of freestanding Cylinder-Plate and Cylinder-Cylinder geometries are investigated, which are commonly encountered in real nanodevices. To compute the Casimir force, two approaches, i.e. the proximity force approximation (PFA) for small separations and Dirichlet asymptotic approximation (scattering theory) for large separations, are considered. A continuum mechanics theory is employed, in conjunction with the Euler-beam model, to obtain constitutive equations of the systems. The governing nonlinear constitutive equations of the nanostructures are solved using two different approaches, i.e. the analytical modified Adomian decomposition (MAD) and the numerical finite difference method (FDM). The detachment length and minimum gap, both of which prevent the Casimir force-induced adhesion, are computed for both configurations.
Dalvit, Diego A. R.; Onofrio, Roberto
2009-09-15
We discuss the role of the proximity force approximation in deriving limits to the existence of Yukawian forces--predicted in the submillimeter range by many unification models--from Casimir force experiments using the sphere-plane geometry. Two forms of this approximation are discussed, the first used in most analyses of the residuals from the Casimir force experiments performed so far, and the second recently discussed in this context in R. Decca et al.[Phys. Rev. D 79, 124021 (2009)]. We show that the former form of the proximity force approximation overestimates the expected Yukawa force and that the relative deviation from the exact Yukawa force is of the same order of magnitude, in the realistic experimental settings, as the relative deviation expected between the exact Casimir force and the Casimir force evaluated in the proximity force approximation. This implies both a systematic shift making the actual limits to the Yukawa force weaker than claimed so far, and a degree of uncertainty in the {alpha}-{lambda} plane related to the handling of the various approximations used in the theory for both the Casimir and the Yukawa forces. We further argue that the recently discussed form for the proximity force approximation is equivalent, for a geometry made of a generic object interacting with an infinite planar slab, to the usual exact integration of any additive two-body interaction, without any need to invoke approximation schemes. If the planar slab is of finite size, an additional source of systematic error arises due to the breaking of the planar translational invariance of the system, and we finally discuss to what extent this may affect limits obtained on power-law and Yukawa forces.
Castillo-Garza, R.; Chang, C.-C.; Jimenez, D.; Mohideen, U.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2007-06-15
We propose two experiments on the measurement of the Casimir force acting between a gold coated sphere and semiconductor plates with markedly different charge carrier densities. In the first of these experiments a patterned Si plate is used which consists of two sections of different dopant densities and oscillates in the horizontal direction below a sphere. The measurement scheme in this experiment is differential, i.e., it allows the direct high-precision measurement of the difference of the Casimir forces between the sphere and sections of the patterned plate or the difference of the equivalent pressures between Au and patterned parallel plates with static and dynamic techniques, respectively. The second experiment proposes to measure the Casimir force between the same sphere and a VO{sub 2} film which undergoes the insulator-metal phase transition with the increase of temperature. We report the present status of the interferometer based variable temperature apparatus developed to perform both experiments and present the first results on the calibration and sensitivity. The magnitudes of the Casimir forces and pressures in the experimental configurations are calculated using different theoretical approaches to the description of optical and conductivity properties of semiconductors at low frequencies proposed in the literature. It is shown that the suggested experiments will aid in the resolution of theoretical problems arising in the application of the Lifshitz theory at nonzero temperature to real materials. They will also open new opportunities in nanotechnology.
Casimir friction force and energy dissipation for moving harmonic oscillators. II
NASA Astrophysics Data System (ADS)
Høye, J. S.; Brevik, I.
2011-01-01
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)]). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is finite at finite temperatures, whereas in the case of two oscillators moving with constant relative velocity the force becomes zero at zero temperature, due to slowly varying coupling.
Thermal Casimir-Polder forces on a V-type three-level atom
NASA Astrophysics Data System (ADS)
Xu, Chen-Ran; Xu, Jing-Ping; Al-amri, M.; Zhu, Cheng-Jie; Xie, Shuang-Yuan; Yang, Ya-Ping
2017-09-01
We study the thermal Casimir-Polder (CP) forces on a V-type three-level atom. The competition between the thermal effect and the quantum interference of the two transition dipoles on the force is investigated. To shed light onto the role of the quantum interference, we analyze two kinds of initial states of the atom, i.e., the superradiant state and the subradiant state. Considering the atom being in the thermal reservoir, the resonant CP force arising from the real photon emission dominates in the evolution of the CP force. Under the zero-temperature condition, the quantum interference can effectively modify the amplitude and the evolution of the force, leading to a long-time force or even the cancellation of the force. Our results reveal that in the finite-temperature case, the thermal photons can enhance the amplitude of all force elements, but have no influence on the net resonant CP force in the steady state, which means that the second law of thermodynamics still works. For the ideal degenerate V-type atom with parallel dipoles under the initial subradiant state, the robust destructive quantum interference overrides the thermal fluctuations, leading to the trapping of the atom in the subradiant state and the disappearance of the CP force. However, in terms of a realistic Zeeman atom, the thermal photons play a significant role during the evolution of the CP force. The thermal fluctuations can enhance the amplitude of the initial CP force by increasing the temperature, and weaken the influence of the quantum interference on the evolution of the CP force from the initial superradiant (subradiant) state to the steady state.
NASA Astrophysics Data System (ADS)
Rosa, F. S. S.; Dalvit, D. A. R.; Milonni, P. W.
2010-03-01
The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step toward a better understanding of this situation we consider in this article the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic field in the dielectric. The model leads naturally to expressions for the quantized electric and magnetic fields that are consistent with those obtained in approaches that diagonalize the coupled system of oscillators for the dielectric medium, the reservoir, and the electromagnetic field. It also results in a fluctuation-dissipation relation between the noise polarization and the imaginary part of the permittivity; comparison with the Rytov fluctuation-dissipation relation employed in the well-known Lifshitz theory for the van der Waals (or Casimir) force shows that the Lifshitz theory is actually a classical stochastic electrodynamical theory. The approximate classical expression for the energy density in a band of frequencies at which absorption in a dielectric is negligible is shown to be exact as a spectral thermal equilibrium expectation value in quantum electrodynamic theory. Our main result is the derivation of an expression for the QED energy density of a uniform dispersive, absorbing media in thermal equilibrium. The spectral density of the energy is found to have the same form with or without absorption. We also show how the fluctuation-dissipation theorem ensures a detailed balance of energy exchange between the (absorbing) medium, the reservoir, and the electromagnetic field in thermal equilibrium.
Bezerra, V. B.; Romero, C.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2011-04-01
We report constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the gradient of the Casimir force in the configuration of an Au-coated sphere above a Si plate covered with corrugations of trapezoidal shape. For this purpose, the exact expression for the gradient of Yukawa force in the experimental configuration is derived and compared with that obtained using the proximity force approximation. The reported constraints are of almost the same strength as those found previously from several different experiments on the Casimir force and extend over a wide interaction range from 30 to 1260 nm. It is discussed how to make them stronger by replacing the material of the plate.
NASA Astrophysics Data System (ADS)
Dantchev, Daniel M.; Vassilev, Vassil M.; Djondjorov, Peter A.
2016-09-01
When massless excitations are limited or modified by the presence of material bodies one observes a force acting between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) relief map of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below but close to the finite-size critical point.
Casimir force between a half-space and a plate of finite thickness
NASA Astrophysics Data System (ADS)
Høye, Johan S.; Brevik, Iver
2016-05-01
Zero-frequency Casimir theory is analyzed from different viewpoints, with the aim of obtaining further insight into the delicate Drude-plasma issue that turns up when one considers thermal corrections to the Casimir force. The problem is essentially that the plasma model, physically inferior in comparison to the Drude model since it leaves out dissipation in the material, apparently gives the best results when comparing with recent experiments. Our geometric setup is quite conventional, namely, a dielectric plate separated from a dielectric half-space by a vacuum gap, both media being made of the same material. Our investigation is divided into the following categories: (1) Making use of the statistical-mechanical method developed by J. S. Høye and I. Brevik [Physica A (Amsterdam, Neth.) 259, 165 (1998), 10.1016/S0378-4371(98)00249-0], implying that the quantized electromagnetic field is replaced by interaction between dipole moments oscillating in harmonic potentials, we first verify that the Casimir force is in agreement with the Drude prediction. No use of Fresnel's reflection coefficients is made at this stage. (2) Then turning to the field-theoretic description implying use of the reflection coefficients, we derive results in agreement with the forgoing when first setting the frequency equal to zero, before letting the permittivity become large. With the plasma relation the reflection coefficient for TE zero-frequency modes depends on the component of the wave vector parallel to the surfaces and lies between 0 and 1. This contradicts basic electrostatic theory. (3) Turning to high-permeability magnetic materials, the TE zero-frequency mode describes the static magnetic field in the same way the TM zero-frequency modes describe the static electric fields in electrostatics. With the plasma model magnetic fields, except for a small part, cannot pass through metals; that is, metals effectively become superconductors. However, recent experimental results clearly
Dohm, Volker
2014-09-01
Thermodynamic Casimir forces of film systems in the O(n) universality classes with Dirichlet boundary conditions are studied below bulk criticality. Substantial progress is achieved in resolving the long-standing problem of describing analytically the pronounced minimum of the scaling function observed experimentally in ^{4}He films (n=2) by Garcia and Chan [Phys. Rev. Lett. 83, 1187 (1999)] and in Monte Carlo simulations for the three-dimensional Ising model (n=1) by O. Vasilyev et al. [Europhys. Lett. 80, 60009 (2007)]. Our finite-size renormalization-group approach describes the film systems as the limit of finite-slab systems with vanishing aspect ratio. This yields excellent agreement with the depth and the position of the minimum for n=1 and semiquantitative agreement with the minimum for n=2. Our theory also predicts a pronounced minimum for the n=3 Heisenberg universality class.
Electromagnetic Casimir forces of parabolic cylinder and knife-edge geometries
Graham, Noah; Shpunt, Alexander; Kardar, Mehran; Emig, Thorsten; Rahi, Sahand Jamal; Jaffe, Robert L.
2011-06-15
An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the 'knife-edge' limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.
NASA Astrophysics Data System (ADS)
Zhou, Wenting; Yu, Hongwei
2014-09-01
We study the energy shift and the Casimir-Polder force of an atom out of thermal equilibrium near the surface of a dielectric substrate. We first generalize, adopting the local source hypothesis, the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji [J. Phys. (Paris) 43, 1617 (1982), 10.1051/jphys:0198200430110161700; J. Phys. (Paris) 45, 637 (1984), 10.1051/jphys:01984004504063700], which separates the contributions of thermal fluctuations and radiation reaction to the energy shift and allows a distinct treatment of atoms in the ground and excited states, to the case out of thermal equilibrium, and then we use the generalized formalism to calculate the energy shift and the Casimir-Polder force of an isotropically polarizable neutral atom. We identify the effects of the thermal fluctuations that originate from the substrate and the environment and discuss in detail how the Casimir-Polder force out of thermal equilibrium behaves in three different distance regions in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, with special attention devoted to the distinctive features as opposed to thermal equilibrium. In particular, we recover the distinctive behavior of the atom-wall force out of thermal equilibrium at large distances in the low-temperature limit recently found in a different theoretical framework, and furthermore we give a concrete region where this behavior holds.
NASA Astrophysics Data System (ADS)
Hasenbusch, Martin
2010-04-01
We discuss the relation of the excess specific heat, the excess energy per area, and the thermodynamic Casimir force in thin films. A priori these quantities depend on the reduced temperature t and the thickness L0 of the film. However finite-size scaling theory predicts that the scaling functions h″(x) , h'(x) , and θ(x) of these quantities depend only on the combination x=t[L0/ξ0]1/ν , where ν is the critical exponent and ξ0 the amplitude of the correlation length. Furthermore, the finite-size scaling function θ(x) of the thermodynamic Casimir force per area can be expressed in terms of the scaling functions h'(x) and h(x) of the excess energy per area and the excess free energy per area. Here we study this relation at the example of thin films of the improved two-component ϕ4 model on the simple cubic lattice. Note that this model undergoes a second-order phase transition that belongs to the three-dimensional XY universality class. First we simulate films with periodic boundary conditions in the short direction and a thickness up to L0=13 lattice spacings. We find that even for these rather thin films, the predictions of finite-size scaling are well satisfied. We repeat the analysis for films with free boundary conditions. To this end we use Monte Carlo data for the energy per area obtained in previous work. It turns our that corrections to scaling caused by the boundary conditions are very prominent in this case. Only by taking into account these corrections we are able to obtain θ(x) from the excess energy. Finally we repeat this exercise using experimental data for the excess specific heat of H4e films near the λ transition. The finite-size scaling behavior of the excess specific heat is governed by h″(x) , which is proportional to the scaling function f2 discussed in the literature.
Harber, D.M.; Obrecht, J.M.; McGuirk, J.M.; Cornell, E.A.
2005-09-15
We have performed a measurement of the Casimir-Polder force using a magnetically trapped {sup 87}Rb Bose-Einstein condensate. By detecting perturbations of the frequency of center-of-mass oscillations of the condensate perpendicular to the surface, we are able to detect this force at a distance {approx}5 {mu}m, significantly farther than has been previously achieved, and at a precision approaching that needed to detect the modification due to thermal radiation. Additionally, this technique provides a limit for the presence of non-Newtonian gravity forces in the {approx}1 {mu}m range.
Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
NASA Astrophysics Data System (ADS)
Hobrecht, Hendrik; Hucht, Alfred
2017-02-01
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.
Casimir frictional drag force between a SiO2 tip and a graphene-covered SiO2 substrate
NASA Astrophysics Data System (ADS)
Volokitin, A. I.
2016-12-01
The possibility of the mechanical detection of the Casimir friction using noncontact force microscope is discussed. On a SiO2 tip situated above a graphene-covered SiO2 substrate will act the frictional drag force mediated by a fluctuating electromagnetic field produced by a current in the graphene sheet. This friction force will produce the bending of the cantilever, which can be measured by state-of-art noncontact force microscope. Both the thermal and quantum contributions to the Casimir frictional drag force can be studied using this experimental setup. This result paves the way for the mechanical detection of the Casimir friction and for the application of the frictional drag effect in micro- and nanoelectromechanical devices (MEMS and NEMS).
NASA Astrophysics Data System (ADS)
Bimonte, G.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2017-09-01
The rigorous finite-temperature QED formalism of the polarization tensor is used to study the combined effect of nonzero mass gap m and chemical potential μ on the Casimir force and its thermal correction in the experimentally relevant configuration of a Au sphere interacting with a real graphene sheet or with graphene-coated dielectric substrates made of different materials. It is shown that for both a free-standing graphene sheet and for graphene-coated substrates the magnitude of the Casimir force decreases as m is increased, while it increases as μ is increased, indicating that these parameters act in opposite directions. According to our results, the impact of m and/or μ on the Casimir force for graphene-coated plates is much smaller than for a free-standing graphene sheet. Furthermore, computations show that the Casimir force is much stronger for graphene-coated substrates than for a free-standing graphene sample, but the thermal correction and its fractional weight in the total force are smaller in the former case. These results are applied to a differential setup that was recently proposed to observe the giant thermal effect in the Casimir force for graphene. We show that this experiment remains feasible even after taking into account the influence of the nonzero mass-gap and chemical potential of real graphene samples. Possible further applications of the obtained results are discussed.
Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges.
Dean, David S; Podgornik, Rudolf
2014-03-01
We investigate the dynamics of thermal Casimir interactions between plates described within a living conductor model, with embedded mobile anions and cations, whose density field obeys a stochastic partial differential equation which can be derived starting from the Langevin equations of the individual particles. This model describes the thermal Casimir interaction in the same way that the fluctuating dipole model describes van der Waals interactions. The model is analytically solved in a Debye-Hückel-like approximation. We identify several limiting dynamical regimes where the time dependence of the thermal Casimir interactions can be obtained explicitly. Most notably we find a regime with diffusive scaling, even though the charges are confined to the plates and do not diffuse into the intervening space, which makes the diffusive scaling difficult to anticipate and quite unexpected on physical grounds.
Esteso, Victoria; Carretero-Palacios, Sol; Míguez, Hernán
2015-03-12
We report on the theoretical analysis of equilibrium distances in real plane-parallel systems under the influence of Casimir and gravity forces at thermal equilibrium. Due to the balance between these forces, thin films of Teflon, silica, or polystyrene in a single-layer configuration and immersed in glycerol stand over a silicon substrate at certain stable or unstable positions depending on the material and the slab thickness. Hybrid systems containing silica and polystyrene, materials which display Casimir forces and equilibrium distances of opposite nature when considered individually, are analyzed in either bilayer arrangements or as composite systems made of a homogeneous matrix with small inclusions inside. For each configuration, equilibrium distances and their stability can be adjusted by fine-tuning of the volume occupied by each material. We find the specific conditions under which nanolevitation of realistic films should be observed. Our results indicate that thin films of real materials in plane-parallel configurations can be used to control suspension or stiction phenomena at the nanoscale.
2015-01-01
We report on the theoretical analysis of equilibrium distances in real plane-parallel systems under the influence of Casimir and gravity forces at thermal equilibrium. Due to the balance between these forces, thin films of Teflon, silica, or polystyrene in a single-layer configuration and immersed in glycerol stand over a silicon substrate at certain stable or unstable positions depending on the material and the slab thickness. Hybrid systems containing silica and polystyrene, materials which display Casimir forces and equilibrium distances of opposite nature when considered individually, are analyzed in either bilayer arrangements or as composite systems made of a homogeneous matrix with small inclusions inside. For each configuration, equilibrium distances and their stability can be adjusted by fine-tuning of the volume occupied by each material. We find the specific conditions under which nanolevitation of realistic films should be observed. Our results indicate that thin films of real materials in plane-parallel configurations can be used to control suspension or stiction phenomena at the nanoscale. PMID:26405466
Reply to "Comment on 'Casimir force in the O(n→∞) model with free boundary conditions' ".
Dantchev, Daniel; Bergknoff, Jonathan; Rudnick, Joseph
2015-02-01
The preceding Comment raises a few points concerning our paper [Phys. Rev. E 89, 042116 (2014)]. In this Reply we stress that although Diehl et al. [Europhys. Lett. 100, 10004 (2012) and Phys. Rev. E 89, 062123 (2014)] use three different models to study the Casimir force for the O(n→∞) model with free boundary conditions we study a single model over the entire range of temperatures from above the bulk critical temperature T(c) to absolute temperatures down to T=0. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the Comment, we make no claim for the superiority of our model over any of those considered by Diehl et al. [Europhys. Lett. 100, 10004 (2012) and Phys. Rev. E 89, 062123 (2014)]. We also present additional evidence supporting our conclusion in Dantchev et al. [Phys. Rev. E 89, 042116 (2014)] that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as L grows and remains accurate for values of the ratio T/T(c) that become closer and closer to unity, whereas T remains well outside of the critical region.
Bimonte, Giuseppe
2011-04-15
The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for submicron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute {epsilon}(i{xi}). By making important improvements to the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersion relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulas presented in this paper permit us to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need for uncontrolled data extrapolations toward zero frequency that are necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate the viability of the dispersion formulas presented in this paper.
Klimchitskaya, G. L.; Romero, C.
2010-12-01
We discuss the possibility of obtaining stronger constraints on non-Newtonian gravity from measuring the gradient of the Casimir force between a cylinder and a plate. The exact analytical expression for the Yukawa-type force in a cylinder-plate configuration is obtained, as well as its asymptotic expansions. The gravitational force is compared with the Casimir force acting between a cylinder and a plate. Numerical computations for the prospective constraints on non-Newtonian gravity are performed for a recently proposed experiment using a microfabricated cylinder attached to a micromachined oscillator. Specifically, it is shown that this experiment is expected to obtain up to 70 times stronger constraints on the Yukawa-type force, compared with the best present day limits, over a wide interaction range from 12.5 to 630 nm.
NASA Astrophysics Data System (ADS)
Chen, Xiang
2012-11-01
We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases: de Sitter space-time, de Sitter space-time with weak gravitational field and Schwarzschild-de Sitter space-time. In de Sitter space-time the resulting net force follows the square inverse law but unfortunately it is too weak to be measurable due to the large universe radius. By introducing a weak gravitational field into the de Sitter space-time, we find that the net force can now be split into two parts, one is the gravitational force due to the induced effective mass between the two plates and the other one is generated by the metric structure of de Sitter space-time. In order to investigate the vacuum fluctuation force on the rigid cavity under strong gravitational field, we perform a similar analysis in Schwarzschild-de Sitter space-time and results are obtained in three different limits. The most interesting one is when the cavity gets closer to the horizon of a blackhole, square inverse law is recovered and the repulsive force due to negative energy/mass of the cavity now has an observable strength. More importantly the force changes from being repulsive to attractive when the cavity crosses the event horizon, so that the energy/mass of the cavity switches the sign, which suggests the unusual time direction inside the event horizon.
NASA Astrophysics Data System (ADS)
Rajabpour, M. A.
2016-11-01
We classify the sign of the critical Casimir force between two finite objects separated by a large distance in the two-dimensional systems that can be described by conformal field theory (CFT). Specifically, we show that, as long as the smallest scaling dimension present in the spectrum of the system is smaller than one, the sign of the force is independent of the shape of the objects and can be determined by the elements of the modular S matrix of the CFT. The provided formula for the sign of the force indicates that the force is always attractive for equal boundary conditions, independent of the shape of the objects. However, different boundary conditions can lead to attractive or repulsive forces. Using the derived formula, we prove the known results regarding the Ising model and the free bosons. As new examples, we give detailed results regarding the Q =3 state Potts model and the compactified bosons. For example, for the latter model we show that the Dirichlet boundary condition does not always lead to an attractive force.
NASA Astrophysics Data System (ADS)
Razmi, H.; Abdollahi, M.
2008-11-01
We want to introduce an atomic pendulum whose driving force (torque) is due to the quantum vacuum fluctuations. Applying the well-known Casimir-Polder effect to a special configuration (a combined structure of an atomic nanostring and a conducting plate), an atomic pendulum (Casimir atomic pendulum) is designed. Using practically acceptable data corresponding to the already known world of nanotechnology and based on reasonable/reliable numerical estimates, the period of oscillation for the pendulum is computed. This pendulum can be considered as both a new micro(nano)-electromechanical system and a new simple vacuum machine. Its design may be considered as a first step towards realizing the visualized vacuum (Casimir) clock!
NASA Astrophysics Data System (ADS)
Latella, Ivan; Ben-Abdallah, Philippe; Biehs, Svend-Age; Antezza, Mauro; Messina, Riccardo
2017-05-01
A general theory of photon-mediated energy and momentum transfer in N -body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equilibrium temperatures in such systems. An analogous formulation is introduced to quantify momentum transfer coefficients describing Casimir-Lifshitz forces out of thermal equilibrium. Forces at thermal equilibrium are readily obtained as a particular case. As an illustration of this general theoretical framework, we show on three-body systems how the presence of a fourth slab can impact equilibrium temperatures in heat-transfer problems and equilibrium positions resulting from the forces acting on the system.
Flachi, Antonino; Tanaka, Takahiro
2009-12-15
We consider the Casimir effect between two parallel plates localized on a brane. We argue that in order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the Kaluza-Klein modes. When the bulk field configuration is such that no massless mode appears in the spectrum, as, for instance, when the higher dimensional field obeys twisted boundary conditions across the branes, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. However, when the bulk field is massless and strongly coupled to brane matter, the model is already excluded without resorting to any Casimir force experiment. The case which is in principle interesting is when the massless mode is not localized on the visible brane. We illustrate a method to compute the Casimir energy between two parallel plates, localized on the visible brane, approximating the Kaluza-Klein spectrum by truncation at the first excited mode. We treat this case by considering a pistonlike configuration and introduce a small parameter, {epsilon}, that takes into account the relative amplitude of the zero-mode wave function on the visible brane with respect to the massive excitation. We find that the Casimir energy is suppressed by two factors: at lowest order in {epsilon}, the correction to the Casimir energy comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in {epsilon} follows, instead, a power-law suppression due to the small wave-function overlap of the zero mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.
Casimir repulsion in moving media
Maslovski, Stanislav I.
2011-08-15
The Casimir-Lifshitz interaction emerging from the relative movement of layers in stratified dielectric media (e.g., nonuniformly moving fluids) is considered. It is shown that such movement may result in a repulsive Casimir-Lifshitz force exerted on the layers, with the simplest possible structure consisting of three adjacent layers of the same dielectric medium at zero temperature, where the middle one is stationary and the other two are sliding along a direction parallel to the interfaces of the layers.
Casimir Repulsion between Metallic Objects in Vacuum
2010-08-27
Casimir Repulsion between Metallic Objects in Vacuum Michael Levin,1 Alexander P. McCauley,2 Alejandro W. Rodriguez,2 M. T. Homer Reid,2 and Steven G...Received 19 March 2010; published 26 August 2010) We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir ...12.20.m Introduction.—The Casimir force between two parallel metal plates in vacuum is always attractive. A longstanding question is whether this is
From optical lattice clocks to the measurement of forces in the Casimir regime
Wolf, Peter; Lemonde, Pierre; Bize, Sebastien; Landragin, Arnaud; Clairon, Andre; Lambrecht, Astrid
2007-06-15
We describe an experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations (0.6-10 {mu}m). In this range the dominant potential is the QED interaction (Casimir-Polder and van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa-type potentials with sub-millimeter range, arising from new physics related to gravity. The proposed setup is very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state-of-the-art measurement of the phase difference and a duration of the superposition of about 0.1 s, we expect to be able to measure the potential difference between separated states with an uncertainty of {approx_equal}10{sup -4} Hz. An analysis of systematic effects for different atoms and surfaces indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and surface material. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by {>=} 2 orders of magnitude, while gaining up to four orders of magnitude on the best present limits on new interactions in the range between 100 nm and 100 {mu}m.
Fundamental optics: On-chip Casimir effect
NASA Astrophysics Data System (ADS)
Milton, Kimball A.
2017-02-01
Measurement of the forces that arise from quantum vacuum fluctuations between closely spaced surfaces typically requires large apparatus, making applications difficult. Now, an experiment on a silicon chip to measure the Casimir force has been realized.
Mode Contributions to the Casimir Effect
NASA Astrophysics Data System (ADS)
Intravaia, F.; Henkel, C.
2010-04-01
Applying a sum-over-modes approach to the Casimir interaction between two plates with finite conductivity, we isolate and study the contributions of surface plasmons and Foucault (eddy current) modes. We show in particular that for the TE-polarization eddy currents provide a repulsive force that cancels, at high temperatures, the Casimir free energy calculated with the plasma model.
Casimir-Lifshitz Theory and Metamaterials
Rosa, F. S. S.; Dalvit, D. A. R.; Milonni, P. W.
2008-05-09
Based on a generalization of the Lifshiftz theory, we calculate Casimir forces involving magnetodielectric and possibly anisotropic metamaterials, focusing on the possibility of repulsive forces. It is found that Casimir repulsion decreases with magnetic dissipation, and even a small Drude background in metallic-based metamaterials acts to make attractive a Casimir force that would otherwise be predicted to be repulsive. The sign of the force also depends sensitively on the degree of optical anisotropy of the metamaterial and on the form of the frequency dependency of the magnetic response.
Casimir experiments showing saturation effects
Sernelius, Bo E.
2009-10-15
We address several different Casimir experiments where theory and experiment disagree. First out is the classical Casimir force measurement between two metal half spaces; here both in the form of the torsion pendulum experiment by Lamoreaux and in the form of the Casimir pressure measurement between a gold sphere and a gold plate as performed by Decca et al.; theory predicts a large negative thermal correction, absent in the high precision experiments. The third experiment is the measurement of the Casimir force between a metal plate and a laser irradiated semiconductor membrane as performed by Chen et al.; the change in force with laser intensity is larger than predicted by theory. The fourth experiment is the measurement of the Casimir force between an atom and a wall in the form of the measurement by Obrecht et al. of the change in oscillation frequency of a {sup 87}Rb Bose-Einstein condensate trapped to a fused silica wall; the change is smaller than predicted by theory. We show that saturation effects can explain the discrepancies between theory and experiment observed in all these cases.
Casimir force for a scalar field in a single brane world
Linares, R.; Morales-Tecotl, H. A.; Pedraza, O.
2010-02-10
Vacuum force is an interesting low energy test for brane worlds due to its dependence on field's modes and its role in submillimeter gravity experiments. In this contribution we obtain the scalar field vacuum force between two parallel plates lying in the brane of a Randall-Sundrum scenario extended by p compact dimensions (RSII-{sub p}). We obtain the force using the Green's function technique and we compare our results with the ones obtained by using the zeta function regularization method. As a result we obtain agreement in the expression for the force independently of the method used, thus we solve a previous discrepancy between the two approaches.
Dynamical approach to the Casimir effect.
Rodriguez-Lopez, P; Brito, R; Soto, R
2011-03-01
Casimir forces can appear between intrusions placed in different media driven by several fluctuation mechanisms, either in equilibrium or out of it. Herein, we develop a general formalism to obtain such forces from the dynamical equations of the fluctuating medium, the statistical properties of the driving noise, and the boundary conditions of the intrusions (which simulate the interaction between the intrusions and the medium). As a result, an explicit formula for the Casimir force over the intrusions is derived. This formalism contains the thermal Casimir effect as a particular limit and generalizes the study of the Casimir effect to such systems through their dynamical equations, with no appeal to their Hamiltonian, if any exists. In particular, we study the Casimir force between two infinite parallel plates with Dirichlet or Neumann boundary conditions, immersed in several media with finite correlation lengths (reaction-diffusion system, liquid crystals, and two coupled fields with non-Hermitian evolution equations). The driving Gaussian noises have vanishing or finite spatial or temporal correlation lengths; in the first case, equilibrium is reobtained and finite correlations produce nonequilibrium dynamics. The results obtained show that, generally, nonequilibrium dynamics leads to Casimir forces, whereas Casimir forces are obtained in equilibrium dynamics if the stress tensor is anisotropic.
Casimir stress in an inhomogeneous medium
Philbin, T.G. Xiong, C.; Leonhardt, U.
2010-03-15
The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.
Dalvit, Diego A; Kim, W J; Borwn-hayes, M; Brownell, J H; Onofrio, R
2008-01-01
In a recent Comment, Decca et al. [Phys. Rev. A 79, 026101 (2009)] discussed the origin of the anomalies recently reported by us in Phys. Rev. A 78, 036102(R) (2008). Here we restate our view corroborated by their considerations that quantitative geometrical and electrostatic characterizations of the conducting surfaces (a topic not discussed explicitly in the literature until very recently) are critical for the assessment of precision and accuracy of the demonstration of the Casimir force and for deriving meaningful limits on the existence of Yukawian components possibly superimposed to the Newtonian gravitational interaction.
Theoretical ingredients of a Casimir analog computer.
Rodriguez, Alejandro W; McCauley, Alexander P; Joannopoulos, John D; Johnson, Steven G
2010-05-25
We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green's function are well known, so one might expect that any experimental measurement of the Green's function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.
Theoretical ingredients of a Casimir analog computer
Rodriguez, Alejandro W.; McCauley, Alexander P.; Joannopoulos, John D.; Johnson, Steven G.
2010-01-01
We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green’s function are well known, so one might expect that any experimental measurement of the Green’s function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required. PMID:20460309
Structural Anisotropy and Orientation-Induced Casimir Repulsion in Fluids
2011-05-10
PHYSICAL REVIEW A 83, 052503 (2011) Structural anisotropy and orientation-induced Casimir repulsion in fluids Alexander P. McCauley,1 F. S. S. Rosa...Massachusetts 02139, USA (Received 22 September 2010; published 10 May 2011) In this work we theoretically consider the Casimir force between two...the dependence of the exact Casimir force between the arrays under both lateral translations and rotations. Although typically the force between such
NASA Astrophysics Data System (ADS)
Joulain, K.; Henkel, C.; Greffet, J.-J.
2006-10-01
Nous évaluons la force de Casimir entre deux surfaces planes métalliques constituées d'argent. Nous prenons, pour effectuer cette évaluation, des propriétés optiques de l'argent à différentes températures [1]. Nous montrons que cette dépendance en température modifie la force de Casimir (de 0.2%) y compris à des distances inférieures à la longueur d'onde thermique.
Fermions on the low-buckled honey-comb structured lattice plane and classical Casimir-Polder force
NASA Astrophysics Data System (ADS)
Goswami, Partha
2016-05-01
We start with the well-known expression for the vacuum polarization and suitably modify it for 2+1-dimensional spin-orbit coupled (SOC) fermions on the low-buckled honey-comb structured lattice plane described by the low-energy Liu-Yao-Feng-Ezawa (LYFE) model Hamiltonian involving the Dirac matrices in the chiral representation obeying the Clifford algebra. The silicene and germanene fit this description suitably. They have the Dirac cones similar to those of graphene and SOC is much stronger. The system could be normal or ferromagnetic in nature. The silicene turns into the latter type if there is exchange field arising due to the proximity coupling to a ferromagnet (FM) such as depositing Fe atoms to the silicene surface. For the silicene, we find that the many-body effects considerably change the bare Coulomb potential by way of the dependence of the Coulomb propagator on the real-spin, iso-spin and the potential due to an electric field applied perpendicular to the silicene plane. The computation aspect of the Casimir-Polder force (CPF) needs to be investigated in this paper. An important quantity in this process is the dielectric response function (DRF) of the material. The plasmon branch was obtained by finding the zeros of DRF in the long-wavelength limit. This leads to the plasmon frequencies. We find that the collective charge excitations at zero doping, i.e., intrinsic plasmons, in this system, are absent in the Dirac limit. The valley-spin-split intrinsic plasmons, however, come into being in the case of the massive Dirac particles with characteristic frequency close to 10 THz. Our scheme to calculate the Casimir-Polder interaction (CPI) of a micro-particle with a sheet involves replacing the dielectric constant of the sample in the CPI expression obtained on the basis of the Lifshitz theory by the static DRF obtained using the expressions for the polarization function we started with. Though the approach replaces a macroscopic constant by a microscopic
Casimir piston for massless scalar fields in three dimensions
Edery, Ariel
2007-05-15
We study the Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in a three-dimensional cavity with sides of arbitrary lengths a, b, and c where a is the plate separation. We obtain an exact expression for the Casimir force on the piston valid for any values of the three lengths. As in the electromagnetic case with perfect-conductor conditions, we find that the Casimir force is negative (attractive) regardless of the values of a, b, and c. Though cases exist where the interior contributes a positive (repulsive) Casimir force, the total Casimir force on the piston is negative when the exterior contribution is included. We also obtain an alternative expression for the Casimir force that is useful computationally when the plate separation a is large.
Casimir pistons with hybrid boundary conditions
Zhai Xianghua; Li Xinzhou
2007-08-15
The Casimir effect giving rise to an attractive or repulsive force between the configuration boundaries that confine the massless scalar field is reexamined for one- to three-dimensional pistons in this paper. Especially, we consider Casimir pistons with hybrid boundary conditions, where the boundary condition on the piston is Neumann and those on other surfaces are Dirichlet. We show that the Casimir force on the piston is always repulsive, in contrast with the same problem where the boundary conditions are Dirichlet on all surfaces.
Bulk Casimir densities and vacuum interaction forces in higher dimensional brane models
Saharian, Aram A.
2006-03-15
Vacuum expectation value of the energy-momentum tensor and the vacuum interaction forces are evaluated for a massive scalar field with general curvature coupling parameter satisfying Robin boundary conditions on two codimension one parallel branes embedded in (D+1)-dimensional background spacetime AdS{sub D{sub 1}}{sub +1}x{sigma} with a warped internal space {sigma}. The vacuum energy-momentum tensor is presented as a sum of boundary-free, single brane-induced, and interference parts. The latter is finite everywhere including the points on the branes and is exponentially small for large interbrane distances. Unlike to the purely anti-de Sitter (AdS) bulk, the part induced by a single brane, in addition to the distance from the brane, depends also on the position of the brane in the bulk. The asymptotic behavior of this part is investigated for the points near the brane and for the position of the brane close to the AdS horizon and AdS boundary. The contribution of Kaluza-Klein modes along {sigma} is discussed in various limiting cases. The vacuum forces acting on the branes are presented as a sum of the self-action and interaction terms. The first one contains well-known surface divergences and needs a further renormalization. The interaction forces between the branes are finite for all nonzero interbrane distances and are investigated as functions of the brane positions and the length scale of the internal space. We show that there is a region in the space of parameters in which these forces are repulsive for small distances and attractive for large distances. As an example, the case {sigma}=S{sup D{sub 2}} is considered. An application to the higher dimensional generalization of the Randall-Sundrum brane model with arbitrary mass terms on the branes is discussed. Taking the limit with infinite curvature radius for the AdS bulk, from the general formulas we derive the results for two parallel Robin plates on background of R{sup (D{sub 1},1)}x{sigma} spacetime.
Fermionic Casimir effect with helix boundary condition
NASA Astrophysics Data System (ADS)
Zhai, Xiang-hua; Li, Xin-zhou; Feng, Chao-Jun
2011-05-01
In this paper, we consider the fermionic Casimir effect under a new type of space-time topology using the concept of quotient topology. The relation between the new topology and that in Feng and Li (Phys. Lett. B 691:167, 2010), Zhai et al. (Mod. Phys. Lett. A 26:669, 2011) is something like that between a Möbius strip and a cylindric. We obtain the exact results of the Casimir energy and force for the massless and massive Dirac fields in the ( D+1)-dimensional space-time. For both massless and massive cases, there is a Z 2 symmetry for the Casimir energy. To see the effect of the mass, we compare the result with that of the massless one and we found that the Casimir force approaches the result of the force in the massless case when the mass tends to zero and vanishes when the mass tends to infinity.
Three-dimensional Casimir piston for massive scalar fields
Lim, S.C. Teo, L.P.
2009-08-15
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/a{sup 4} when a{yields}0{sup +} and decays exponentially when a{yields}{infinity}. 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.
Casimir effect in swimmer suspensions.
Parra-Rojas, C; Soto, R
2014-07-01
We show that the Casimir effect can emerge in microswimmer suspensions. In principle, two effects conspire against the development of Casimir effects in swimmer suspensions. First, at low Reynolds number, the force on any closed volume vanishes, but here the relevant effect is the drag by the flow produced by the swimmers, which can be finite. Second, the fluid velocity and the pressure are linear on the swimmer force dipoles, and averaging over the swimmer orientations would lead to a vanishing effect. However, being that the suspension is a discrete system, the noise terms of the coarse-grained equations depend on the density, which itself fluctuates, resulting in effective nonlinear dynamics. Applying the tools developed for other nonequilibrium systems to general coarse-grained equations for swimmer suspensions, the Casimir drag is computed on immersed objects, and it is found to depend on the correlation function between the rescaled density and dipolar density fields. By introducing a model correlation function with medium-range order, explicit expressions are obtained for the Casimir drag on a body. When the correlation length is much larger than the microscopic cutoff, the average drag is independent of the correlation length, with a range that depends only on the size of the immersed bodies.
Casimir effect in swimmer suspensions
NASA Astrophysics Data System (ADS)
Parra-Rojas, C.; Soto, R.
2014-07-01
We show that the Casimir effect can emerge in microswimmer suspensions. In principle, two effects conspire against the development of Casimir effects in swimmer suspensions. First, at low Reynolds number, the force on any closed volume vanishes, but here the relevant effect is the drag by the flow produced by the swimmers, which can be finite. Second, the fluid velocity and the pressure are linear on the swimmer force dipoles, and averaging over the swimmer orientations would lead to a vanishing effect. However, being that the suspension is a discrete system, the noise terms of the coarse-grained equations depend on the density, which itself fluctuates, resulting in effective nonlinear dynamics. Applying the tools developed for other nonequilibrium systems to general coarse-grained equations for swimmer suspensions, the Casimir drag is computed on immersed objects, and it is found to depend on the correlation function between the rescaled density and dipolar density fields. By introducing a model correlation function with medium-range order, explicit expressions are obtained for the Casimir drag on a body. When the correlation length is much larger than the microscopic cutoff, the average drag is independent of the correlation length, with a range that depends only on the size of the immersed bodies.
Detecting Casimir torque with an optically levitated nanorod
NASA Astrophysics Data System (ADS)
Xu, Zhujing; Li, Tongcang
2017-09-01
The linear momentum and angular momentum of virtual photons of quantum vacuum fluctuations can induce the Casimir force and the Casimir torque, respectively. While the Casimir force has been measured extensively, the Casimir torque has not been observed experimentally though it was predicted over 40 years ago. Here we propose to detect the Casimir torque with an optically levitated nanorod near a birefringent plate in vacuum. The axis of the nanorod tends to align with the polarization direction of the linearly polarized optical tweezer. When its axis is not parallel or perpendicular to the optical axis of the birefringent crystal, it will experience a Casimir torque that shifts its orientation slightly. We calculate the Casimir torque and Casimir force acting on a levitated nanorod near a birefringent crystal. We also investigate the effects of thermal noise and photon recoils on the torque and force detection. We prove that a levitated nanorod in vacuum will be capable of detecting the Casimir torque under realistic conditions, and will be an important tool in precision measurements.
Nonequilibrium Tuning of the Thermal Casimir Effect.
Dean, David S; Lu, Bing-Sui; Maggs, A C; Podgornik, Rudolf
2016-06-17
In net-neutral systems correlations between charge fluctuations generate strong attractive thermal Casimir forces and engineering these forces to optimize nanodevice performance is an important challenge. We show how the normal and lateral thermal Casimir forces between two plates containing Brownian charges can be modulated by decorrelating the system through the application of an electric field, which generates a nonequilibrium steady state with a constant current in one or both plates, reducing the ensuing fluctuation-generated normal force while at the same time generating a lateral drag force. This hypothesis is confirmed by detailed numerical simulations as well as an analytical approach based on stochastic density functional theory.
Nonequilibrium Tuning of the Thermal Casimir Effect
NASA Astrophysics Data System (ADS)
Dean, David S.; Lu, Bing-Sui; Maggs, A. C.; Podgornik, Rudolf
2016-06-01
In net-neutral systems correlations between charge fluctuations generate strong attractive thermal Casimir forces and engineering these forces to optimize nanodevice performance is an important challenge. We show how the normal and lateral thermal Casimir forces between two plates containing Brownian charges can be modulated by decorrelating the system through the application of an electric field, which generates a nonequilibrium steady state with a constant current in one or both plates, reducing the ensuing fluctuation-generated normal force while at the same time generating a lateral drag force. This hypothesis is confirmed by detailed numerical simulations as well as an analytical approach based on stochastic density functional theory.
Giant Casimir effect in fluids in nonequilibrium steady states.
Kirkpatrick, T R; Ortiz de Zárate, J M; Sengers, J V
2013-06-07
In this Letter, we consider the fluctuation-induced force exerted between two plates separated by a distance L in a fluid with a temperature gradient. We predict that for a range of distances L, this nonequilibrium force is anomalously large compared to other Casimir forces. The physical reason is that correlations in a nonequilibrium fluid are generally of longer range than other correlations, even than those near an equilibrium critical point. This giant Casimir force is related to a divergent Burnett coefficient that characterizes an Onsager cross effect between the pressure and the temperature gradient. The predicted Casimir force should be detectable with currently available experimental techniques.
Thermal Casimir interaction between two magnetodielectric plates
Geyer, B.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2010-03-01
We investigate the thermal Casimir interaction between two magnetodielectric plates made of real materials. On the basis of the Lifshitz theory, it is shown that for diamagnets and for paramagnets in the broad sense (with exception of ferromagnets) the magnetic properties do not influence the magnitude of the Casimir force. For ferromagnets, taking into account the realistic dependence of magnetic permeability on frequency, we conclude that the impact of magnetic properties on the Casimir interaction arises entirely from the contribution of the zero-frequency term in the Lifshitz formula. The computations of the Casimir free energy and pressure are performed for the configurations of two plates made of ferromagnetic metals (Co and Fe), for one plate made of ferromagnetic metal and the other of nonmagnetic metal (Au), for two ferromagnetic dielectric plates (on the basis of polystyrene), and for a ferromagnetic dielectric plate near a nonmagnetic metal plate. The dielectric permittivity of metals is described using both the Drude and the plasma model approaches. It is shown that the Casimir repulsion through the vacuum gap can be realized in the configuration of a ferromagnetic dielectric plate near a nonmagnetic metal plate described by the plasma model. In all cases considered, the respective analytical results in the asymptotic limit of large separations between the plates are obtained. The impact of the magnetic phase transition through the Curie temperature on the Casimir interaction is considered. In conclusion, we propose several experiments allowing to determine whether the magnetic properties really influence the Casimir interaction and to independently verify the Drude and plasma model approaches to the thermal Casimir force.
Casimir interaction of strained graphene
NASA Astrophysics Data System (ADS)
Bordag, M.; Fialkovsky, I.; Vassilevich, D.
2017-08-01
We calculate the Casimir interaction of two freestanding graphene samples under uniaxial strain. Our approach fully takes retardation and dispersion into account and is based on quantum field theoretical expressions for conductivities in terms of the polarization operator. Contrary to some recent results the force shows a rather weak dependence on the realistic values of strain, changing just by a few percent in its maximum as compared to the non-strained case.
Is zero-point energy physical? A toy model for Casimir-like effect
NASA Astrophysics Data System (ADS)
Nikolić, Hrvoje
2017-08-01
Zero-point energy is generally known to be unphysical. Casimir effect, however, is often presented as a counterexample, giving rise to a conceptual confusion. To resolve the confusion we study foundational aspects of Casimir effect at a qualitative level, but also at a quantitative level within a simple toy model with only 3 degrees of freedom. In particular, we point out that Casimir vacuum is not a state without photons, and not a ground state for a Hamiltonian that can describe Casimir force. Instead, Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformation, and it is a ground state only for an effective Hamiltonian describing Casimir plates at a fixed distance. At the fundamental microscopic level, Casimir force is best viewed as a manifestation of van der Waals forces.
NASA Astrophysics Data System (ADS)
Quach, James Q.
2015-02-01
We derive the gravitonic Casimir effect with nonidealized boundary conditions. This allows the quantification of the gravitonic contribution to the Casimir effect from real bodies. We quantify the meagerness of the gravitonic Casimir effect in ordinary matter. We also quantify the enhanced effect produced by the speculated Heisenberg-Couloumb (HC) effect in superconductors, thereby providing a test for the validity of the HC theory, and, consequently, the existence of gravitons.
Quach, James Q
2015-02-27
We derive the gravitonic Casimir effect with nonidealized boundary conditions. This allows the quantification of the gravitonic contribution to the Casimir effect from real bodies. We quantify the meagerness of the gravitonic Casimir effect in ordinary matter. We also quantify the enhanced effect produced by the speculated Heisenberg-Couloumb (HC) effect in superconductors, thereby providing a test for the validity of the HC theory, and, consequently, the existence of gravitons.
Casimir interactions for anisotropic magnetodielectric metamaterials
Da Rosa, Felipe S; Dalvit, Diego A; Milonni, Peter W
2008-01-01
We extend our previous work on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces.
Casimir effect on graphene resonator
NASA Astrophysics Data System (ADS)
Inui, Norio
2016-03-01
We theoretically investigated the influence of the Casimir effect on mechanical properties of a graphene resonator, where a graphene sheet is located in parallel with a perfectly conducting plate. The Casimir force arising from this effect strongly attracts a graphene sheet to a perfectly conducting plate and increases the tension of a graphene sheet as the separation distance between them decreases. The maximum vertical displacement of a graphene sheet to the substrate increases obeying a power law of a separation distance with an exponent of 4/3 as the separation distance decreases. For small separation distances, the Casimir force is excessively strong for the graphene sheet to maintain a free-standing shape, consequently resulting in the adhesion of the sheet to the substrate below a critical separation distance. The resonant frequency increases over a wide range as the separation distance decreases for large separation distances. However, it then rapidly decreases for small separations and converges to zero at a critical separation. These various behaviors enable the control of a graphene resonator.
NASA Astrophysics Data System (ADS)
Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor
2016-04-01
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z <0 and rises like zα, α >0 , for z >0 . Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).
NASA Astrophysics Data System (ADS)
Edison, John R.; Tasios, Nikos; Belli, Simone; Evans, Robert; van Roij, René; Dijkstra, Marjolein
2015-01-01
From experimental studies, it is well known that colloidal particles suspended in a near-critical binary solvent exhibit interesting aggregation phenomena, often associated with colloidal phase transitions and assumed to be driven by long-ranged solvent-mediated (SM) interactions (critical Casimir forces), set by the (diverging) correlation length of the solvent. We present the first simulation and theoretical study of an explicit model of a ternary mixture that mimics this situation. Both the effective SM pair interactions and the full ternary phase diagram are determined for Brownian disks suspended in an explicit two-dimensional supercritical binary liquid mixture. Gas-liquid and fluid-solid transitions are observed in a region that extends well away from criticality of the solvent reservoir. We discuss to what extent an effective pair-potential description can account for the phase behavior we observe. Our study provides a fresh perspective on how proximity to the critical point of the solvent reservoir might influence colloidal self-assembly.
Edison, John R; Tasios, Nikos; Belli, Simone; Evans, Robert; van Roij, René; Dijkstra, Marjolein
2015-01-23
From experimental studies, it is well known that colloidal particles suspended in a near-critical binary solvent exhibit interesting aggregation phenomena, often associated with colloidal phase transitions and assumed to be driven by long-ranged solvent-mediated (SM) interactions (critical Casimir forces), set by the (diverging) correlation length of the solvent. We present the first simulation and theoretical study of an explicit model of a ternary mixture that mimics this situation. Both the effective SM pair interactions and the full ternary phase diagram are determined for Brownian disks suspended in an explicit two-dimensional supercritical binary liquid mixture. Gas-liquid and fluid-solid transitions are observed in a region that extends well away from criticality of the solvent reservoir. We discuss to what extent an effective pair-potential description can account for the phase behavior we observe. Our study provides a fresh perspective on how proximity to the critical point of the solvent reservoir might influence colloidal self-assembly.
NASA Astrophysics Data System (ADS)
Frassino, Antonia M.; Nicolini, Piero; Panella, Orlando
2017-09-01
In this paper we present the un-Casimir effect, namely the study of the Casimir energy in the presence of an unparticle component in addition to the electromagnetic field contribution. The distinctive feature of the un-Casimir effect is a fractalization of metallic plates. This result emerges through a new dependence of the Casimir energy on the plate separation that scales with a continuous power controlled by the unparticle dimension. As long as the perfect conductor approximation is valid, we find bounds on the unparticle scale that are independent of the effective coupling constant between the scale invariant sector and ordinary matter. We find regions of the parameter space such that for plate distances around 5 μm and larger the un-Casimir bound wins over the other bounds.
First-principles study of Casimir repulsion in metamaterials.
Yannopapas, Vassilios; Vitanov, Nikolay V
2009-09-18
We examine theoretically the Casimir effect between a metallic plate and several types of magnetic metamaterials in pursuit of Casimir repulsion, by employing a rigorous multiple-scattering theory for the Casimir effect. We first examine metamaterials in the form of two-dimensional lattices of inherently nonmagnetic spheres such as spheres made from materials possessing phonon-polariton and exciton-polariton resonances. Although such systems are magnetically active in infrared and optical regimes, the force between finite slabs of these materials and metallic slabs is plainly attractive since the effective electric permittivity is larger than the magnetic permeability for the studied spectrum. When lattices of magnetic spheres made from superparamagnetic composites are employed, we achieve not only Casimir repulsion but almost total suppression of the Casimir effect itself in the micrometer scale.
First-Principles Study of Casimir Repulsion in Metamaterials
Yannopapas, Vassilios; Vitanov, Nikolay V.
2009-09-18
We examine theoretically the Casimir effect between a metallic plate and several types of magnetic metamaterials in pursuit of Casimir repulsion, by employing a rigorous multiple-scattering theory for the Casimir effect. We first examine metamaterials in the form of two-dimensional lattices of inherently nonmagnetic spheres such as spheres made from materials possessing phonon-polariton and exciton-polariton resonances. Although such systems are magnetically active in infrared and optical regimes, the force between finite slabs of these materials and metallic slabs is plainly attractive since the effective electric permittivity is larger than the magnetic permeability for the studied spectrum. When lattices of magnetic spheres made from superparamagnetic composites are employed, we achieve not only Casimir repulsion but almost total suppression of the Casimir effect itself in the micrometer scale.
Role of surface plasmons in the Casimir effect
Intravaia, F.; Henkel, C.; Lambrecht, A.
2007-09-15
In this paper we study the role of surface plasmon modes in the Casimir effect. The Casimir energy can be written as a sum over the modes of a real cavity and one may identify two sorts of modes, two evanescent surface plasmon modes and propagative modes. As one of the surface plasmon modes becomes propagative for some choice of parameters we adopt an adiabatic mode definition where we follow this mode into the propagative sector and count it together with the surface plasmon contribution, calling this contribution 'plasmonic'. We evaluate analytically the contribution of the plasmonic modes to the Casimir energy. Surprisingly we find that this becomes repulsive for intermediate and large mirror separations. The contribution of surface plasmons to the Casimir energy plays a fundamental role not only at short but also at large distances. This suggests possibilities to tailor the Casimir force via a manipulation of the surface plasmons properties.
Casimir effect for regions with broken symmetry of boundaries
Zayaev, Yu.B.; Kazakov, A.Ya.; Mostepanenko, V.M.; Trunov, N.N.
1989-01-01
A method is proposed for computing corrections to the Casimir force caused by a broken symmetry of the boundaries. The values of these corrections are obtained for a parallelepiped in the case of scalar and electromagnetic fields.
Quantum field theory of the Casimir effect for real media
Mostepanenko, V.M.; Trunov, N.N.
1985-11-01
The quantum field theory is developed for the corrections to the Casimir force arising when the field penetrates the material of the plates. A new type of divergence arising from the corresponding modification of the boundary conditions is analyzed. General expressions are obtained for the vacuum energy of the electromagnetic field in the space between nonideal plates, and the actual corrections to the Casimir force are calculated in first-order perturbation theory in the penetration depth.
Casimir friction: relative motion more generally.
Høye, Johan S; Brevik, Iver
2015-06-03
This paper extends our recent study on Casimir friction forces for dielectric plates moving parallel to each other (Høye and Brevik 2014 Eur. Phys. J. D 68 61), to a case where the plates are no longer restricted to rectilinear motion. Part of the mathematical formalism thereby becomes more cumbersome, but reduces in the end to the form that we expected to be the natural one in advance. As an example, we calculate the Casimir torque on a planar disc rotating with constant angular velocity around its vertical symmetry axis next to another plate.
Repulsive and attractive Casimir interactions in liquids
Phan, Anh D.; Viet, N. A.
2011-12-15
The Casimir interactions in solid-liquid-solid systems as a function of separation distance have been studied by the Lifshitz theory. The dielectric permittivity functions for a wide range of materials are described by Drude, Drude-Lorentz, and oscillator models. We find that the Casimir forces between gold and silica or MgO materials are both repulsive and attractive. We also find the stable forms for the systems. Our studies would provide good guidance for future experimental studies on dispersion interactions.
Valchev, Galin; Dantchev, Daniel
2015-07-01
We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance L from each other, confining some fluctuating fluid medium, say a nonpolar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called (+,+) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization-group sense. Under such conditions, one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system L(crit) for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T, the chemical potential of the fluid μ, or L. The last implies that by choosing specific materials for the slabs, coatings, and the fluid for L≲L(crit) one can realize repulsive Casimir force with nonuniversal behavior which, upon increasing L, gradually turns into an attractive one described by a universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L≫L(crit). We present arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can
NASA Astrophysics Data System (ADS)
Valchev, Galin; Dantchev, Daniel
2015-07-01
We study, using general scaling arguments and mean-field type calculations, the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance L from each other, confining some fluctuating fluid medium, say a nonpolar one-component fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials ensuring the so-called (+,+) boundary conditions. The slabs, on the other hand, influence the fluid by long-range competing dispersion potentials, which represent irrelevant interactions in renormalization-group sense. Under such conditions, one usually expects attractive Casimir force governed by universal scaling function, pertinent to the extraordinary surface universality class of Ising type systems, to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given threshold thickness of the system Lcrit for a suitable set of slabs-fluid and fluid-fluid coupling parameters the competition between the effects due to the coatings and the slabs can result in sign change of the Casimir force acting between the surfaces confining the fluid when one changes the temperature T , the chemical potential of the fluid μ , or L . The last implies that by choosing specific materials for the slabs, coatings, and the fluid for L ≲Lcrit one can realize repulsive Casimir force with nonuniversal behavior which, upon increasing L , gradually turns into an attractive one described by a universal scaling function, depending only on the relevant scaling fields related to the temperature and the excess chemical potential, for L ≫Lcrit . We present arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force. It can
NASA Astrophysics Data System (ADS)
Valchev, Galin; Dantchev, Daniel
2017-08-01
We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The latter arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar one-component fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab and between two spherical colloid particles. We do that using general scaling arguments and mean-field-type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance L from each other, confining the fluctuating fluid medium characterized by its temperature T and chemical potential μ . The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particles influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters, the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes T , μ , or L , in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding
Valchev, Galin; Dantchev, Daniel
2017-08-01
We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The latter arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar one-component fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab and between two spherical colloid particles. We do that using general scaling arguments and mean-field-type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance L from each other, confining the fluctuating fluid medium characterized by its temperature T and chemical potential μ. The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particles influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters, the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes T, μ, or L, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding
Roberts, D.C.; Pomeau, Y.
2005-09-30
We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.
NASA Astrophysics Data System (ADS)
Ashourvan, Arash; Faez Miri, Mir; Golestanian, Ramin
2007-11-01
As the technological advances lead to miniaturization of mechanical devices, engineers face new challenges that are brought about by the fundamentally different rules that apply at small scales. One of the biggest problems in small machines is the excessive wear of the many surfaces that work in contact with each other, which severely constrains the durability of such machine parts. Here, a force that is caused by the quantum fluctuations of electromagnetic field— known as the lateral Casimir force—is employed to propose a design for a potentially wear-proof rack and pinion with no contact, which can be miniaturized to nano-scale. We demonstrate that both uniform and harmonic lateral motion of the rack can be converted into unidirectional rotation of the pinion. The robustness of the design is studied by exploring the relation between the pinion velocity and the rack velocity in the different domains of the parameter space. The effects of friction and added external load are also examined.
An ``Anatomic approach" to study the Casimir effect
NASA Astrophysics Data System (ADS)
Intravaia, Francesco; Haakh, Harald; Henkel, Carsten
2010-03-01
The Casimir effect, in its simplest definition, is a quantum mechanical force between two objects placed in vacuum. In recent years the Casimir force has been the object of an exponentially growing attention both from theorists and experimentalists. A new generation of experiments paved the way for new challenges and spotted some shadows in the comparison to theory. Here we are going to isolate different contributions to the Casimir interaction and perform a detailed study to shine new light on this phenomenon. As an example, the contributions of Foucault (eddy current) modes will be discussed in different configurations. This ``anatomic approach'' allows to clearly put into evidence special features and to explain unusual behaviors. This brings new physical understanding on the undergoing physical mechanisms and suggests new ways to engineer the Casimir effect.
Casimir energy between media-separated cylinders: The scalar case
Lombardo, F. C.; Mazzitelli, F. D.; Villar, P. I.; Dalvit, D. A. R.
2010-10-15
We derive exact expressions for the Casimir scalar interaction energy between media-separated eccentric dielectric cylinders and for the media-separated cylinder-plane geometry using a mode-summation approach. Similarly to the electromagnetic Casimir-Lifshitz interaction energy between fluid-separated planar plates, the force between cylinders is attractive or repulsive depending on the relative values of the permittivities of the three intervening media.
Electromagnetic Casimir piston in higher-dimensional spacetimes
Teo, L. P.
2011-05-15
We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form MxN, where M is the four-dimensional Minkowski spacetime and N is an n-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in M is large. It is found that if the separation between the plates is much smaller than the size of N, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the (4+n)-dimensional Minkowski spacetime. However, if the size of N is much smaller than the separation between the plates, the leading term of the Casimir force is 1+h/2 times the Casimir force on a pair of large parallel plates in the four-dimensional Minkowski spacetime, where h is the first Betti number of N. In the limit the manifold N vanishes, one does not obtain the Casimir force in the four-dimensional Minkowski spacetime if h is nonzero. Therefore the data obtained from Casimir experiments suggest that the first Betti number of the extra dimensions should be zero.
Quantum spring from the Casimir effect
NASA Astrophysics Data System (ADS)
Feng, Chao-Jun; Li, Xin-Zhou
2010-07-01
The Casimir effect arises not only in the presence of material boundaries but also in space with nontrivial topology. In this Letter, we choose a topology of the flat (D + 1)-dimensional spacetime, which causes the helix boundary condition for a Hermitian massless scalar field. Especially, Casimir effect for a massless scalar field on the helix boundary condition is investigated in two and three dimensions by using the zeta function techniques. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio r of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it quantum spring. When r is large, this force behaves like the Newton's law of universal gravitation in the leading order. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio r. Both forces are attractive and their behaviors are the same in two and three dimensions.
Perfect magnetic conductor Casimir piston in d+1 dimensions
Edery, Ariel; Marachevsky, Valery
2008-07-15
Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC's, and Casimir experiments involving structures that approximate PMC's may be carried out in the not-too-distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in d+1 dimensions. The PMC Casimir energy is explicitly evaluated by summing over p+1-dimensional Dirichlet energies where p ranges from 2 to d inclusively. We derive two exact d-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in 3+1 dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest.
Perfect magnetic conductor Casimir piston in d+1 dimensions
NASA Astrophysics Data System (ADS)
Edery, Ariel; Marachevsky, Valery
2008-07-01
Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC’s, and Casimir experiments involving structures that approximate PMC’s may be carried out in the not-too-distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in d+1 dimensions. The PMC Casimir energy is explicitly evaluated by summing over p+1-dimensional Dirichlet energies where p ranges from 2 to d inclusively. We derive two exact d-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in 3+1 dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest.
The Casimir effect: From quantum to critical fluctuations
NASA Astrophysics Data System (ADS)
Gambassi, Andrea
2009-04-01
The Casimir effect in quantum electrodynamics (QED) is perhaps the best-known example of fluctuation-induced long-ranged force acting on objects (conducting plates) immersed in a fluctuating medium (quantum electromagnetic field in vacuum). A similar effect emerges in statistical physics, where the force acting, e.g., on colloidal particles immersed in a binary liquid mixture is affected by the classical thermal fluctuations occurring in the surrounding medium. The resulting Casimir-like force acquires universal features upon approaching a critical point of the medium and becomes long-ranged at criticality. In turn, this universality allows one to investigate theoretically the temperature dependence of the force via representative models and to stringently test the corresponding predictions in experiments. In contrast to QED, the Casimir force resulting from critical fluctuations can be easily tuned with respect to strength and sign by surface treatments and temperature control. We present some recent advances in the theoretical study of the universal properties of the critical Casimir force arising in thin films. The corresponding predictions compare very well with the experimental results obtained for wetting layers of various fluids. We discuss how the Casimir force between a colloidal particle and a planar wall immersed in a binary liquid mixture has been measured with femto-Newton accuracy, comparing these experimental results with the corresponding theoretical predictions.
Fluctuations, Dissipation and the Dynamical Casimir Effect
NASA Astrophysics Data System (ADS)
Dalvit, Diego A. R.; Neto, Paulo A. Maia; Mazzitelli, Francisco Diego
Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leading to a new kind of friction mechanism without mechanical contact. In this paper, we review recent advances on the dynamical Casimir and non-contact friction effects, highlighting their common physical origin.
Casimir effect between pinned particles in two-dimensional jammed systems.
Liétor-Santos, Juan-José; Burton, Justin C
2017-02-08
The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.
Casimir energy in Kerr space-time
NASA Astrophysics Data System (ADS)
Sorge, F.
2014-10-01
We investigate the vacuum energy of a scalar massless field confined in a Casimir cavity moving in a circular equatorial orbit in the exact Kerr space-time geometry. We find that both the orbital motion of the cavity and the underlying space-time geometry conspire in lowering the absolute value of the (renormalized) Casimir energy ⟨ɛvac⟩ren , as measured by a comoving observer, with respect to whom the cavity is at rest. This, in turn, causes a weakening in the attractive force between the Casimir plates. In particular, we show that the vacuum energy density ⟨ɛvac⟩ren→0 when the orbital path of the Casimir cavity comes close to the corotating or counter-rotating circular null orbits (possibly geodesic) allowed by the Kerr geometry. Such an effect could be of some astrophysical interest on relevant orbits, such as the Kerr innermost stable circular orbits, being potentially related to particle confinement (as in some interquark models). The present work generalizes previous results obtained by several authors in the weak field approximation.
Casimir entropy for magnetodielectrics.
Klimchitskaya, G L; Korikov, C C
2015-06-03
We find the analytic expressions for the Casimir free energy, entropy and pressure at low temperature in the configuration of two parallel plates made of magnetodielectic material. The cases of constant and frequency-dependent dielectic permittivity and magnetic permeability of the plates are considered. Special attention is paid to the account of dc conductivity. It is shown that in the case of finite static dielectric permittivity and magnetic permeability the Nernst heat theorem for the Casimir entropy is satisfied. If the dc conductivity is taken into account, the Casimir entropy goes to a positive nonzero limit depending on the parameters of a system when the temperature vanishes, i.e. the Nernst theorem is violated. The experimental situation is also discussed.
Classical Casimir interaction of a perfectly conducting sphere and plate
NASA Astrophysics Data System (ADS)
Bimonte, Giuseppe
2017-03-01
We study the Casimir interaction between a perfectly conducting sphere and plate in the classical limit of high temperatures. By taking the small-distance expansion of the exact scattering formula, we compute the leading correction to the Casimir energy beyond the commonly employed proximity force approximation. We find that for a sphere of radius R at a distance d from the plate the correction is of the form ln2(d /R ), in agreement with indications from recent large-scale numerical computations. We develop a fast-converging numerical scheme for computing the Casimir interaction to high precision, based on bispherical partial waves, and we verify that the short-distance formula provides precise values of the Casimir energy also for fairly large distances.
Onsager-Casimir relations revisited
Hubmer, G.F.; Titulaer, U.M.
1987-10-01
The authors study the fate of the Onsager-Casimir reciprocity relations for a continuous system when some of its variables are eliminated adiabatically. Just as for discrete systems, deviations appear in correction terms to the reduced evolution equation that are of higher order in the time scale ratio. The deviations are not removed by including correction terms to the coarse-grained thermodynamic potential. However, via a reformulation of the theory, in which the central role of the thermodynamic potential is taken over by an associated Lagrangian-type expression, they arrive at a modified form of the Onsager-Casimir relations that survives the adiabatic elimination procedure. There is a simple relation between the time evolution of the redefined thermodynamic forces and that of the basic thermodynamic variables; this relation also survives the adiabatic elimination. The formalism is illustrated by explicit calculations for the Klein-Kramers equation, which describes the phase space distribution of Brownian particles, and for the corrected Smoluchowski equation derived from it by adiabatic elimination of the velocity variable. The symmetry relation for the latter leads to a simple proof that the reality of the eigenvalues of the simple Smoluchowski equation is not destroyed by the addition of higher order corrections, at least not within the framework of a formal perturbation expansion in the time scale ratio.
Casimir Effect in de Sitter Spacetime
NASA Astrophysics Data System (ADS)
Saharian, A. A.
2011-06-01
The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.
Casimir Effect in de Sitter Spacetime
NASA Astrophysics Data System (ADS)
Saharian, A. A.
The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background space-time decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.
Optical and Casimir effects in topological materials
NASA Astrophysics Data System (ADS)
Wilson, Justin H.
Two major electromagnetic phenomena, magneto-optical effects and the Casimir effect, have seen much theoretical and experimental use for many years. On the other hand, recently there has been an explosion of theoretical and experimental work on so-called topological materials, and a natural question to ask is how such electromagnetic phenomena change with these novel materials. Specifically, we will consider are topological insulators and Weyl semimetals. When Dirac electrons on the surface of a topological insulator are gapped or Weyl fermions in the bulk of a Weyl semimetal appear due to time-reversal symmetry breaking, there is a resulting quantum anomalous Hall effect (2D in one case and bulk 3D in the other, respectively). For topological insulators, we investigate the role of localized in-gap states which can leave their own fingerprints on the magneto-optics and can therefore be probed. We have shown that these states resonantly contribute to the Hall conductivity and are magneto-optically active. For Weyl semimetals we investigate the Casimir force and show that with thickness, chemical potential, and magnetic field, a repulsive and tunable Casimir force can be obtained. Additionally, various values of the parameters can give various combinations of traps and antitraps. We additionally probe the topological transition called a Lifshitz transition in the band structure of a material and show that in a Casimir experiment, one can observe a non-analytic "kink'' in the Casimir force across such a transition. The material we propose is a spin-orbit coupled semiconductor with large g-factor that can be magnetically tuned through such a transition. Additionally, we propose an experiment with a two-dimensional metal where weak localization is tuned with an applied field in order to definitively test the effect of diffusive electrons on the Casimir force---an issue that is surprisingly unresolved to this day. Lastly, we show how the time-continuous coherent state
Critical Casimir interactions between Janus particles.
Labbé-Laurent, M; Dietrich, S
2016-08-21
Recently there has been strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve a directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a laterally homogeneous substrate as well as a substrate with a chemical step. We have used the Derjaguin approximation and compared it with results from full mean field theory. A modification of the Derjaguin approximation turns out to be generally reliable. Based on this approach we have derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.
Casimir interactions between graphene sheets and metamaterials
Drosdoff, D.; Woods, Lilia M.
2011-12-15
The Casimir force between graphene sheets and metamaterials is studied. Theoretical results based on the Lifshitz theory for layered, planar, two-dimensional systems in media are presented. We consider graphene-graphene, graphene-metamaterial, and metal-graphene-metamaterial configurations. We find that quantum effects of the temperature-dependent force are not apparent until the submicron range. In contrast to results with bulk dielectric and bulk metallic materials, no Casimir repulsion is found when graphene is placed on top of a magnetically active metamaterial substrate, regardless of the strength of the low-frequency magnetic response. In the case of the metal-graphene-metamaterial setting, repulsion between the metamaterial and the metal-graphene system is possible only when the dielectric response from the metal contributes significantly.
Casimir interactions between scatterers in metallic carbon nanotubes
Zhabinskaya, Dina; Mele, E. J.
2009-10-15
We study interactions between localized scatterers on metallic carbon nanotubes by a mapping onto a one-dimensional Casimir problem. Backscattering of electrons between localized scattering potentials mediates long-range forces between them. We model spatially localized scatterers by local and nonlocal potentials and treat simultaneously the effects of intravalley and intervalley backscattering. We find that the long-range forces between scatterers exhibit the universal power-law decay of the Casimir force in one dimension, with prefactors that control the sign and strength of the interaction. These prefactors are nonuniversal and depend on the symmetry and degree of localization of the scattering potentials. We find that local potentials inevitably lead to a coupled valley scattering problem, though by contrast nonlocal potentials lead to two decoupled single-valley problems in a physically realized regime. The Casimir effect due to two-valley scattering potentials is characterized by the appearance of spatially periodic modulations of the force.
Exact solution for the Casimir stress in a spherically symmetric medium
Leonhardt, Ulf; Simpson, William M. R.
2011-10-15
We calculated the stress of the quantum vacuum, the Casimir stress, in a spherically symmetric medium, Maxwell's fish eye, surrounded by a perfect mirror and derived an exact analytic solution. Our solution questions the idea that the Casimir force of a spherical mirror is repulsive--we found an attractive stress in the medium that diverges at the mirror.
Casimir Repulsion between Metallic Objects in Vacuum
Levin, Michael; McCauley, Alexander P.; Rodriguez, Alejandro W.; Reid, M. T. Homer; Johnson, Steven G.
2010-08-27
We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.
Casimir effect, quantum fluctuations and related topics
NASA Astrophysics Data System (ADS)
Hushwater, Velvel Shaia
Casimir forces are the very long-range (retarded) forces between electrically neutral systems. Such forces may be thought of as arising from the quantum fluctuations of the electromagnetic field. Contrary to popular opinion such forces need not be attractive. After giving a foundation of the method of the change in the 'zero-point energy' we show how other methods to compute Casimir forces follow from it. We consider the repulsion between electric and magnetic dipoles induced by vacuum fluctuations of electromagnetic field. The calculation are made by the use of the Heisenberg picture operators and by the stochastic electrodynamics approach. We present a purely geometrical proof of the image method, and use it to discuss the Casimir interaction between an atom and a plate. We study the Casimir repulsion between a perfectly conducting and an infinitely permeable plate with the radiation pressure approach. This example illustrates how a repulsive force arises as a consequence of the redistribution of vacuum-field modes corresponding to specific boundary conditions. We show that result is independent of a cutoff function. Discussing the connection with perturbation theory, we prove the negativity of the leading order shift in the ground state. The Casimir effect supports the reality of the 'zero- point energy.' To clarify this we present a novel approach to quantum theory, based on the principle of the quantization of the ensemble-averaged action variable. This quantization leads to the probabilistic description of coordinates and momentum as random variables, which satisfy the uncertainty relation. Using such variables we show that the 'quantum momentum function' must satisfy the Riccati differential equation, which can be converted to the Schrodinger equation for the Ψ function. We derive also the form of basic operators and the rule for probabilities in quantum mechanics. We show that the approach leads to a simple interpretation of gauge invariance, and discuss
A robust superconducting setup to probe the thermal Casimir effect.
Bimonte, Giuseppe
2015-06-03
We describe a superconducting Casimir apparatus inspired by a recently proposed setup involving magnetic surfaces (Bimonte G 2014 Phys. Rev. Lett. 112 240401). The present setup consists of a superconducting Nb sphere and a flat gold plate including in its interior a superconducting Nb strip. The experimental scheme involves a differential measurement of the Casimir force at a point of the gold plate above the Nb strip and away from it. We show that similar to the previous setup, the superconducting system considered here implies widely different modulations of the Casimir force, depending on whether the thermal force is computed using the Drude or the plasma model, thus paving the way to an unambiguous discrimination between these alternative prescriptions.
Hide it to see it better: a robust setup to probe the thermal Casimir effect.
Bimonte, Giuseppe
2014-06-20
We describe a Casimir setup consisting of two aligned sinusoidally corrugated Ni surfaces, one of which is "hidden" by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass filter that allows for a clean observation of the controversial thermal Casimir force between the corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the apparatus, and is unaffected by uncertainties in the knowledge of the optical properties of the surfaces. This scheme should allow for an unambiguous discrimination between alternative theoretical prescriptions that have been proposed in the literature for the thermal Casimir effect.
Hide It to See It Better: A Robust Setup to Probe the Thermal Casimir Effect
NASA Astrophysics Data System (ADS)
Bimonte, Giuseppe
2014-06-01
We describe a Casimir setup consisting of two aligned sinusoidally corrugated Ni surfaces, one of which is "hidden" by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass filter that allows for a clean observation of the controversial thermal Casimir force between the corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the apparatus, and is unaffected by uncertainties in the knowledge of the optical properties of the surfaces. This scheme should allow for an unambiguous discrimination between alternative theoretical prescriptions that have been proposed in the literature for the thermal Casimir effect.
Interplay between geometry and temperature for inclined Casimir plates
Weber, Alexej; Gies, Holger
2009-09-15
We provide further evidence for the nontrivial interplay between geometry and temperature in the Casimir effect. We investigate the temperature dependence of the Casimir force between an inclined semi-infinite plate above an infinite plate in D dimensions using the worldline formalism. Whereas the high-temperature behavior is always found to be linear in T in accordance with dimensional-reduction arguments, different power-law behaviors at small temperatures emerge. Unlike the case of infinite parallel plates, which shows the well-known T{sup D} behavior of the force, we find a T{sup D-1} behavior for inclined plates, and a {approx}T{sup D-0.3} behavior for the edge effect in the limit where the plates become parallel. The strongest temperature dependence {approx}T{sup D-2} occurs for the Casimir torque of inclined plates. Numerical as well as analytical worldline results are presented.
On the possibility of Casimir repulsion using metamaterials
Da Rosa, Felipe S
2008-01-01
It is well known that the Casimir force between two half-spaces is dictated by their electromagnetic properties. In particular, when one of the half-spaces is mainly metallic or dielectric and the other is mainly magnetic, it is possible to show that the force is repulsive. This has attracted lots of interest towards the study of metamaterials (MMs) in the context of Casimir effect, as their magnetic activity might help bring the idea of Casimir repulsion from the theoretical realm to experimental verification. In this paper we investigate the possibility of repulsion when the MM magnetic permeability is given not by a Drude-Lorentz behavior, but by a model put forward by Pendry et al. [16]. After introducing the model and deriving the necessary formulas, we show that it is impossible to achieve repulsion with such a model and present a qualitative discussion of why this is so.
Casimir attraction in multilayered plane parallel magnetodielectric systems
NASA Astrophysics Data System (ADS)
Ellingsen, Simen A.
2007-03-01
A powerful procedure is presented for calculating the Casimir attraction between plane parallel multilayers made up of homogeneous regions with arbitrary magnetic and dielectric properties by the use of the Minkowski energy-momentum tensor. The theory is applied to numerous geometries and shown to reproduce a number of results obtained by other authors. Although the various pieces of theory drawn upon are well known, the relative ease with which the Casimir force density in even complex planar structures may be calculated, appears not to be widely appreciated, and no single paper to the author's knowledge renders explicitly the procedure demonstrated herein. Results may be seen as an important building block in the settling of issues of fundamental interest, such as the long-standing dispute over the thermal behaviour of the Casimir force or the question of what is the correct stress tensor to apply, a discussion requickened by the newly suggested alternative theory due to Raabe and Welsch.
Materials perspective on Casimir and van der Waals interactions
NASA Astrophysics Data System (ADS)
Woods, L. M.; Dalvit, D. A. R.; Tkatchenko, A.; Rodriguez-Lopez, P.; Rodriguez, A. W.; Podgornik, R.
2016-10-01
Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nanostructured devices. In the past decade, many new materials have become available, which has stimulated the need for understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights into related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed-matter physics, high-energy physics, chemistry, and biology. This review summarizes major breakthroughs and emphasizes the common origin of van der Waals and Casimir interactions. Progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter are examined. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.
Materials perspective on Casimir and van der Waals interactions
Woods, L. M.; Dalvit, D. A. R.; Tkatchenko, A.; Rodriguez-Lopez, P.; Rodriguez, A. W.; Podgornik, R.
2016-11-02
Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems. In such interactions these are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nanostructured devices. In the past decade, many new materials have become available, which has stimulated the need for understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights into related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed-matter physics, high-energy physics, chemistry, and biology. Our review summarizes major breakthroughs and emphasizes the common origin of van der Waals and Casimir interactions. Progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter are examined. Finally, the outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.
Materials perspective on Casimir and van der Waals interactions
Woods, L. M.; Dalvit, D. A. R.; Tkatchenko, A.; ...
2016-11-02
Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems. In such interactions these are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nanostructured devices. In the past decade, many new materials have become available, which has stimulated the need for understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insightsmore » into related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed-matter physics, high-energy physics, chemistry, and biology. Our review summarizes major breakthroughs and emphasizes the common origin of van der Waals and Casimir interactions. Progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter are examined. Finally, the outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.« less
Casimir piston of real materials and its application to multilayer models
Teo, L. P.
2010-03-15
In this article, we derive the formula for the Casimir force acting on a piston made of real material moving inside a perfectly conducting rectangular box. It is shown that by taking suitable limits, one recovers the formula for the Casimir force acting on a perfectly conducting piston or an infinitely permeable piston. The Lifshitz formula for finite temperature Casimir force acting on parallel plates made of real materials is re-derived by considering the five-layer model in the context of the piston approach. It is observed that the divergences of the Casimir force will only cancel under certain conditions, for example, when the regions separated by the plates are filled with media of the same refractive index.
Casimir dynamics: Interactions of surfaces with codimension >1 due to quantum fluctuations
Scardicchio, A.
2005-09-15
We study the Casimir force between defects (branes) of codimension larger than 1 due to quantum fluctuations of a scalar field {phi} living in the bulk. We show that the Casimir force is attractive and that it diverges as the distance between the branes approaches a critical value L{sub c}. Below this critical distance L{sub c} the vacuum state {phi}=0 of the theory is unstable, due to the birth of a tachyon, and the field condenses.
Gravitational Casimir-Polder effect
NASA Astrophysics Data System (ADS)
Hu, Jiawei; Yu, Hongwei
2017-04-01
The interaction due to quantum gravitational vacuum fluctuations between a gravitationally polarizable object modelled as a two-level system and a gravitational boundary is investigated. This quantum gravitational interaction is found to be position-dependent, which induces a force in close analogy to the Casimir-Polder force in the electromagnetic case. For a Dirichlet boundary, the quantum gravitational potential for the polarizable object in its ground-state is shown to behave like z-5 in the near zone, and z-6 in the far zone, where z is the distance to the boundary. For a concrete example, where a Bose-Einstein condensate is taken as a gravitationally polarizable object, the relative correction to the radius of the BEC caused by fluctuating quantum gravitational waves in vacuum is found to be of order 10-21. Although the correction is far too small to observe in comparison with its electromagnetic counterpart, it is nevertheless of the order of the gravitational strain caused by a recently detected black hole merger on the arms of the LIGO.
Casimir energy for a dielectric cylinder
Cavero-Pelaez, Ines . E-mail: cavero@nhn.ou.edu; Milton, Kimball A. . E-mail: milton@nhn.ou.edu
2005-11-01
In this paper, we calculate the Casimir energy for a dielectric-diamagnetic cylinder with the speed of light differing on the inside and outside. Although the result is in general divergent, special cases are meaningful. The well-known results for a uniform speed of light are reproduced. The self-stress on a purely dielectric cylinder is shown to vanish through second order in the deviation of the permittivity from its vacuum value, in agreement with the result calculated from the sum of van der Waals forces. These results are unambiguously separated from divergent terms.
Pressures and Energies of Vacuum in a Magnetic Field. Differences and Analogies with Casimir Effect
Perez Rojas, H.; Rodriguez Querts, E.
2005-09-28
We study the electron-positron vacuum in a strong magnetic field B in parallel with Casimir effect. Starting from the energy eigenvalues, anisotropic pressures are obtained in both magnetic field and Casimir cases. In the first case the pressure transversal to the field B is negative due to the effect of vacuum magnetization, whereas along B an usual positive pressure arises. Similarly, in addition to the usual negative Casimir pressure perpendicular to the plates, the existence of a positive pressure along the plates is predicted. By assuming regions of the universe having random orientation of the lines of force, cosmological consequences are discussed in the magnetic field case.
Casimir effect for parallel plates involving massless Majorana fermions at finite temperature
Cheng Hongbo
2010-08-15
We study the Casimir effect for parallel plates with massless Majorana fermions obeying the bag boundary conditions at finite temperature. The thermal influence will modify the effect. It is found that the sign of the Casimir energy remains negative if the product of the plate distance and the temperature is larger than a special value, otherwise the energy will change to positive. The Casimir energy rises with the stronger thermal influence. We show that the attractive Casimir force between two parallel plates becomes greater with increasing temperature. In the case of the piston system involving the same Majorana fermions with the same boundary conditions, the attractive force on the piston will be weaker in higher-temperature surroundings.
Quantum Field Energy Sensor based on the Casimir Effect
NASA Astrophysics Data System (ADS)
Ludwig, Thorsten
The Casimir effect converts vacuum fluctuations into a measurable force. Some new energy technologies aim to utilize these vacuum fluctuations in commonly used forms of energy like electricity or mechanical motion. In order to study these energy technologies it is helpful to have sensors for the energy density of vacuum fluctuations. In today's scientific instrumentation and scanning microscope technologies there are several common methods to measure sub-nano Newton forces. While the commercial atomic force microscopes (AFM) mostly work with silicon cantilevers, there are a large number of reports on the use of quartz tuning forks to get high-resolution force measurements or to create new force sensors. Both methods have certain advantages and disadvantages over the other. In this report the two methods are described and compared towards their usability for Casimir force measurements. Furthermore a design for a quantum field energy sensor based on the Casimir force measurement will be described. In addition some general considerations on extracting energy from vacuum fluctuations will be given.
Casimir pressure in a multilayer system with a fixed total length
Lenac, Z.
2010-08-15
We consider Casimir pressure on a slab in a configuration consisting of various dielectrics with planar symmetry. In such configurations, one usually calculates the Casimir pressure (force) on a particular slab assuming that lengths of all other slabs remain unchanged. Alternatively, one can consider a multilayer system with a fixed total length. With this restriction only, the length of each slab can eventually be changed under the Casimir pressure that will try to minimize the total Casimir energy of the system. Here we calculate the Casimir pressure on the slab in such a 'constrained' configuration and compare the results with the standard approach. It turns out that, by applying different boundary conditions, one can obtain significantly different Casimir pressures on the same object. In particular, when the thicknesses of the slab and surrounding layers are on the nanometer scale, the Casimir pressure on the slab can change from strongly squeezing in the case of fixed thicknesses of surrounding slabs to strongly relaxing in the case when only the length of the total system remains fixed.
Casimir rack and pinion as a miniaturized kinetic energy harvester.
Miri, MirFaez; Etesami, Zahra
2016-08-01
We study a nanoscale machine composed of a rack and a pinion with no contact, but intermeshed via the lateral Casimir force. We adopt a simple model for the random velocity of the rack subject to external random forces, namely, a dichotomous noise with zero mean value. We show that the pinion, even when it experiences random thermal torque, can do work against a load. The device thus converts the kinetic energy of the random motions of the rack into useful work.
Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space-time
NASA Astrophysics Data System (ADS)
Zhai, Xiang-Hua; Lin, Rui-Hui; Feng, Chao-Jun; Li, Xin-Zhou
2014-12-01
The Casimir effect for rectangular boxes has been studied for several decades. But there are still some unclear points. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the p-dimensional cavity in (D + 1)-dimensional space-time, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.
Casimir interaction between a sphere and a cylinder
NASA Astrophysics Data System (ADS)
Teo, L. P.
2013-02-01
We study the Casimir interaction between a sphere and a cylinder both subjected to Dirichlet, Neumann, or perfectly conducting boundary conditions. Generalizing the operator approach developed by Wittman [IEEE Trans. Antennas Propag. 36, 1078 (1988)IETPAK0018-926X], we compute the scalar and vector translation matrices between a sphere and a cylinder, and thus write down explicitly the exact TGTG formula for the Casimir interaction energy. In the scalar case, the formula shows manifestly that the Casimir interaction force is attractive at all separations. The large separation leading term of the Casimir interaction energy is computed directly from the exact formula. It is of order ˜ℏcR1/[L2ln(L/R2)], ˜ℏcR13R22/L6, and ˜ℏcR13/[L4ln(L/R2)], respectively, for Dirichlet, Neumann, and perfectly conducting boundary conditions, where R1 and R2 are, respectively, the radii of the sphere and the cylinder, and L is the distance between their centers.
Casimir probe based upon metallized high Q SiN nanomembrane resonator.
Garcia-Sanchez, Daniel; Fong, King Yan; Bhaskaran, Harish; Lamoreaux, Steve; Tang, Hong X
2013-01-01
We present the instrumentation and measurement scheme of a new Casimir force probe that bridges Casimir force measurements at microscale and macroscale. A metallized high Q silicon nitride nanomembrane resonator is employed as a sensitive force probe. The high tensile stress present in the nanomembrane not only enhances the quality factor but also maintains high flatness over large area serving as the bottom electrode in a sphere-plane configuration. A fiber interferometer is used to readout the oscillation of the nanomembrane and a phase-locked loop scheme is applied to track the change of the resonance frequency. Because of the high quality factor of the nanomembrane and the high stability of the setup, a frequency resolution down to 2 × 10(-9) and a corresponding force gradient resolution of 3 μN/m is achieved. Besides sensitive measurement of Casimir force, our measurement technique simultaneously offers Kelvin probe measurement capability that allows in situ imaging of the surface potentials.
Reid, M. T. Homer; White, Jacob; Johnson, Steven G.
2011-07-15
We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett. 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface-surface separation at which finite-size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.
Casimir Effect in Hemisphere Capped Tubes
NASA Astrophysics Data System (ADS)
Bezerra de Mello, E. R.; Saharian, A. A.
2016-02-01
In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2 + 1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.
Casimir energies of cylinders: Universal function
Abalo, E. K.; Milton, K. A.; Kaplan, L.
2010-12-15
New exact results are given for the interior Casimir energies of infinitely long waveguides of triangular cross section (equilateral, hemiequilateral, and isosceles right triangles). Results for cylinders of rectangular cross section are rederived. In particular, results are obtained for interior modes belonging to Dirichlet and Neumann boundary conditions (TM and TE modes). These results are expressed in rapidly convergent series using the Chowla-Selberg formula, and in fact may be given in closed form, except for general rectangles. The energies are finite because only the first three heat-kernel coefficients can be nonzero for the case of polygonal boundaries. What appears to be a universal behavior of the Casimir energy as a function of the shape of the regular or quasiregular cross-sectional figure is presented. Furthermore, numerical calculations for arbitrary right triangular cross sections suggest that the universal behavior may be extended to waveguides of general polygonal cross sections. The new exact and numerical results are compared with the proximity force approximation (PFA).
Noncommutative Complex Scalar Field and Casimir Effect
NASA Astrophysics Data System (ADS)
Khelili, Farid
2012-06-01
Using the noncommutative deformed canonical commutation relations proposed by Carmona et al. [J. M. Carmona, J. L. Cortés, J. Gamboa, and F. Mendez, J. High Energy Phys.JHEPFG1029-8479 03 (2003) 058.10.1088/1126-6708/2003/03/058][J. Gamboa, J. Lopéz-Sarrion, and A. P. Polychronakos, Phys. Lett. B 634, 471 (2006).PYLBAJ0370-269310.1016/j.physletb.2006.02.014][J. M. Carmona, J. L. Cortés, Ashok Das, J. Gamboa, and F. Mendez, Mod. Phys. Lett. A 21, 883 (2006).MPLAEQ0217-732310.1142/S0217732306020111], a model describing the dynamics of the noncommutative complex scalar field is proposed. The noncommutative field equations are solved, and the vacuum energy is calculated to the second order in the parameter of noncommutativity. As an application to this model, the Casimir effect, due to the zero-point fluctuations of the noncommutative complex scalar field, is considered. It turns out that in spite of its smallness, the noncommutativity gives rise to a repulsive force at the microscopic level, leading to a modified Casimir potential with a minimum at the point amin=(5)/(84)πθ.
Single-interface Casimir torque
NASA Astrophysics Data System (ADS)
Morgado, Tiago A.; Silveirinha, Mário G.
2016-10-01
A different type of Casimir-type interaction is theoretically predicted: a single-interface torque at a junction of an anisotropic material and a vacuum or another material system. The torque acts to reorient the polarizable microscopic units of the involved materials near the interface, and thus to change the internal structure of the materials. The single-interface torque depends on the zero-point energy of the interface localized and extended modes. Our theory demonstrates that the single-interface torque is essential to understand the Casimir physics of material systems with anisotropic elements and may influence the orientation of the director of nematic liquid crystals.
Nonmonotonic Casimir interaction: The role of amplifying dielectrics
NASA Astrophysics Data System (ADS)
Soltani, Morteza; Sarabadani, Jalal; Zakeri, S. Peyman
2017-02-01
The normal and the lateral Casimir interactions between corrugated ideal metallic plates in the presence of an amplifying or an absorptive dielectric slab is studied by the path-integral quantization technique. The effect of the amplifying slab, which is located between corrugated conductors, is to increase the normal and lateral Casimir interactions, while the presence of the absorptive slab diminishes the interactions. These effects are more pronounced if the thickness of the slab increases and, also, if the slab comes closer to one of the bounding conductors. When both bounding ideal conductors are flat, the normal Casimir force is nonmonotonic in the presence of the amplifying slab and the system has a stable mechanical equilibrium state, while the force is attractive and is weakened by intervening the absorptive dielectric slab in the cavity. Upon replacing one of the flat conductors with a flat ideal permeable plate the force becomes nonmonotonic and the system has an unstable mechanical equilibrium state in the presence of either an amplifying or an absorptive slab. When the left-side plate is a conductor and the right one is permeable, the force is nonmonotonic in the presence of a double-layer dissipative-amplifying dielectric slab with a stable mechanical equilibrium state, while it is purely repulsive in the presence of a double-layer amplifying-dissipative dielectric slab.
Casimir potential of a compact object enclosed by a spherical cavity
Zaheer, Saad; Rahi, Sahand Jamal; Emig, Thorsten; Jaffe, Robert L.
2010-11-15
We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading-order correction to the proximity force approximation for two metallic spheres both outside and within one another.
Perivolaropoulos, L.
2008-05-15
We consider a universe with a compact extra dimension and a cosmological constant emerging from a suitable ultraviolet cutoff on the zero-point energy of the vacuum. We derive the Casimir force between parallel conducting plates as a function of the following scales: plate separation, radius of the extra dimension and cutoff energy scale. We find that there are critical values of these scales where the Casimir force between the plates changes sign. For the cutoff energy scale required to reproduce the observed value of the cosmological constant, we find that the Casimir force changes sign and becomes repulsive for plate separations less than a critical separation d{sub 0}=0.6 mm, assuming a zero radius of the extra dimension (no extra dimension). This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of 100 nm. For a nonzero extra dimension radius, the critical separation d{sub 0} gets even larger than 0.6 mm and remains inconsistent with Casimir force experiments. We conclude that with or without the presence of a compact extra dimension, vacuum energy with any suitable cutoff cannot play the role of the cosmological constant.
Bellucci, S.; Saharian, A. A.
2009-11-15
We evaluate the Casimir energy and force for a massive fermionic field in the geometry of two parallel plates on background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions. The bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The Casimir energy is decomposed into purely topological, single plate and interaction parts. With independence of the lengths of the compact dimensions and the phases in the periodicity conditions, the interaction part of the Casimir energy is always negative. In order to obtain the resulting force, the contributions from both sides of the plates must be taken into account. Then, the forces coming from the topological parts of the vacuum energy cancel out and only the interaction term contributes to the Casimir force. Applications of the general formulae to Kaluza-Klein-type models and carbon nanotubes are given. In particular, we show that for finite-length metallic nanotubes, the Casimir forces acting on the tube edges are always attractive, whereas for semiconducting-type ones, they are attractive for small lengths of the nanotube and repulsive for large lengths.
Mimicking Boyer's Casimir repulsion with a nanowire material
Maslovski, Stanislav I.; Silveirinha, Mario G.
2011-02-15
It is shown that the electromagnetic Casimir force acting on a conducting body (e.g., a realistic metallic piston) sliding in a background formed by cut silver nanorods (with the body perforated by the nanorods) is repulsive at distances larger than the separation of the nanorods, even if the host material of the nanorods is air. It is demonstrated that the physical origin of this effect is in essence related to Boyer's prediction that magnetic and conducting walls repel each other. Indeed, we show that from the point of view of an observer inside the nanowire structure, the interface formed by severing the nanowires mimics accurately the behavior of a magnetic wall for P-polarized waves. In contrast to other piston configurations reported in the literature, the Casimir interaction in the nanowire background is an ultralong-range force that decays with the distance to the nearby interface as 1/a{sup 2}.
Casimir Interaction between Plane and Spherical Metallic Surfaces
Canaguier-Durand, Antoine; Cavero-Pelaez, Ines; Lambrecht, Astrid; Reynaud, Serge; Maia Neto, Paulo A.
2009-06-12
We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the nontrivial situation where the sphere radius R, the plane-sphere distance L and the plasma wavelength {lambda}{sub P} have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of L/R. For metallic nanospheres where R, L and {lambda}{sub P} have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments which are performed with spheres of large radius R>>L.
Thermal Fluctuations in Casimir Pistons
NASA Astrophysics Data System (ADS)
Lomnitz, M.; Villarreal, C.
2012-07-01
We present analytical and simple expressions to determine the free energy, internal energy, entropy, as well as the pressure acting at the interface of a perfectly conducting rectangular Casimir piston. We show that infrared divergencies linear in temperature become cancelled within the piston configuration, and show a continuous behavior consistent with intuitive expectations.
Critical Casimir effect for colloids close to chemically patterned substrates
Troendle, M.; Kondrat, S.; Harnau, L.; Dietrich, S.; Gambassi, A.
2010-08-21
Colloids immersed in a critical or near-critical binary liquid mixture and close to a chemically patterned substrate are subject to normal and lateral critical Casimir forces of dominating strength. For a single colloid, we calculate these attractive or repulsive forces and the corresponding critical Casimir potentials within mean-field theory. Within this approach we also discuss the quality of the Derjaguin approximation and apply it to Monte Carlo simulation data available for the system under study. We find that the range of validity of the Derjaguin approximation is rather large and that it fails only for surface structures which are very small compared to the geometric mean of the size of the colloid and its distance from the substrate. For certain chemical structures of the substrate, the critical Casimir force acting on the colloid can change sign as a function of the distance between the particle and the substrate; this provides a mechanism for stable levitation at a certain distance which can be strongly tuned by temperature, i.e., with a sensitivity of more than 200 nm/K.
Thermodynamic Casimir effect in films: the exchange cluster algorithm.
Hasenbusch, Martin
2015-02-01
We study the thermodynamic Casimir force for films with various types of boundary conditions and the bulk universality class of the three-dimensional Ising model. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. In particular, we employ the exchange or geometric cluster cluster algorithm [Heringa and Blöte, Phys. Rev. E 57, 4976 (1998)]. In a previous work, we demonstrated that this algorithm allows us to compute the thermodynamic Casimir force for the plate-sphere geometry efficiently. It turns out that also for the film geometry a substantial reduction of the statistical error can achieved. Concerning physics, we focus on (O,O) boundary conditions, where O denotes the ordinary surface transition. These are implemented by free boundary conditions on both sides of the film. Films with such boundary conditions undergo a phase transition in the universality class of the two-dimensional Ising model. We determine the inverse transition temperature for a large range of thicknesses L(0) of the film and study the scaling of this temperature with L(0). In the neighborhood of the transition, the thermodynamic Casimir force is affected by finite size effects, where finite size refers to a finite transversal extension L of the film. We demonstrate that these finite size effects can be computed by using the universal finite size scaling function of the free energy of the two-dimensional Ising model.
The Casimir effect for fields with arbitrary spin
Stokes, Adam; Bennett, Robert
2015-09-15
The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.
Effect of the heterogeneity of metamaterials on the Casimir-Lifshitz interaction
Azari, Arash; Golestanian, Ramin; Miri, MirFaez
2010-09-15
The Casimir-Lifshitz interaction between metamaterials is studied using a model that takes into account the structural heterogeneity of the dielectric and magnetic properties of the bodies. A recently developed perturbation theory for the Casimir-Lifshitz interaction between arbitrary material bodies is generalized to include nonuniform magnetic permeability profiles and used to study the interaction between the magneto-dielectric heterostructures within the leading order. The metamaterials are modeled as two-dimensional arrays of domains with varying permittivity and permeability. In the case of two semi-infinite bodies with flat boundaries, the patterned structure of the material properties is found to cause the normal Casimir-Lifshitz force to develop an oscillatory behavior when the distance between the two bodies is comparable to the wavelength of the patterned features in the metamaterials. The nonuniformity also leads to the emergence of lateral Casimir-Lifshitz forces, which tend to strengthen as the gap size becomes smaller. Our results suggest that the recent studies on Casimir-Lifshitz forces between metamaterials, which have been performed with the aim of examining the possibility of observing the repulsive force, should be revisited to include the effect of the patterned structure at the wavelength of several hundred nanometers that coincides with the relevant gap size in the experiments.
Nonperturbative approach for the electronic Casimir-Polder effect in a one-dimensional semiconductor
NASA Astrophysics Data System (ADS)
Tanaka, Satoshi; Passante, Roberto; Fukuta, Taku; Petrosky, Tomio
2013-08-01
We present the electronic Casimir-Polder effect for a system consisting of two impurities on a one-dimensional semiconductor quantum wire. Due to the charge transfer from the impurity to a one-dimensional conduction band, the impurity states are dressed by a virtual cloud of the electron field. The attractive electronic Casimir force arises due to the overlap of the virtual clouds. The Van Hove singularity causes the persistent bound state (PBS) to appear below the band edge even when the bare impurity state energy is above the band edge. Since the decay rate of the virtual cloud of the PBS in space is small, the Casimir force can be of a very long range. While the overlap of the electronic virtual cloud is consistent with the idea of the radiation reaction, it is shown that also vacuum fluctuations play a role in the electronic Casimir force as a result of the fermionic anticommutation relations. We introduce an effective mass, different from the effective band mass of the conduction band, which is associated with the distance of the energy of the PBS from the band edge where the Van Hove singularity is located and determines the decay rate of the electronic Casimir-Polder force.
Anisotropies in thermal Casimir interactions: ellipsoidal colloids trapped at a fluid interface.
Noruzifar, Ehsan; Oettel, Martin
2009-05-01
We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long-ranged interface fluctuations by particles gives rise to fluctuation-induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example of the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge-density-like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive, and long ranged (double logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.
Hamiltonian Approach to the Dynamical Casimir Effect
Haro, Jaume; Elizalde, Emilio
2006-09-29
A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term--proportional to the mirrors' acceleration - which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors - while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.
Casimir effect in the nonequilibrium steady state of a quantum spin chain
Gonzalez-Cabrera, D. L.; Racz, Z.
2010-05-15
We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely, an energy-flux-driven quantum XX chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux-carrying steady state.
Numerical and semiclassical analysis of some generalized Casimir pistons
Schaden, M.
2009-05-15
The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation a<
Casimir interaction between spheres in ( D + 1)-dimensional Minkowski spacetime
NASA Astrophysics Data System (ADS)
Teo, L. P.
2014-05-01
We consider the Casimir interaction between two spheres in ( D + 1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coordinate frames differ by a translation, we generalize the operator approach employed in [39]. The result is expressed in terms of an integral over Gegenbauer polynomials. In contrast to the D=3 case, we do not re-express the integral in terms of 3 j-symbols and hyper-spherical waves, which in principle, can be done but does not simplify the formula. Using our expression for the Casimir interaction energy, we derive the large separation and small separation asymptotic expansions of the Casimir interaction energy. In the large separation regime, we find that the Casimir interaction energy is of order L -2 D+3, L -2 D+1 and L -2 D-1 respectively for Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions, where L is the center-to-center distance of the two spheres. In the small separation regime, we confirm that the leading term of the Casimir interaction agrees with the proximity force approximation, which is of order , where d is the distance between the two spheres. Another main result of this work is the analytic computations of the next-to-leading order term in the small separation asymptotic expansion. This term is computed using careful order analysis as well as perturbation method. In the case the radius of one of the sphere goes to infinity, we find that the results agree with the one we derive for sphere-plate configuration. When D=3, we also recover previously known results. We find that when D is large, the ratio of the next-to-leading order term to the leading
Nonperturbative Casimir effect and monopoles: Compact Abelian gauge theory in two spatial dimensions
NASA Astrophysics Data System (ADS)
Chernodub, M. N.; Goy, V. A.; Molochkov, A. V.
2017-04-01
We demonstrate that Casimir forces associated with zero-point fluctuations of quantum vacuum may be substantially affected by the presence of dynamical topological defects. In order to illustrate this nonperturbative effect we study the Casimir interactions between dielectric wires in a compact formulation of Abelian gauge theory in two spatial dimensions. The model possesses topological defects, instantonlike monopoles, which are known to be responsible for nonperturbative generation of a mass gap and for a linear confinement of electrically charged probes. Despite the fact the model has no matter fields, the Casimir energy depends on the value of the gauge coupling constant. We show, both analytically and numerically, that in the strong coupling regime the Abelian monopoles make the Casimir forces short ranged. Simultaneously, their presence increases the interaction strength between the wires at short distances for a certain range of values of the gauge coupling. The wires suppress monopole density in the space between them compared to the density outside the wires. In the weak coupling regime the monopoles become dilute and the Casimir potential reduces to a known theoretical result that does not depend on the gauge coupling.
Casimir interactions of an object inside a spherical metal shell
Zaheer, Saad; Rahi, Sahand Jamal; Emig, Thorsten; Jaffe, Robert L.
2010-03-15
We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.
Critical Casimir effect in classical binary liquid mixtures
NASA Astrophysics Data System (ADS)
Gambassi, A.; Maciołek, A.; Hertlein, C.; Nellen, U.; Helden, L.; Bechinger, C.; Dietrich, S.
2009-12-01
If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy with femtonewton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere—planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.
Critical Casimir effect in classical binary liquid mixtures.
Gambassi, A; Maciołek, A; Hertlein, C; Nellen, U; Helden, L; Bechinger, C; Dietrich, S
2009-12-01
If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy with femtonewton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.
Decca, R. S.; Fischbach, E.; Klimchitskaya, G. L.; Krause, D. E.; Lopez, D.; Mostepanenko, V. M.
2010-11-15
We investigate the possibility of measuring the thermal Casimir force and its gradient in the configuration of a plate and a microfabricated cylinder attached to a micromachined oscillator. The Lifshitz-type formulas in this configuration are derived using the proximity force approximation. The accuracy of the obtained expressions is determined from a comparison with exact results available in ideal metal case. Computations of the thermal correction to both the Casimir force and its gradient are performed in the framework of different theoretical approaches proposed in the literature. The correction to the Casimir force and its gradient due to lack of parallelism of the plate and cylinder is determined using the nonmultiplicative approach. The error introduced in the theory due to the finite length of the cylinder is estimated. We propose that both static and dynamic experiments measuring the thermal Casimir interaction between a cylinder and a plate using a micromachined oscillator can shed additional light on the thermal Casimir force problem. Specifically, it is shown that the static experiment is better adapted for the measurement of thermal effects.
Casimir Forces Between Thermally Activated Nanocomposites
2001-11-01
M6xico, Circuito de la Investigaci6n Cientifica, Ciudad Universitaria , M6xico, DF, 04510, M6xico. ABSTRACT We present a theoretical study of the...function of the slabs is needed. For a nanocomposite slab made of a host material with a dielectric function cj,(o) and inclusions with dielectric...8-2a wheref is the volume fraction of the inclusions and ox is the effective polarizability given by the Maxwell Garnett theory. This expression for
Supersymmetry Breaking Casimir Warp Drive
Obousy, Richard K.; Cleaver, Gerald
2007-01-30
This paper utilizes a recent model which relates the cosmological constant to the Casimir energy of the extra dimensions in brane-world theories. The objective of this paper is to demonstrate that, given some sufficiently advanced civilization with the ability to manipulate the radius of the extra dimension, a local adjustment of the cosmological constant could be created. This adjustment would facilitate an expansion/contraction of the spacetime around a spacecraft creating an exotic form of field-propulsion. This idea is analogous to the Alcubierre bubble, but differs entirely in the approach, utilizing the physics of higher dimensional quantum field theory, instead of general relativity.
The holographic supersymmetric Casimir energy
NASA Astrophysics Data System (ADS)
Benetti Genolini, Pietro; Cassani, Davide; Martelli, Dario; Sparks, James
2017-01-01
We consider a general class of asymptotically locally AdS5 solutions of minimal gauged supergravity, which are dual to superconformal field theories on curved backgrounds S1×M3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S1×R4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory supersymmetric relation between charges.
Casimir interaction of arbitrarily shaped conductors.
Straley, Joseph P; Kolomeisky, Eugene B
2017-04-12
We review a systematic practical implementation of the multiple scattering formalism due to Balian and Duplantier (1977 Ann. Phys. 104 300, 1978 Ann. Phys. 112 165) for the calculation of the Casimir interaction between arbitrarily shaped smooth conductors. The leading two-point scattering term of the expansion has a simple compact form, amenable to exact or accurate numerical evaluation. It is a general expression which improves upon the proximity force and pairwise summation approximations. We show that for many geometries it captures the bulk of the interaction effect. The inclusion of terms beyond the two-point approximation provides an accuracy check and explains screening. As an illustration of the power and versatility of the method we re-evaluate sphere-sphere and sphere-plane interactions and compared the results with previous findings that employed different methods. We also compute for the first time interaction of a hyperboloid (mimicking an atomic force microscope tip) and a plane. We also analyze the anomalous situations involving long cylindrical conductors where the two-point scattering approximation fails qualitatively. In such cases analytic summation of the entire scattering series is carried out and a topological argument is put forward as an explanation of the result. We give the extension of this theory to the case of finite temperatures where the two-point scattering approximation result has a simple compact form, also amenable to exact or accurate numerical evaluation.
Casimir interaction of arbitrarily shaped conductors
NASA Astrophysics Data System (ADS)
Straley, Joseph P.; Kolomeisky, Eugene B.
2017-04-01
We review a systematic practical implementation of the multiple scattering formalism due to Balian and Duplantier (1977 Ann. Phys. 104 300, 1978 Ann. Phys. 112 165) for the calculation of the Casimir interaction between arbitrarily shaped smooth conductors. The leading two-point scattering term of the expansion has a simple compact form, amenable to exact or accurate numerical evaluation. It is a general expression which improves upon the proximity force and pairwise summation approximations. We show that for many geometries it captures the bulk of the interaction effect. The inclusion of terms beyond the two-point approximation provides an accuracy check and explains screening. As an illustration of the power and versatility of the method we re-evaluate sphere–sphere and sphere–plane interactions and compared the results with previous findings that employed different methods. We also compute for the first time interaction of a hyperboloid (mimicking an atomic force microscope tip) and a plane. We also analyze the anomalous situations involving long cylindrical conductors where the two-point scattering approximation fails qualitatively. In such cases analytic summation of the entire scattering series is carried out and a topological argument is put forward as an explanation of the result. We give the extension of this theory to the case of finite temperatures where the two-point scattering approximation result has a simple compact form, also amenable to exact or accurate numerical evaluation.
Finite-temperature Casimir effect in the presence of nonlinear dielectrics
Kheirandish, Fardin; Soltani, Morteza; Amooghorban, Ehsan
2011-03-15
Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupling functions are determined. Finally, the Casimir energy and force in the presence of a nonlinear medium at finite temperature are calculated.
Silveirinha, Mario G.
2010-08-15
It is theoretically shown that the Casimir force between two planar metamaterial slabs formed by metal-dielectric inclusions with a completely arbitrary shape, size, and material parameters, is invariably attractive at distances a few times larger than the characteristic period of the metamaterials.
Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons
Elizalde, E.; Odintsov, S. D.; Saharian, A. A.
2009-03-15
We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a (D+1)-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.
L'effet Casimir : théorie et expériences
NASA Astrophysics Data System (ADS)
Lambrecht, A.; Genet, C.; Intravaia, F.; Reynaud, S.
2004-11-01
L'existence de fluctuations irréductibles de champ dans le vide est une prédiction importante de la théorie quantique. Ces fluctuations ont de nombreuses conséquences observables comme l'effet Casimir, qui est maintenant mesuré avec une bonne précision et un bon accord avec la théorie, pourvu que celle-ci tienne compte des différences entre les expériences rélles et la situation idéale considérée par H.G.B. Casimir. Nous présenterons quelqu'unes des expériences récentes et discuterons les principales corrections à la force de Casimir liées à la situation expérimentale.
Eab, C. H.; Lim, S. C.; Teo, L. P.
2007-08-15
This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed.
Theoretical analysis of Casimir and thermal Casimir effect in stationary space-time
NASA Astrophysics Data System (ADS)
Zhang, Anwei
2017-10-01
We investigate Casimir effect as well as thermal Casimir effect for a pair of parallel perfectly plates placed in general stationary space-time background. It is found that the Casimir energy is influenced by the 00-component of metric and the corresponding quantity in dragging frame. We give a scheme to renormalize thermal correction to free energy in curved space-time. It is shown that the thermal corrections to Casimir thermodynamic quantities not only depend on the proper temperature and proper geometrical parameters of the plates, but also on the determinant of space-time metric.
Casimir Interaction from Magnetically Coupled Eddy Currents
Intravaia, Francesco; Henkel, Carsten
2009-09-25
We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasistatic magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.
Determination of the Contact Angle Based on the Casimir Effect
NASA Technical Reports Server (NTRS)
Mazuruk, K.; Volz, M. P.
2015-01-01
In several crystal growth processed based on capillarity, a melt comes into contact with a crucible wall at an angle defined as the contact angle. For molten metals and semiconductors, this contact angle is dependent upon both the crucible and melt material and typical values fall in the range 80-170deg. However, on a microscopic scale, there does not exist a precise and sharp contact angle but rather the melt and solid surfaces merge smoothly and continuously over a distance of up to several micrometers. Accurate modeling requires a more advanced treatment of this interaction. The interaction between the melt and solid surfaces can be calculated by considering two forces: a short-range repulsive force and a longer range (up to a few micrometers) Casimir force. The Casimir force between the two bodies of complex geometry is calculated using a retarded temperature Green's function (Matsubara type) for the photon in the medium. The governing equations are cast in the form of a set of boundary integral equations which are then solved numerically for the case of molten Ge on SiO2. The shape of the molten surface approaching the flat solid body is determined, and the contact angle is defined as the angle between the two surfaces at the microscopically asymptotic distance of 1-2 micrometers. The formulation of this model and the results of the numerical calculations will be presented and discussed.
Direct Measurement of Intermediate-Range Casimir-Polder Potentials
Bender, H.; Courteille, Ph. W.; Marzok, C.; Zimmermann, C.; Slama, S.
2010-02-26
We present the first direct measurements of Casimir-Polder forces between solid surfaces and atomic gases in the transition regime between the electrostatic short-distance and the retarded long-distance limit. The experimental method is based on ultracold ground-state Rb atoms that are reflected from evanescent wave barriers at the surface of a dielectric glass prism. Our novel approach does not require assumptions about the potential shape. The experimental data are compared to the theoretical predictions valid in the different regimes. They agree best with a full QED calculation.
Geometrical investigations of the Casimir effect: Thickness and corrugation dependencies
NASA Astrophysics Data System (ADS)
Parashar, Prachi
2011-12-01
In the quantum theory the vacuum is not empty space. It is considered as a state of infinite energy arising due to zero point fluctuations of the vacuum. Calculation of any physically relevant process requires subtracting this infinite energy using a procedure called normalization. As such the vacuum energy is treated as an infinite constant. However, it has been established beyond doubt that mere subtraction of this infinite constant does not remove the effect of vacuum fluctuations and it cannot be treated just as a mathematical artifact. The presence of boundaries, which restricts the vacuum field, causes vacuum polarization. Any non-trivial space-time topology can cause similar effects. This is manifested as the Casimir effect, whereby the boundaries experience a force due to a change in the energy of the vacuum. To calculate the vacuum energy we treat the boundaries or other restrictive conditions as classical backgrounds, which impose boundary conditions on the solution of the vacuum field equations. Alternatively, we can incorporate the classical background in the Lagrangian of the system as classical potentials, which automatically include the boundary conditions in the field equations. Any change in the boundary conditions changes the vacuum energy and consequently the Casimir force is experienced by the boundaries. In this dissertation we study the geometric aspect of the Casimir effect. We consider both the scalar field and the physically relevant electromagnetic field. After a brief survey of the field in Chapter 1, we derive the energy expression using the Schwinger's quantum action principle in Chapter 2. We present the multiple scattering formalism for calculating the vacuum energy, which allows us to calculate the interaction energy between disjoint bodies and subtract out the divergent terms from the beginning. We then solve the Green's dyadic equation for the electromagnetic field interacting with the planar background surfaces, where we can
PREFACE: International Workshop '60 Years of the Casimir Effect'
NASA Astrophysics Data System (ADS)
Barton, Gabriel; Carugno, Giovanni; Dodonov, Victor; Man'ko, Margarita
2009-07-01
In 1948 Hendrick Casimir published a short article predicting that (neutral) ideal metallic plates attract each other. This attraction is widely ascribed to the quantum vacuum fluctuations of the electromagnetic field (even though away from the limit of ideal metals it depends demonstrably on the physics of the charge carriers vanishing when they cease to carry). Casimir's remarkable discovery, nowadays called the Casimir effect, has charmed several generations of physicists. In the last decade alone, more than a thousand publications have addressed its many consequences, generalizations, and possible applications in different areas from particle physics to cosmology. Interest in the field is still growing driven by impressive progress in experimental skills and its importance for the recently opened-up area of micro- and nano-electromechanical systems: according to the Thompson ISI Web of Science database, in 2005 the number of papers related to the Casimir effect or to Casimir forces jumped to over 125, compared to approximately 60 in 2000 and 30 in 1995. The increase continues, with more than 170 papers in 2008. The International Workshop '60 Years of the Casimir Effect' took place on 23-27June 2008, in Brasilia (Brazil) organized by the International Center for Condensed Matter Physics (ICCMP). The purpose was to celebrate this anniversary of Casimir's pioneering paper by inviting the leading specialists in the area, both theorists and experimentalists, together with young researchers and post-graduate students interested in hearing about the most recent achievements in the field. The Workshop was attended by 65 participants from 14 countries, who presented 41 talks and 12 posters. These Proceedings contain extended versions of almost all the talks and some posters, plus several papers by authors who had planned to attend but for various reasons could not. The contributions are divided (with some inevitable arbitrariness) into four groups. The largest one
Casimir Energy Associated With Fractional Derivative Field
Lim, S. C.
2007-04-28
Casimir energy associated with fractional derivative scalar massless field at zero and positive temperature can be obtained using the regularization based on generalized Riemann zeta function of Epstein-Hurwitz type.
Thermal Brownian motor coupled by Casimir interaction.
Nie, Wenjie; Liao, Qinghong; He, Jizhou
2010-10-01
We study a Feynman-like thermal Brownian motor, in which the asymmetric corrugated cylinder as the ratchet is coupled with a corrugated plate by the noncontact Casimir interaction between them. The source of driving of the system is the thermal fluctuations and its dynamic evolution is described by a set of Langevin equations. Further, the mean velocity and thermal efficiency of the motor in the overdamped limit are studied in detail as a function of the temperature of the baths, external load applied, magnitude of the Casimir interaction, and other relevant parameters by the numerical stimulation. The transport properties attained here and the essential roles of the Casimir interaction can be explicitly demonstrated by designing a Casimir Brownian motor with present nanotechnology.
The Casimir Energy for the Riemann Caps
NASA Astrophysics Data System (ADS)
Palesheva, E. V.; Pecheritsyn, A. A.
2017-03-01
The Casimir energy of a massive scalar field on a Riemann cap with the Dirichlet boundary conditions is calculated. The problem is considered in the quasi-stationary approximation. Formulas are derived which are suitable for numerical calculations.
The Casimir Energy for the Riemann Caps
NASA Astrophysics Data System (ADS)
Palesheva, E. V.; Pecheritsyn, A. A.
2017-03-01
The Casimir energy of a massive scalar field on a Riemann cap with the Dirichlet boundary conditions is calculated. The problem is considered in the quasi-stationary approximation. Formulas are derived which are suitable for numerical calculations.
Dynamical Casimir effect entangles artificial atoms.
Felicetti, S; Sanz, M; Lamata, L; Romero, G; Johansson, G; Delsing, P; Solano, E
2014-08-29
We show that the physics underlying the dynamical Casimir effect may generate multipartite quantum correlations. To achieve it, we propose a circuit quantum electrodynamics scenario involving superconducting quantum interference devices, cavities, and superconducting qubits, also called artificial atoms. Our results predict the generation of highly entangled states for two and three superconducting qubits in different geometric configurations with realistic parameters. This proposal paves the way for a scalable method of multipartite entanglement generation in cavity networks through dynamical Casimir physics.
Ultrahigh Casimir interaction torque in nanowire systems.
Morgado, Tiago A; Maslovski, Stanislav I; Silveirinha, Mário G
2013-06-17
We study the Casimir torque arising from the quantum electromagnetic fluctuations due to the interaction of two interfaces in a system formed by a dense array of metallic nanorods embedded in dielectric fluids. It is demonstrated that as a consequence of the ultrahigh density of photonic states in the nanowire array it is possible to channel the quantum fluctuations, and thereby boost the Casimir torque by several orders of magnitude as compared to other known systems (e.g., birefringent parallel plates).
Casimir effect for curved boundaries in Robertson-Walker spacetime
NASA Astrophysics Data System (ADS)
Saharian, A. A.; Setare, M. R.
2010-11-01
Vacuum expectation values of the energy-momentum tensor and the Casimir forces are evaluated for scalar and electromagnetic fields in the geometry of two curved boundaries on the background of the Robertson-Walker spacetime with negative spatial curvature. The boundaries under consideration are conformal images of the flat boundaries in Rindler spacetime. Robin boundary conditions are imposed in the case of the scalar field and perfect conductor boundary conditions are assumed for the electromagnetic field. We use the conformal relation between the Robertson-Walker and Rindler spacetimes and the corresponding results for two parallel plates moving with uniform proper acceleration through the Fulling-Rindler vacuum. For the general scale factor the vacuum energy-momentum tensor is decomposed into the boundary-free and boundary-induced parts. The latter is non-diagonal. The Casimir forces are directed along the normals to the boundaries. For the Dirichlet and Neumann scalars and for the electromagnetic field these forces are attractive for all separations.
Casimir effect for parallel plates in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Elizalde, E.; Saharian, A. A.; Vardanyan, T. A.
2010-06-01
The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows one to explicitly extract the contributions to the expectation values, which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power law (monotonic or oscillating), with independence of the value of the field mass.
Casimir effect for parallel plates in de Sitter spacetime
Elizalde, E.; Saharian, A. A.; Vardanyan, T. A.
2010-06-15
The Wightman function and the vacuum expectation values of the field squared and of the energy-momentum tensor are obtained, for a massive scalar field with an arbitrary curvature coupling parameter, in the region between two infinite parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. For the calculation, a mode-summation method is used, supplemented with a variant of the generalized Abel-Plana formula. This allows one to explicitly extract the contributions to the expectation values, which come from each single boundary, and to expand the second-plate-induced part in terms of exponentially convergent integrals. Several limiting cases of interest are then studied. Moreover, the Casimir forces acting on the plates are evaluated, and it is shown that the curvature of the background spacetime decisively influences the behavior of these forces at separations larger than the curvature scale of de Sitter spacetime. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively. The decay of the Casimir force at large plate separation is shown to be power law (monotonic or oscillating), with independence of the value of the field mass.
Out-of-equilibrium relaxation of the thermal Casimir effect in a model polarizable material.
Dean, David S; Démery, Vincent; Parsegian, V Adrian; Podgornik, Rudolf
2012-03-01
Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out-of-equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. For the interaction between dielectric slabs, it is found that the spatial dependence of the out-of-equilibrium force is the same as the equilibrium one, but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation of the force to its equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.
NASA Astrophysics Data System (ADS)
Markun, B.; Žumer, S.
2006-03-01
A theoretical study of the Casimir interaction in smectic-A systems, considering fluctuations of both types of smectic ordering—positional and orientational—including the coupling between them, is presented. Two model systems with plan-parallel geometry are studied: homeotropic cell and free-standing film. At large thicknesses of the system the behavior of the Casimir force is found to be primarily determined by positional fluctuations, whereas at small thicknesses also the orientational degrees of freedom greatly contribute to the interaction. The influence of different coupling strengths between orientational and positional order is presented. The dependence of the Casimir force on the director anchoring and surface-tension parameters is studied. The possibilities of experimental detection of the interaction are discussed.
Sphere-plate Casimir interaction in (D + 1)-dimensional spacetime
Teo, L. P.
2014-04-15
In this paper, we derive the formula for the Casimir interaction energy between a sphere and a plate in (D + 1)-dimensional Minkowski spacetime. It is assumed that the scalar field satisfies the Dirichlet or Neumann boundary conditions on the sphere and the plate. As in the D = 3 case, the formula is of TGTG type. One of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general D. Using orthogonality of Gegenbauer polynomials, it turns out that the final TGTG formula for the Casimir interaction energy can be simplified to one that is similar to the D = 3 case. To illustrate the application of the formula, both large separation and small separation asymptotic behaviors of the Casimir interaction energy are computed. The large separation leading term is proportional to L{sup −D+1} if the sphere is imposed with Dirichlet boundary condition, and to L{sup −D−1} if the sphere is imposed with Neumann boundary condition, where L is distance from the center of the sphere to the plane. For the small separation asymptotic behavior, it is shown that the leading term is equal to the one obtained using proximity force approximation. The next-to-leading order term is also computed using perturbation method. It is shown that when the space dimension D is larger than 5, the next-to-leading order has sign opposite to the leading order term. Moreover, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions.
Casimir-Polder effect with thermally excited surfaces
NASA Astrophysics Data System (ADS)
Laliotis, A.; Ducloy, M.
2015-05-01
We take a closer look at the fundamental Casimir-Polder (CP) interaction between quantum particles and dispersive dielectric surfaces with surface polariton or plasmon resonances. Linear response theory shows that in the near-field, van der Waals regime the free-energy shift of a particle contains a thermal component that depends exclusively on the excitation of the evanescent surface polariton (plasmon or phonon) modes. Our work makes evident the link between particle surface interaction and near-field thermal emission and demonstrates how this can be used to engineer Casimir-Polder forces. We also examine how the exotic effects of surface waves are washed out as the distance from the surface increases. In the case of molecules or excited-state atoms, far-field approximations result in a classical dipole-dipole interaction which depends on the surface reflectivity and the mean number of photons at the frequency of the atomic or molecular transition. Finally we present numerical results for the CP interaction between Cs atoms and various dielectric surfaces with a single polariton resonance and discuss the implications of temperature and retardation effects for specific spectroscopic experiments.
Casimir energy of smooth compact surfaces
NASA Astrophysics Data System (ADS)
Straley, Joseph P.; Kolomeisky, Eugene B.
2014-07-01
We discuss the formalism of Balian and Duplantier [Balian and Duplantier, Ann. Phys. (NY) 104, 300 (1977), 10.1016/0003-4916(77)90334-7; Balian and Duplantier, Ann. Phys. (NY) 112, 165 (1978), 10.1016/0003-4916(78)90083-0] for the calculation of the Casimir energy for an arbitrary smooth compact surface and use it to give some examples: a finite cylinder with hemispherical caps, a torus, an ellipsoid of revolution, a cube with rounded corners and edges, and a drum made of disks and part of a torus. We propose a model function that approximately captures the shape dependence of the Casimir energy.
Bezerra, V. B.; Romero, C.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2010-03-01
We report stronger constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the lateral Casimir force between sinusoidally corrugated surfaces of a sphere and a plate. In the interaction range from 1.6 to 14 nm the strengthening of previously known high confidence constraints up to a factor of 2.4x10{sup 7} is achieved using these measurements. It is shown that the replacement of a plane plate with a corrugated one in the measurements of the normal Casimir force by means of an atomic force microscope would result in the strengthening of respective high confidence constraints on the Yukawa-type interaction by a factor of 1.1x10{sup 12}. The use of a corrugated plate instead of a plane plate in the experiment by means of a micromachined oscillator also leads to strengthening of the obtained constraints. We further obtain constraints on the parameters of Yukawa-type interaction from the data of experiments measuring the gradient of the Casimir pressure between two parallel plates and the gradient of the Casimir-Polder force between an atom and a plate. The obtained results are compared with the previously known constraints. The possibilities of how to further strengthen the constraints on non-Newtonian gravity are discussed.
Soltani, Morteza; Sarabadani, Jalal; Kheirandish, Fardin; Rabbani, Hasan
2010-10-15
Path-integral formalism is employed to study normal and lateral Casimir interactions in a system composed of a dispersive medium surrounded by two semi-infinite ideal conductors. The dispersive medium is modeled by a continuum of harmonic oscillators, and it is shown that for smooth conductors, the normal force at small distances in the presence of a dispersive medium coincides with the original Casimir force, while at large distances, it tends to the original form with a renormalized coefficient. The correction to the normal force because of the roughness on one of the conductors is calculated. When the inner surfaces of both conductors have roughness, the lateral Casimir interaction occurs because of translational symmetry breaking, which is studied. It is shown that both normal and lateral Casimir forces in the presence of a dispersive medium are weaker in comparison with the original one and are proportional to the roughness amplitude squared. The dependence of the normal and lateral interactions on the memory and strength of the dispersive medium is considered.
NASA Astrophysics Data System (ADS)
Bezerra, V. B.; Klimchitskaya, G. L.; Mostepanenko, V. M.; Romero, C.
2010-03-01
We report stronger constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the lateral Casimir force between sinusoidally corrugated surfaces of a sphere and a plate. In the interaction range from 1.6 to 14 nm the strengthening of previously known high confidence constraints up to a factor of 2.4×107 is achieved using these measurements. It is shown that the replacement of a plane plate with a corrugated one in the measurements of the normal Casimir force by means of an atomic force microscope would result in the strengthening of respective high confidence constraints on the Yukawa-type interaction by a factor of 1.1×1012. The use of a corrugated plate instead of a plane plate in the experiment by means of a micromachined oscillator also leads to strengthening of the obtained constraints. We further obtain constraints on the parameters of Yukawa-type interaction from the data of experiments measuring the gradient of the Casimir pressure between two parallel plates and the gradient of the Casimir-Polder force between an atom and a plate. The obtained results are compared with the previously known constraints. The possibilities of how to further strengthen the constraints on non-Newtonian gravity are discussed.
NASA Astrophysics Data System (ADS)
Bimonte, G.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2017-05-01
We propose a universal experiment to measure the differential Casimir force between a Au-coated sphere and two halves of a structured plate covered with a P-doped Si overlayer. The concentration of free charge carriers in the overlayer is chosen slightly below the critical one, for which the phase transition from dielectric to metal occurs. One half of the structured plate is insulating, while the second half is made of gold. For the former we consider two structures, one consisting of bulk high-resistivity Si and the other of a layer of SiO 2 followed by bulk high-resistivity Si. The differential Casimir force is computed within the Lifshitz theory using four approaches that have been proposed in the literature to account for the role of free charge carriers in metallic and dielectric materials interacting with quantum fluctuations. According to these approaches, Au at low frequencies is described by either the Drude or the plasma model, whereas the free charge carriers in dielectric materials at room temperature are either taken into account or disregarded. It is shown that the values of differential Casimir forces, computed in the micrometer separation range using these four approaches, are widely distinct from each other and can be easily discriminated experimentally. It is shown that for all approaches the thermal component of the differential Casimir force is sufficiently large for direct observation. The possible errors and uncertainties in the proposed experiment are estimated and its importance for the theory of quantum fluctuations is discussed.
Long-Range Interactions in Polymer Melts: The Anti-Casimir Effect
NASA Astrophysics Data System (ADS)
Obukhov, S. P.; Semenov, A. N.
2005-07-01
It is well known that small neutral particles normally tend to aggregate due to the van der Waals forces. We discover a new universal long-range interaction between solid objects in polymer media that is directly opposite the van der Waals attraction. The new force could reverse the sign of the net interaction, possibly leading to the net repulsion. This universal repulsion comes from the subtracted soft fluctuation modes, which are not present in the real polymer system, but rather are in its ideal counterpart. The predicted effect has a deep relation to the classical Casimir interactions, providing an unusual example of fluctuation-induced repulsion instead of normal attraction. That is why it is referred to as the anti-Casimir effect. We also find that the correlation function of monomer units in a concentrated solution of infinite polymer chains follows a power-law rather than an exponential decay at large distances.
Casimir torque on a cylindrical gear
NASA Astrophysics Data System (ADS)
Vaidya, Varun
2014-08-01
I utilize effective field theory(EFT) techniques to calculate the Casimir torque on a cylindrical gear in the presence of a polarizable but neutral object and present results for the energy and torque as a function of angle for a gear with multiple cogs, as well as for the case of a concentric cylindrical gear.
Quantum coherence in the dynamical Casimir effect
NASA Astrophysics Data System (ADS)
Samos-Sáenz de Buruaga, D. N.; Sabín, Carlos
2017-02-01
We propose to use quantum coherence as the ultimate proof of the quantum nature of the radiation that appears by means of the dynamical Casimir effect in experiments with superconducting microwave waveguides. We show that, unlike previously considered measurements such as entanglement and discord, quantum coherence does not require a threshold value of the external pump amplitude and is highly robust to thermal noise.
Electromagnetic thermal corrections to Casimir energy
NASA Astrophysics Data System (ADS)
Nazari, Borzoo
2016-07-01
In [B. Nazari, Mod. Phys. Lett. A 31, 1650007 (2016)], we calculated finite temperature corrections to the energy of the Casimir effect of two conducting parallel plates in a general weak gravitational field. The calculations was done for the case a scalar field was present between the plates. Here we find the same results in the presence of an electromagnetic field.
Casimir effect of the electromagnetic field in D-dimensional spherically symmetric cavities
Teo, L. P.
2010-10-15
Eigenmodes of the electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE modes and one polarization for TM modes, giving rise to a total of (D-1) polarizations. In case of a D-dimensional ball, the eigenfrequencies of the electromagnetic field with perfectly conducting boundary condition coincides with the eigenfrequencies of gauge 1-forms with relative boundary condition; whereas the eigenfrequencies of the electromagnetic field with infinitely permeable boundary condition coincides with the eigenfrequencies of gauge 1-forms with absolute boundary condition. Casimir energies of single and concentric spherical shells in D-dimensions are computed. The Casimir energy of concentric spherical shells can be written as a sum of the single spherical shell contributions and an interacting term, and the latter is free of divergence. The interacting term always gives rise to an attractive force between the two spherical shells. Its leading term is the Casimir force acting between two parallel plates of the same area, as expected by proximity force approximation.
Casimir energies of cavities: The geometry question
NASA Astrophysics Data System (ADS)
Abalo, Iroko Komi Elom
The question of how the Casimir effect relates to a system's geometry is of fundamental interest. In this thesis, we present new results for interior Casimir self-energies of various integrable geometries and show interesting systematic relations between these energies. In particular, we consider prisms with triangular cross sections (equilateral, hemiequilateral, and right isosceles triangles), triangular polygons of the same cross sections, and three tetrahedra. The triangular prisms are of infinite or finite lengths. These geometries are integrable and unique in the sense that the Laplacian eigenvalues may be found using the method of images. We obtain interior Casimir energies for these cavities subject to Dirichlet and Neumann boundary conditions. In addition to these boundary conditions, we also obtain electromagnetic Casimir energies for the infinite prisms. These energies are regularized using various consistent methods, one of which is regularization by point-splitting. Summing these modes explicitly using a cylinder kernel formulation, we show that the correct Weyl divergences are obtained. We also give closed-form results for the infinite triangular prisms. In order to understand the geometry dependence of these energies, we rederive well-known results for rectangular parallelepipeds (including the cube) and infinite rectangular prisms. The analysis of these self-energies yields intriguing results. By plotting the scaled energies against the appropriately chosen isoperimetric or isoareal quotients, we observe interesting patterns, which hint towards a systematic functional dependence. In addition to the calculation of new Casimir energies, this constitutes a significant contribution to the theoretical understanding of self-energies and has interesting implications.
Thermal Casimir effect in closed Friedmann universe revisited
Bezerra, V. B.; Romero, C.; Klimchitskaya, G. L.; Mostepanenko, V. M.
2011-05-15
We reconsider Casimir free energy and internal energy at nonzero temperature in the static Einstein and closed Friedmann universe. It is shown that the Casimir free energy is given by the difference between the free energy of a topologically nontrivial manifold and a tangential Minkowski space-time. We derive exact expressions for the Casimir free energy, internal energy and pressure in Einstein and Friedmann universes in terms of single sums. The Casimir entropy is shown to satisfy the Nernst heat theorem. Exact expressions for corresponding total quantities in the Einstein universe are obtained from the Casimir ones by adding a contribution of the black-body radiation. The asymptotic expressions for the Casimir free energy and internal energy at both high and low temperature are shown to be in direct analogy with those for two ideal-metal plates and an ideal-metal spherical shell. Specifically, at high temperature the classical limit holds.
Thermal Casimir effect in closed Friedmann universe revisited
NASA Astrophysics Data System (ADS)
Bezerra, V. B.; Klimchitskaya, G. L.; Mostepanenko, V. M.; Romero, C.
2011-05-01
We reconsider Casimir free energy and internal energy at nonzero temperature in the static Einstein and closed Friedmann universe. It is shown that the Casimir free energy is given by the difference between the free energy of a topologically nontrivial manifold and a tangential Minkowski space-time. We derive exact expressions for the Casimir free energy, internal energy and pressure in Einstein and Friedmann universes in terms of single sums. The Casimir entropy is shown to satisfy the Nernst heat theorem. Exact expressions for corresponding total quantities in the Einstein universe are obtained from the Casimir ones by adding a contribution of the black-body radiation. The asymptotic expressions for the Casimir free energy and internal energy at both high and low temperature are shown to be in direct analogy with those for two ideal-metal plates and an ideal-metal spherical shell. Specifically, at high temperature the classical limit holds.
Casimir microsphere diclusters and three-body effects in fluids
Varela, Jaime; McCauley, Alexander P.; Rodriguez, Alejandro W.; Johnson, Steven G.
2011-04-15
Our previous paper [Phys. Rev. Lett. 104, 060401 (2010)] predicted that Casimir forces induced by the material-dispersion properties of certain dielectrics can give rise to stable configurations of objects. This phenomenon was illustrated via a dicluster configuration of nontouching objects consisting of two spheres immersed in a fluid and suspended against gravity above a plate. Here, we examine these predictions from the perspective of a practical experiment and consider the influence of nonadditive, three-body, and nonzero-temperature effects on the stability of the two spheres. We conclude that the presence of Brownian motion reduces the set of experimentally realizable silicon-teflon spherical diclusters to those consisting of layered microspheres, such as the hollow core (spherical shells) considered here.
NASA Astrophysics Data System (ADS)
Tomaš, M. S.
We discuss some implications of a very recently obtained result for the force on a slab in a planar cavity based on the calculation of the vacuum Lorentz force [C.Raabe and D.-G. Welsch, Phys. Rev. A 71 (2005) 013814]. We demonstrate that, according to this formula, the total force on the slab consists of a medium-screened Casimir force and, in addition to it, a medium-assisted force. The sign of of the medium-assisted force is determined solely by the properties of the cavity mirrors. In the Lifshitz configuration, this force is proportional to 1/d at small distances and is very small compared with the corresponding van der Waals force. At large distances, however, it is proportional to 1/d4 and comparable with the Casimir force, especially for denser media. The exponents in these power laws decrease by 1 in the case of a thin slab. The formula for the medium-assisted force also describes the force on a layer of the cavity medium, which has similar properties. For dilute media, it implies an atom-mirror interaction of the Coulomb type at small and of the Casimir-Polder type at large atom-mirror distances. For a perfectly reflecting mirror, the latter force is effectively only three-times smaller than the Casimir-Polder force.
Fermionic Casimir energy in a three-dimensional box
Seyedzahedi, A.; Saghian, R.; Gousheh, S. S.
2010-09-15
In this paper we calculate the Casimir energy for a massless fermionic field confined inside a three-dimensional rectangular box. We use the MIT bag model boundary condition for the confinement. We use the direct mode summation method along with the Abel-Plana summation formula to compute the Casimir energy, without any use of regularization or analytic continuation techniques. We obtain a negative Casimir energy, as opposed to the previously reported result for the interior of a three-dimensional sphere.
Casimir-Polder potential and transition rate in resonating cylindrical cavities
Ellingsen, Simen A.; Buhmann, Stefan Yoshi; Scheel, Stefan
2010-09-15
We consider the Casimir-Polder potential of particles placed inside a metallic cylindrical cavity at finite temperatures, taking account of thermal nonequilibrium effects. In particular, we study how the resonant (thermal nonequilibrium) potential and transition rates can be enhanced by fine tuning the radius of the cavity to match the transition wavelength of the dominant transitions of the particle. Numerical calculations show that the cavity-induced energy-level shift of atoms prepared in low-lying Rydberg states can be enhanced beyond 30 kHz, which is within the range of observability of modern experiments. Because the magnitude of the resonance peaks depends sensitively on the low-frequency dissipation of the cavity metal, experiments in this setup could be a critical test of the disputed thermal correction to the Casimir force between metal plates.
Gravitational Casimir effect, the Lifshitz theory, and the existence of gravitons
NASA Astrophysics Data System (ADS)
Pinto, Fabrizio
2016-12-01
It has been predicted that, if gravitational wave reflectors exist, two such parallel plane gravitational mirrors separated by an empty gap will interact not only via the well-known Casimir effect of quantum electrodynamics but also because of an analogous gravitational Casimir force. It has been further claimed that this phenomenon would demonstrate the existence of gravitons. In this note, we discuss epistemological pitfalls of such a conclusion connected to the logical structure of the Lifshitz theory and we show such an experiment cannot prove gravity quantization. We also expose interpretative challenges of any future data due to extreme uncertainties on the spectrum of the predicted stochastic astrophysical and cosmological gravitational wave background.
Magnetic anisotropy due to the Casimir effect
Metalidis, G.; Bruno, P.
2010-02-15
We consider the Casimir interaction between a ferromagnetic and a nonmagnetic mirror and show how the Casimir effect gives rise to a magnetic anisotropy in the ferromagnetic layer. The anisotropy is out of plane if the nonmagnetic plate is optically isotropic. If the nonmagnetic plate shows a uniaxial optical anisotropy (with optical axis in the plate plane), we find an in-plane magnetic anisotropy. In both cases, the energetically most favorable magnetization orientation is given by the competition between polar, longitudinal, and transverse contributions to the magneto-optical Kerr effect and will therefore depend on the interplate distance. Numerical results will be presented for a magnetic plate made out of Fe and nonmagnetic plates of Au (optically isotropic), quartz, calcite, and barium titanate (all uniaxially birefringent).
Effective Casimir conditions and group coherent states
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Tsobanjan, Artur
2014-06-01
Properties of group coherent states can be derived ‘effectively’ without knowing full wave functions. The procedure is detailed in this paper as an example of general methods for effective constraints. The role of constraints in the present context is played by a Casimir condition that puts states within an irreducible representation of a Lie group (or, equivalently, on a quantization of a co-adjoint orbit of the dual Lie algebra). Simplifications implied by a Casimir condition, compared with general first-class constraints, allows one to show that the correct number of degrees of freedom is obtained after imposing the condition. When combined with conditions to saturate uncertainty relations, moments of group coherent states can be derived. A detailed example in quantum cosmology (cosmic forgetfulness) illustrates the usefulness of the methods.
Casimir effect of massive vector fields
Teo, L. P.
2010-11-15
We study the Casimir effect due to a massive vector field in a system of two parallel plates made of real materials, in an arbitrary magnetodielectric background. The plane waves satisfying the Proca equations are classified into transverse modes and longitudinal modes which have different dispersion relations. Transverse modes are further divided into type I and type II corresponding to TE and TM modes in the massless case. For general magnetodielectric media, we argue that the correct boundary conditions are the continuities of H{sub ||}, {phi}, A, and {partial_derivative}{sub x}A{sub x}, where x is the direction normal to the plates. Although there are type I transverse modes that satisfy all the boundary conditions, it is impossible to find type II transverse modes or longitudinal modes that satisfy all the boundary conditions. To circumvent this problem, type II transverse modes and longitudinal modes have to be considered together. We call the contribution to the Casimir energy from type I transverse modes TE contribution, and the contribution from the superposition of type II transverse modes and longitudinal modes TM contribution. Their massless limits give, respectively, the TE and TM contributions to the Casimir energy of a massless vector field. The limit where the plates become perfectly conducting is discussed in detail. For the special case where the background has a unity refractive index, it is shown that the TM contribution to the Casimir energy can be written as a sum of contributions from two different types of modes, corresponding to type II discrete modes and type III continuum modes discussed by Barton and Dombey [G. Barton and N. Dombey, Ann. Phys. (N.Y.) 162, 231 (1985).]. For general background, this splitting does not work. The limit where both plates become infinitely permeable and the limit where one plate becomes perfectly conducting and one plate becomes infinitely permeable are also investigated.
Nonequilibrium Casimir-Polder plasmonic interactions
Bartolo, Nicola; Messina, Riccardo; Dalvit, Diego Alejandro Roberto; ...
2016-04-18
Here we investigate how the combination of nonequilibrium effects and material properties impacts on the Casimir-Polder interaction between an atom and a surface. By addressing systems with temperature inhomogeneities and laser interactions, we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear. Lastly, our treatment provides a self-consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom-surface interactions.
Functional approach to the fermionic Casimir effect
Fosco, C. D.; Losada, E. L.
2008-07-15
We use a functional approach to calculate the Casimir energy due to Dirac fields in interaction with thin, flat, parallel walls, which implement imperfect baglike boundary conditions. These are simulated by the introduction of {delta}-like interactions with the walls. We show that, with a proper choice for the corresponding coupling constants, bag-model boundary conditions are properly implemented. We obtain explicit expressions for the energies in 1+1 and 3+1 dimensions, for massless and massive fields.
Nonequilibrium Casimir-Polder plasmonic interactions
Bartolo, Nicola; Messina, Riccardo; Dalvit, Diego Alejandro Roberto; Intravaia, Francesco
2016-04-18
Here we investigate how the combination of nonequilibrium effects and material properties impacts on the Casimir-Polder interaction between an atom and a surface. By addressing systems with temperature inhomogeneities and laser interactions, we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear. Lastly, our treatment provides a self-consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom-surface interactions.
An experimental apparatus for Casimir torque measurements
NASA Astrophysics Data System (ADS)
Somers, David A. T.; Munday, Jeremy N.
We have developed an experiment to measure the Casimir torque. In our experiment, a solid birefringent crystal causes a nematic liquid crystal director to rotate such that the extraordinary axes are aligned. A transparent and isotropic dielectric spacer layer is used to separate the two birefringent materials and an all-optical technique is used for detection. In this talk, we report on the progress of this experiment. Department of Physics, Institute for Research in Electronics and Applied Physics.
Edges and diffractive effects in Casimir energies
Kabat, Daniel; Karabali, Dimitra; Nair, V. P.
2010-06-15
The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single plate with a slit in it, perpendicular plates separated by a gap, and two parallel plates, one of which has a long slit of large width, related to the case of one plate being semi-infinite. We develop a general formalism for studying such problems, based on the wave functional for the field in the gap between the plates. This formalism leads to a lower-dimensional theory defined on the open regions of the plates or boundaries. The Casimir energy is then given in terms of the determinant of the nonlocal differential operator which defines the lower-dimensional theory. We develop perturbative methods for computing these determinants. Our results are in good agreement with known results based on Monte Carlo simulations. The method is well suited to isolating the diffractive contributions to the Casimir energy.
Dynamical Casimir effect in a Josephson metamaterial
Lähteenmäki, Pasi; Paraoanu, G. S.; Hassel, Juha; Hakonen, Pertti J.
2013-01-01
The zero-point energy stored in the modes of an electromagnetic cavity has experimentally detectable effects, giving rise to an attractive interaction between the opposite walls, the static Casimir effect. A dynamical version of this effect was predicted to occur when the vacuum energy is changed either by moving the walls of the cavity or by changing the index of refraction, resulting in the conversion of vacuum fluctuations into real photons. Here, we demonstrate the dynamical Casimir effect using a Josephson metamaterial embedded in a microwave cavity at 5.4 GHz. We modulate the effective length of the cavity by flux-biasing the metamaterial based on superconducting quantum interference devices (SQUIDs), which results in variation of a few percentage points in the speed of light. We extract the full 4 × 4 covariance matrix of the emitted microwave radiation, demonstrating that photons at frequencies symmetrical with respect to half of the modulation frequency are generated in pairs. At large detunings of the cavity from half of the modulation frequency, we find power spectra that clearly show the theoretically predicted hallmark of the Casimir effect: a bimodal, “sparrow-tail” structure. The observed substantial photon flux cannot be assigned to parametric amplification of thermal fluctuations; its creation is a direct consequence of the noncommutativity structure of quantum field theory.
Critical Casimir interactions between colloids around the critical point of binary solvents.
Stuij, S G; Labbé-Laurent, M; Kodger, T E; Maciołek, A; Schall, P
2017-08-09
Critical Casimir interactions between colloidal particles arise from the confinement of fluctuations of a near-critical solvent in the liquid gap between closely-spaced particles. So far, the comparison of theoretical predictions and experimental measurements of critical Casimir forces (CCFs) has focused on the critical solvent composition, while it has been lacking for off-critical compositions. We address this issue by investigating CCFs between spherical colloidal particles around the critical point of a binary solvent through a combination of experiments, previous Ising Monte Carlo simulation results and field-theoretical methods. By measuring the correlation length of the near-critical solvent and the pair potentials of the particles in terms of radial distribution functions and by determining the second virial coefficient, we test in detail theoretical predictions. Our results indicate that the critical Casimir theory gives quantitative correct predictions for the interaction potential between particles in a near critical binary mixture if weak preferential adsorption of the particle surface is taken into account.
Casimir Friction and Near-field Radiative Heat Transfer in Graphene Structures
NASA Astrophysics Data System (ADS)
Volokitin, A. I.
2017-02-01
The dependence of the Casimir friction force between a graphene sheet and a (amorphous) SiO2 substrate on the drift velocity of the electrons in the graphene sheet is studied. It is shown that the Casimir friction is strongly enhanced for the drift velocity above the threshold velocity when the friction is determined by the resonant excitation of the surface phonon-polaritons in the SiO2 substrate and the electron-hole pairs in graphene. The theory agrees well with the experimental data for the current-voltage dependence for unsuspended graphene on the SiO2 substrate. The theories of the Casimir friction and the near-field radiative energy transfer are used to study the heat generation and dissipation in graphene due to the interaction with phonon-polaritons in the (amorphous) SiO2 substrate and acoustic phonons in graphene. For suspended graphene, the energy transfer coefficient at nanoscale gap is three orders of magnitude larger than the radiative heat transfer coefficient of the blackbody radiation limit.
Does the transverse electric zero mode contribute to the Casimir effect for a metal?
NASA Astrophysics Data System (ADS)
Høye, J. S.; Brevik, I.; Aarseth, J. B.; Milton, K. A.
2003-05-01
The finite-temperature Casimir free energy, entropy, and internal energy are considered anew for a conventional parallel-plate configuration, in the light of current discussions in the literature. In the case of an “ideal” metal, characterized by a refractive index equal to infinity for all frequencies, we recover, via a somewhat unconventional method, conventional results for the temperature dependence, meaning that the zero-frequency transverse electric mode contributes the same as the transverse magnetic mode. For a real metal, however, approximately obeying the Drude dispersive model at low frequencies, we find that the zero-frequency transverse electric mode does not contribute at all. This would appear to lead to an observable temperature dependence and a violation of the third law of thermodynamics. It had been suggested that the source of the difficulty was the behavior of the reflection coefficient for perpendicular polarization but we show that this is not the case. By introducing a simplified model for the Casimir interaction, consisting of two harmonic oscillators interacting via a third one, we illustrate the behavior of the transverse electric field. Numerical results are presented based on the refractive index for gold. A linear temperature correction to the Casimir force between parallel plates is indeed found which should be observable in room-temperature experiments, but this does not entail any thermodynamic inconsistency.
Determination of the Contact Angle Based on the Casimir Effect
NASA Technical Reports Server (NTRS)
Mazuruk, Konstantin; Volz, Martin P.
2015-01-01
On a macroscopic scale, a nonreactive liquid partially covering a homogeneous solid surface will intersect the solid at an angle called the contact angle. For molten metals and semiconductors, the contact angle is materially dependent upon both the solid and liquid and typical values fall in the range 80-170 deg, depending on the crucible material. On a microscopic scale, there does not exist a precise and sharp contact angle but rather the liquid and solid surfaces merge smoothly and continuously. Consider the example of the so called detached Bridgman crystal growth process. In this technique, a small gap is formed between the growing crystal and the crucible. At the crystal/melt interface, a meniscus ring is formed. Its width can be in the range of a few micrometers, approaching a microscopic scale. It then becomes questionable to describe the shape of this meniscus by the contact angle. A more advanced treatment of the interface is needed and here we propose such a refined model. The interaction of the liquid surface with the solid can be calculated by considering two forces: a short-range repulsive force and a longer range (up to a few micrometers) Casimir or van der Waals force.
The field theory of symmetrical layered electrolytic systems and the thermal Casimir effect
NASA Astrophysics Data System (ADS)
Dean, D. S.; Horgan, R. R.
2005-06-01
We present a general extension of a field-theoretic approach developed in earlier papers to the calculation of the free energy of symmetrically layered electrolytic systems which is based on the sine-Gordon field theory for the Coulomb gas. The method is to construct the partition function in terms of the Feynman evolution kernel in the Euclidean time variable associated with the coordinate normal to the surfaces defining the layered structure. The theory is applicable to cylindrical systems and its development is motivated by the possibility that a static van der Waals or thermal Casimir force could provide an attractive force stabilizing a dielectric tube formed from a lipid bilayer, an example of which is provided by the t-tubules occurring in certain muscle cells. In this context, we apply the theory to the calculation of the thermal Casimir effect for a dielectric tube of radius R and thickness δ formed from such a membrane in water. In a grand canonical approach we find that the leading contribution to the Casimir energy behaves like -kBTLκC/R which gives rise to an attractive force which tends to contract the tube radius. We find that κC~0.3 for the case of typical lipid membrane t-tubules. We conclude that except in the case of a very soft membrane this force is insufficient to stabilize such tubes against the bending stress which tends to increase the radius. We briefly discuss the role of the lipid membrane reservoir implicit in the approach and whether its nature in biological systems may possibly lead to a stabilizing mechanism for such lipid tubes.
Sign and other aspects of semiclassical Casimir energies
Schaden, Martin
2006-04-15
The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The semiclassical Casimir energies so defined coincide with those of zeta function regularization in the cases studied. Poles in the analytic continuation of zeta function regularization are related to nonuniversal subtractions in the spectral density. The sign of the Casimir energy of a scalar field on a smooth manifold is estimated by the sign of the contribution due to the shortest periodic rays only. Demanding continuity of the Casimir energy under small deformations of the manifold, the method is extended to integrable systems. The Casimir energy of a massless scalar field on a manifold with boundaries includes contributions due to periodic rays that lie entirely within the boundaries. These contributions in general depend on the boundary conditions. Although the Casimir energy due to a massless scalar field may be sensitive to the physical dimensions of manifolds with boundary. In favorable cases its sign can, contrary to conventional wisdom, be inferred without calculation of the Casimir energy.
Generalized Kramers-Kronig transform for Casimir effect computations
NASA Astrophysics Data System (ADS)
Bimonte, Giuseppe
2010-06-01
Recent advances in experimental techniques now permit measurement of the Casimir force with unprecedented precision. To achieve a comparable precision in the theoretical prediction of the force, it is necessary to accurately determine the electric permittivity of the materials constituting the plates along the imaginary frequency axis. The latter quantity is not directly accessible to experiments, but it can be determined via dispersion relations from experimental optical data. In the experimentally important case of conductors, however, a serious drawback of the standard dispersion relations commonly used for this purpose is their strong dependence on the chosen low-frequency extrapolation of the experimental optical data, which introduces a significant and not easily controllable uncertainty in the result. In this paper we show that a simple modification of the standard dispersion relations, involving suitable analytic window functions, resolves this difficulty, making it possible to reliably determine the electric permittivity at imaginary frequencies using solely experimental optical data in the frequency interval where they are available, without any need for uncontrolled data extrapolations.
Generalized Kramers-Kronig transform for Casimir effect computations
Bimonte, Giuseppe
2010-06-15
Recent advances in experimental techniques now permit measurement of the Casimir force with unprecedented precision. To achieve a comparable precision in the theoretical prediction of the force, it is necessary to accurately determine the electric permittivity of the materials constituting the plates along the imaginary frequency axis. The latter quantity is not directly accessible to experiments, but it can be determined via dispersion relations from experimental optical data. In the experimentally important case of conductors, however, a serious drawback of the standard dispersion relations commonly used for this purpose is their strong dependence on the chosen low-frequency extrapolation of the experimental optical data, which introduces a significant and not easily controllable uncertainty in the result. In this paper we show that a simple modification of the standard dispersion relations, involving suitable analytic window functions, resolves this difficulty, making it possible to reliably determine the electric permittivity at imaginary frequencies using solely experimental optical data in the frequency interval where they are available, without any need for uncontrolled data extrapolations.
Huge Casimir effect at finite temperature in electromagnetic Rindler space.
Zhao, Tian-Ming; Miao, Rong-Xin
2011-12-01
We investigate the Casimir effect at a finite temperature in the electromagnetic Rindler space, and we find that the Casimir energy is proportional to T(4)/d(2) in the high-temperature limit, where T ≈ 27 °C is the temperature and d ≈ 100 nm is a small cutoff. We propose to make metamaterials to mimic the Rindler space and measure the predicted Casimir effect. Because the parameters of metamaterials we proposed are quite simple, this experiment would be easily implemented in the laboratory. © 2011 Optical Society of America
Decca, R. S.; Lopez, D.; Fischbach, E.; Klimchitskaya, G. L.; Krause, D. E.; Mostepanenko, V. M.
2007-04-01
A micromechanical torsion oscillator has been used to strengthen the limits on new Yukawa forces by determining the Casimir pressure between two gold-coated plates. By significantly reducing the random errors and obtaining the electronic parameters of the gold coatings, we were able to conclusively exclude the predictions of large thermal effects below 1 {mu}m and strengthen the constraints on Yukawa corrections to Newtonian gravity in the interaction range from 29.5 nm to 86 nm.
The dynamical Casimir effect generates entanglement
NASA Astrophysics Data System (ADS)
Felicetti, Simone; Sanz, Mikel; Lamata, Lucas; Romero, Guillermo; Johansson, Göran; Delsing, Per; Solano, Enrique
2014-03-01
The existence of vacuum fluctuations, i.e., the presence of virtual particles in empty space, represents one of the most distinctive results of quantum mechanics. It is also known, under the name of dynamical Casimir effect, that fast-oscillating boundary conditions can generate real excitations out of the vacuum fluctuations. Long-awaited, the first experimental demonstration of this phenomenon has been realized only recently, in the framework of superconducting circuits [C. M. Wilson et al. Nature 479, 376-379 (2011)]. In this contribution, we will discuss novel theoretical results, showing that the dynamical Casimir effect can be exploited to generate bipartite and multipartite entanglement among qubits. We will also present a superconducting circuit design which can feasibly implement the model considered with current technology. Our scheme is composed of a SQUID device side-coupled to two transmission line resonators, each one interacting with a superconducting qubit. Such proposal can be straightforwardly generalized to the multipartite case, and it can be scaled up to build strongly correlated cavity lattices for quantum simulation and quantum computation. The authors acknowledge support from Spanish MINECO FIS2012-36673-C03-02; UPV/EHU UFI 11/55;Basque Government IT472-10; SOLID, CCQED, PROMISCE and SCALEQIT EU projects.
MHD Gauge Fields: Helicities and Casimirs
NASA Astrophysics Data System (ADS)
Hu, Q.; Webb, G. M.; Zank, G. P.; Anco, S.
2016-12-01
Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963). It is shown how the polarization vector P in Calkin's approach, naturally arises from the Lagrange multiplier constraint equation for Faraday's equation for the magnetic induction B, or alternatively from the magnetic vector potential form of Faraday's equation. Gauss's equation, (divergence of Bis zero), is incorporated in the variational principle by means of a Lagrange multiplier constraint. Noether's theorem, and gauge symmetries are used to derive the conservation laws for (a) magnetic helicity (b) cross helicity, (c) fluid helicity for non-magnetized fluids, and (d) a class of conservation laws associated with curl and divergence equations, which applies to Faraday's equation and Gauss's equation. The magnetic helicity conservation law is due to a gauge symmetry in MHD and not due to a fluid relabelling symmetry. The analysis is carried out for a non-barotropic gas. The cross helicity and fluid helicity conservation are nonlocal conservation laws, that reduce to local conservation laws for the case of a barotropic gas. The connections between gauge symmetries, Clebsch potentials and Casimirs are developed. It is shown that the gauge symmetry functionals in the work of Henyey (1982) satisfy the Casimir equations.
Casimir-Polder interaction between an atom and a cavity wall under the influence of real conditions
Babb, J.F.; Klimchitskaya, G.L.; Mostepanenko, V.M.
2004-10-01
The Casimir-Polder interaction between an atom and a metal wall is investigated under the influence of real conditions including the dynamic polarizability of the atom, finite conductivity of the wall metal, and nonzero temperature of the system. Both analytical and numerical results for the free energy and force are obtained over a wide range of atom-wall distances. Numerical computations are performed for an Au wall and metastable He*, Na, and Cs atoms. For the He* atom we demonstrate, as an illustration, that at short separations of about the Au plasma wavelength at room temperature the free energy deviates up to 35% and the force up to 57% from the classical Casimir-Polder result. Accordingly, such large deviations should be taken into account in precision experiments on atom-wall interactions. The combined account of different corrections to the Casimir-Polder interaction leads to the conclusion that at short separations the corrections due to the dynamic polarizability of an atom play a more important role than--and suppress--the corrections due to the nonideality of the metal wall. By comparison of the exact atomic polarizabilities with those in the framework of the single oscillator model, it is shown that the obtained asymptotic expressions enable calculation of the free energy and force for the atom-wall interaction under real conditions with a precision of 1%.
Casimir-Polder shifts on quantum levitation states
NASA Astrophysics Data System (ADS)
Crépin, P.-P.; Dufour, G.; Guérout, R.; Lambrecht, A.; Reynaud, S.
2017-03-01
An ultracold atom above a horizontal mirror experiences quantum reflection from the attractive Casimir-Polder interaction, which holds it against gravity and leads to quantum levitation states. We analyze this system by using a Liouville transformation of the Schrödinger equation and a Langer coordinate adapted to problems with a classical turning point. Reflection on the Casimir-Polder attractive well is replaced by reflection on a repulsive wall, and the problem is then viewed as an ultracold atom trapped inside a cavity with gravity and Casimir-Polder potentials acting, respectively, as top and bottom mirrors. We calculate numerically Casimir-Polder shifts of the energies of the cavity resonances and propose an approximate treatment which is precise enough to discuss spectroscopy experiments aimed at tests of the weak-equivalence principle on antihydrogen. We also discuss the lifetimes by calculating complex energies associated with cavity resonances.
Casimir: an architecture for mental spatial knowledge processing.
Schultheis, Holger; Barkowsky, Thomas
2011-10-01
Mental spatial knowledge processing often uses spatio-analogical or quasipictorial representation structures such as spatial mental models or mental images. The cognitive architecture Casimir is designed to provide a framework for computationally modeling human spatial knowledge processing relying on these kinds of representation formats. In this article, we present an overview of Casimir and its components. We briefly describe the long-term memory component and the interaction with external diagrammatic representations. Particular emphasis is placed on Casimir's working memory and control mechanisms. Regarding working memory, we describe the conceptual foundations and the processing mechanisms employed in mental spatial reasoning. With respect to control, we explain how it is realized as a distributed, emergent facility within Casimir. Copyright © 2011 Cognitive Science Society, Inc.
Casimir effects in Lorentz-violating scalar field theory
NASA Astrophysics Data System (ADS)
Cruz, M. B.; de Mello, E. R. Bezerra; Petrov, A. Yu.
2017-08-01
In this paper, we consider a Lorentz-breaking extension of the theory for a real massive scalar quantum field in the region between two large parallel plates, with our manner to break the Lorentz symmetry being C P T even and aetherlike. For this system, we calculated the Casimir energy considering different boundary conditions. It turns out that the Casimir energy strongly depends on the direction of the constant vector implementing the Lorentz symmetry breaking as well as on the boundary conditions.
Milton, K.A.; Jack Ng, Y.
1998-05-01
The experimental observation of intense light emission by acoustically driven, periodically collapsing bubbles of air in water (sonoluminescence) has yet to receive an adequate explanation. One of the most intriguing ideas is that the conversion of acoustic energy into photons occurs quantum mechanically, through a dynamical version of the Casimir effect. We have argued elsewhere that in the adiabatic approximation, which should be reliable here, Casimir or zero-point energies cannot possibly be large enough to be relevant. (About 10 MeV of energy is released per collapse.) However, there are sufficient subtleties involved that others have come to opposite conclusions. In particular, it has been suggested that bulk energy, that is, simply the naive sum of (1) /(2) {h_bar}{omega}, which is proportional to the volume, could be relevant. We show that this cannot be the case, based on general principles as well as specific calculations. In the process we further illuminate some of the divergence difficulties that plague Casimir calculations, with an example relevant to the bag model of hadrons. {copyright} {ital 1998} {ital The American Physical Society}
How to confirm and exclude different models of material properties in the Casimir effect.
Mostepanenko, V M
2015-06-03
We formulate a method allowing us to confirm or exclude the alternative models of material properties at some definite confidence level in experiments on measuring the Casimir force. The method is based on the consideration of differences between the theoretical and mean measured quantities and the confidence intervals for these differences found at sufficiently high or low confidence probabilities. The developed method is applied to the data of four recent experiments on measuring the gradient of the Casimir force by means of a dynamic atomic force microscope. It is shown that in experiments with Au-Au and Ni-Ni test bodies, where the Drude model approach is excluded at a 95% confidence level, the plasma model approach agrees with the data at higher than 90% confidence. In experiments using an Au sphere interacting with either a Ni plate or a graphene-coated substrate, the measurement data agree with the common prediction of the Drude and plasma model approaches and theory using the polarization tensor at 90% and 80% confidence levels, respectively.
Disentangling geometric and dissipative origins of negative Casimir entropies.
Umrath, Stefan; Hartmann, Michael; Ingold, Gert-Ludwig; Neto, Paulo A Maia
2015-10-01
Dissipative electromagnetic response and scattering geometry are potential sources for the appearance of a negative Casimir entropy. We show that the dissipative contribution familiar from the plane-plane geometry appears also in the plane-sphere and the sphere-sphere geometries and adds to the negative Casimir entropy known to exist in these geometries even for perfectly reflecting objects. Taking the sphere-sphere geometry as an example, we carry out a scattering-channel analysis, which allows us to distinguish between the contributions of different polarizations. We demonstrate that dissipation and geometry share a common feature making possible negative values of the Casimir entropy. In both cases there exists a scattering channel whose contribution to the Casimir free energy vanishes in the high-temperature limit. While the mode-mixing channel is associated with the geometric origin, the transverse electric channel is associated with the dissipative origin of the negative Casimir entropy. By going beyond the Rayleigh limit, we find even for large distances that negative Casimir entropies can occur also for Drude-type metals provided the dissipation strength is sufficiently small.
Physically sound Hamiltonian formulati on of the dynamical Casimir effect
Haro, Jaume; Elizalde, Emilio
2007-09-15
Recently [J. Haro and E. Elizalde, Phys. Rev. Lett. 97, 130401 (2006)], a Hamiltonian formulation has been introduced in order to address some long-standing severe problems associated with the physical description of the dynamical Casimir effect at all times while the mirrors are moving. Here we present the complete calculation providing precise details, in particular, of the regularization procedure, which is decisive for the correct derivation of physically meaningful quantities. A basic difference when comparing with the results previously obtained by other authors is the fact that the motion force derived in our approach contains a reactive term--proportional to the mirrors' acceleration. This is of the essence in order to obtain particles with a positive energy at all times during the oscillation of the mirrors--while always satisfying the energy conservation law. A careful analysis of the interrelations among the different results previously obtained in the literature is then carried out. For simplicity, the specific case of a neutral scalar field in one dimension, with one or two partially transmitting mirrors (a fundamental proviso for the regularization issue), is considered in more detail, but our general method is shown to be generalizable, without essential problems (Sec. II of this paper), to fields of any kind in two and higher dimensions.
Dynamical Casimir effect for semitransparent mirrors
NASA Astrophysics Data System (ADS)
Fosco, C. D.; Giraldo, A.; Mazzitelli, F. D.
2017-08-01
We study the dynamical Casimir effect resulting from the oscillatory motion of either one or two flat semitransparent mirrors, coupled to a quantum real and massless scalar field. Our approach is based on a perturbative evaluation, in the coupling between mirrors and field, of the corresponding effective action, which is used to compute the particle creation rate. The amplitude of the oscillation is not necessarily small. We first obtain results for a single mirror, both for nonrelativistic and for relativistic motions, showing that only for the latter may the effects be significant. For two mirrors, on the other hand, we show that there are interesting interference effects, and that in some particular cases the results differ from those obtained assuming small amplitudes, already for nonrelativistic motions.
ERIC Educational Resources Information Center
Gamble, Reed
1989-01-01
Discusses pupil misconceptions concerning forces. Summarizes some of Assessment of Performance Unit's findings on meaning of (1) force, (2) force and motion in one dimension and two dimensions, and (3) Newton's second law. (YP)
ERIC Educational Resources Information Center
Gamble, Reed
1989-01-01
Discusses pupil misconceptions concerning forces. Summarizes some of Assessment of Performance Unit's findings on meaning of (1) force, (2) force and motion in one dimension and two dimensions, and (3) Newton's second law. (YP)
Elizalde, E.; Odintsov, S. D.; Saharian, A. A.
2011-05-15
We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive fermionic field in the geometry of two parallel plates on the background of Minkowski spacetime with an arbitrary number of toroidally compactified spatial dimensions, in the presence of a constant gauge field. Bag boundary conditions are imposed on the plates and periodicity conditions with arbitrary phases are considered along the compact dimensions. The nontrivial topology of the background spacetime leads to an Aharonov-Bohm effect for the vacuum expectation values induced by the gauge field. The fermionic condensate and the expectation value of the energy-momentum tensor are periodic functions of the magnetic flux with period equal to the flux quantum. The boundary induced parts in the fermionic condensate and the vacuum energy density are negative, with independence of the phases in the periodicity conditions and of the value of the gauge potential. Interaction forces between the plates are thus always attractive. However, in physical situations where the quantum field is confined to the region between the plates, the pure topological part contributes as well, and then the resulting force can be either attractive or repulsive, depending on the specific phases encoded in the periodicity conditions along the compact dimensions, and on the gauge potential, too. Applications of the general formulas to cylindrical carbon nanotubes are considered, within the framework of a Dirac-like theory for the electronic states in graphene. In the absence of a magnetic flux, the energy density for semiconducting nanotubes is always negative. For metallic nanotubes the energy density is positive for long tubes and negative for short ones. The resulting Casimir forces acting on the edges of the nanotube are attractive for short tubes with independence of the tube chirality. The sign of the force for long nanotubes can be controlled by tuning the magnetic flux
Evanescent radiation, quantum mechanics and the Casimir effect
NASA Technical Reports Server (NTRS)
Schatten, Kenneth H.
1989-01-01
An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.
Casimir effect in the Kerr spacetime with quintessence
NASA Astrophysics Data System (ADS)
Bezerra, V. B.; Cunha, M. S.; Freitas, L. F. F.; Muniz, C. R.; Tahim, M. O.
2017-01-01
We calculate the Casimir energy of a massless scalar field in a cavity formed by nearby parallel plates orbiting a rotating spherical body surrounded by quintessence, investigating the influence of the gravitational field on that energy, at zero temperature. This influence includes the effects due to the spacetime dragging caused by the source rotation as well as those ones due to the quintessence. We show that the energy depends on all the involved parameters, as source mass, angular momentum and quintessence state parameter, for any radial coordinate and polar angle. We show that at the north pole the Casimir energy is not influenced by the quintessential matter. At the equatorial plane, when the quintessence is canceled, the result obtained in the literature is recovered. Finally, constraints in the quintessence parameters are obtained from the uncertainty in the current measurements of Casimir effect.
Development of a Strontium Magneto-Optical Trap for Probing Casimir-Polder Potentials
NASA Astrophysics Data System (ADS)
Martin, Paul J.
In recent years, cold atoms have been the centerpiece of many remarkably sensitive measurements, and much effort has been made to devise miniaturized quantum sensors and quantum information processing devices. At small distances, however, mechanical effects of the quantum vacuum begin to significantly impact the behavior of the cold-atom systems. A better understanding of how surface composition and geometry affect Casimir and Casimir-Polder potentials would benefit future engineering of small-scale devices. Unfortunately, theoretical solutions are limited and the number of experimental techniques that can accurately detect such short-range forces is relatively small. We believe the exemplary properties of atomic strontium--which have enabled unprecedented frequency metrology in optical lattice clocks--make it an ideal candidate for probing slight spectroscopic perturbations caused by vacuum fluctuations. To that end, we have constructed a magneto-optical trap for strontium to enable future study of atom-surface potentials, and the apparatus and proposed detection scheme are discussed herein. Of special note is a passively stable external-cavity diode laser we developed that is both affordable and competitive with high-end commercial options.
Fermionic condensate and the Casimir effect in cosmic string spacetime
NASA Astrophysics Data System (ADS)
Grigoryan, A. Kh.; Mkrtchyan, A. R.; Saharian, A. A.
We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel-Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy-momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative at large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy-momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy-momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.
Casimir effect for parallel plates in a Friedmann-Robertson-Walker universe
NASA Astrophysics Data System (ADS)
Bezerra de Mello, E. R.; Saharian, A. A.; Setare, M. R.
2017-03-01
We evaluate the Hadamard function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with a general curvature coupling parameter in the geometry of two parallel plates on a spatially flat Friedmann-Robertson-Walker background with a general scale factor. On the plates, the field operator obeys the Robin boundary conditions with the coefficients depending on the scale factor. In all the spatial regions, the VEVs are decomposed into the boundary-free and boundary-induced contributions. Unlike the problem with the Minkowski bulk, in the region between the plates, the normal stress is not homogeneous and does not vanish in the geometry of a single plate. Near the plates, it has different signs for accelerated and decelerated expansions of the Universe. The VEV of the energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component describing an energy flux along the direction normal to the boundaries. Expressions are derived for the Casimir forces acting on the plates. Depending on the Robin coefficients and on the vacuum state, these forces can be either attractive or repulsive. An important difference from the corresponding result in the Minkowski bulk is that the forces on the separate plates, in general, are different if the corresponding Robin coefficients differ. We give the applications of general results for the class of α vacua in the de Sitter bulk. It is shown that, compared with the Bunch-Davies vacuum state, the Casimir forces for a given α vacuum may change the sign.
Computing the Casimir energy using the point-matching method
Lombardo, F. C.; Mazzitelli, F. D.; Vazquez, M.; Villar, P. I.
2009-09-15
We use a point-matching approach to numerically compute the Casimir interaction energy for a two perfect-conductor waveguide of arbitrary section. We present the method and describe the procedure used to obtain the numerical results. At first, our technique is tested for geometries with known solutions, such as concentric and eccentric cylinders. Then, we apply the point-matching technique to compute the Casimir interaction energy for new geometries such as concentric corrugated cylinders and cylinders inside conductors with focal lines.
Room-temperature phonon boundary scattering below the Casimir limit
Sadhu, J; Sinha, S
2011-09-26
Thermal conductivity data for rough surface silicon nanowires suggest the breakdown of the Casimir limit which assumes completely diffuse phonon boundary scattering. We show that coherent effects in phonon transport at room temperature indeed lead to such breakdown. Correlated multiple scattering of phonons off the rough surface lead to a reduced thermal conductivity that is dependent not only on the roughness amplitude but more importantly on the roughness correlation length. A correlation length less than the diameter of the wire is typically necessary for lowering the thermal conductivity below the Casimir limit. Our model explains seeming anomalies in data reported for electrolessly etched and electron beam lithography defined nanowires.
Many-body critical Casimir interactions in colloidal suspensions.
Hobrecht, Hendrik; Hucht, Alfred
2015-10-01
We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the Z(2) symmetry of the system is broken by the particles. We present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions.
Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir
NASA Astrophysics Data System (ADS)
Gomis, Joaquim; Longhi, Giorgio
2016-01-01
We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.
Comment on 'Casimir energies: Temperature dependence, dispersion, and anomalies'
Ravndal, Finn
2009-05-15
It is pointed out that the Casimir energy in a medium can be obtained most directly from the zero-point energy of the electromagnetic field because of its reduced propagation velocity. This brings to the fore again the old problem related to how the principle of relativity is combined with the Maxwell field equations in a continuous medium.
Dynamical Casimir effect and minimal temperature in quantum thermodynamics
NASA Astrophysics Data System (ADS)
Benenti, Giuliano; Strini, Giuliano
2015-02-01
We study the fundamental limitations of cooling to absolute zero for a qubit, interacting with a single mode of the electromagnetic field. Our results show that the dynamical Casimir effect, which is unavoidable in any finite-time thermodynamic cycle, forbids the attainability of the absolute zero of temperature, even in the limit of an infinite number of cycles.
NASA Astrophysics Data System (ADS)
Barton, Gabriel; Dodonov, Victor V.; Man'ko, Vladimir I.
2004-05-01
The past few years have seen a growing interest in quantum mechanical systems with moving boundaries. One of its manifestations was the First International Workshop on Problems with Moving Boundaries organized by Professor J Dittrich in Prague in October 2003. Another event in this series will be the (first) International Workshop on the Dynamical Casimir Effect in Padua in June 2004, organized by Professor G Carugno (see webpage www.pd.infn.it/casimir/ for details). As Guest Editors we invite researchers working in any area related to moving boundaries to contribute to a Topical Issue of Journal of Optics B: Quantum and Semiclassical Optics on the nonstationary Casimir effect and quantum systems with moving boundaries. Our intention is to cover a wide range of topics. In particular, we envisage possible contributions in the following areas: Theoretical and experimental studies on quantum fields in cavities with moving boundaries and time-dependent media. This area includes, in particular, various manifestations of the nonstationary (dynamical) Casimir effect, such as creation of quanta and modifications of Casimir force due to the motion of boundaries. Other relevant subjects are: generation and evolution of nonclassical states of fields and moving mirrors; interaction between quantized fields and atoms in cavities with moving boundaries; decoherence and entanglement due to the motion of boundaries; field quantization in nonideal cavities with moving boundaries taking into account losses and dispersion; nano-devices with moving boundaries. Quantum particles in domains confined with moving boundaries. This area includes: new exact and approximate solutions of the evolution equations (Schrödinger, Klein-Gordon, Dirac, Fokker-Planck, etc); quantum carpets and revivals; escape and tunnelling through moving barriers; evolution of quantum packets in the presence of moving boundaries; ultracold atoms (ions) in traps with moving boundaries. The topical issue is scheduled
Dynamics of the Vacuum and Casimir Analogs to the Hydrogen Atom
NASA Technical Reports Server (NTRS)
White, Harold; Vera, Jerry; Bailey, Paul; March, Paul; Lawrence, Tim; Sylvester, Andre; Brady, David
2015-01-01
This paper will discuss the current viewpoint of the vacuum state and explore the idea of a "natural" vacuum as opposed to immutable, non-degradable vacuum. This concept will be explored for all primary quantum numbers to show consistency with observation at the level of Bohr theory. A comparison with the Casimir force per unit area will be made, and an explicit function for the spatial variation of the vacuum density around the atomic nucleus will be derived. This explicit function will be numerically modeled using the industry multi-physics tool, COMSOL(trademark), and the eigenfrequencies for the n = 1 to n = 7 states will be found and compared to expectation.
Optical switching of a graphene mechanical switch using the Casimir effect
NASA Astrophysics Data System (ADS)
Inui, Norio
2017-09-01
We propose a method to control a graphene-based mechanical switch with light. By positioning a self-supporting graphene sheet parallel to a doped silicon membrane, irradiation of the membrane with light can bring the graphene into contact with the membrane. This operation is based on the enhancement of the Casimir force between the graphene sheet and a doped silicon membrane that results from photoionization; therefore, pull-in phenomena can occur even without applying any voltage. We theoretically investigated the dependence of the maximum displacement of a graphene sheet on the power of the irradiation light. Furthermore, the switching time is estimated by analyzing the time-evolution of the carrier density in a doped silicon membrane.
Casimir-Polder interaction between an atom and an infinite boundary in a thermal bath
She Wuying; Yu Hongwei; Zhu Zhiying
2010-01-15
We study the energy level shift of a static two-level atom interacting with a massless scalar field in a thermal bath with the presence of a plane boundary, which gives rise to the Casimir-Polder force. We separately calculate contributions of both thermal fluctuations and radiation reaction using the formalism suggested by J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji [J. Phys. (France) 43, 1617 (1982); 45, 673 (1984)] and analyze in detail the behaviors of the total energy level shifts in three distinct distance regimes in both the low- and high-temperature limits. A comparison of our results with those of a uniformly accelerated atom reveals that uniformly accelerated atoms, in general, do not behave the same as static ones in a thermal bath at the Unruh temperature in terms of the atomic energy level shifts.
Short-range Fundamental forces
Antoniadis, I; Baessler, Stefan; Buechner, M; Fedorov, General Victor; Hoedl, S.; Lambrecht, A; Nesvizhevsky, V.; Pignol, G; Reynaud, S.; Sobolev, Yu.
2011-01-01
We consider theoretical motivations to search for extra short-range fundamental forces as well as experiments constraining their parameters. The forces could be of two types: (1) spin-independent forces; and (2) spin-dependent axion-like forces. Different experimental techniques are sensitive in respective ranges of characteristic distances. The techniques include measurements of gravity at short distances, searches for extra interactions on top of the Casimir force, precision atomic and neutron experiments. We focus on neutron constraints, thus the range of characteristic distances considered here corresponds to the range accessible for neutron experiments.
Onsager-Casimir Principle in the Theory of Bi-Anisotropic Media
2000-09-29
UNCLASSIFIED Defense Technical Information Center Compilation Part Notice ADPO 11624 TITLE: Onsager- Casimir Principle in the Theory of Bi-Anisotropic...following component part numbers comprise the compilation report: ADP011588 thru ADP011680 UNCLASSIFIED 159 Onsager- Casimir Principle in the Theory of Bi...we establish relation between the microscopic and macroscopic Onsager- Casimir principles. It is demonstrated that because of certain symmetries with
Giant vacuum forces via transmission lines
NASA Astrophysics Data System (ADS)
Shahmoon, Ephraim; Mazets, Igor; Kurizki, Gershon
2015-03-01
Quantum electromagnetic fluctuations induce forces between neutral particles, namely, the van der Waals (vdW) and Casimir interactions. Here we show that these fundamental interactions can be enhanced by many orders of magnitude upon changing the character of the mediating vacuum photon-modes. We consider two dipoles in the vicinity of any standard electric transmission line and find analytically that the interaction scales non-trivially with the inter-dipolar distance, resulting in a strong and long-range interaction. This may have profound implications on the non-additivity of vdW and Casimir interactions in many-particle systems, and opens the door for Casimir Physics in 1d. We discuss the possibilities of measuring this effect, e.g. in a coplanar waveguide line. In January 2015, my affiliation is supposed to change to ``Department of Physics, Harvard University.''
Schaden, Martin
2010-08-15
The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries, and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically, the nonvanishing Casimir energy of a metallic cylindrical shell is almost entirely due to Fresnel diffraction.
Diagrammatic expansion of the Casimir energy in multiple reflections: Theory and applications
Maghrebi, Mohammad F.
2011-02-15
We develop a diagrammatic representation of the Casimir energy of a multibody configuration. The diagrams represent multiple reflections between the objects and can be organized by a few simple rules. The lowest-order diagrams (or reflections) give the main contribution to the Casimir interaction which proves the usefulness of this expansion. Among some applications of this, we find analytical formulae describing the interaction between edges, i.e. semi-infinite plates, where we also give a first example of blocking in the context of the Casimir energy. We also find the interaction of edges with a needle and describe analytically a recent model of the repulsion due to the Casimir interaction.
NASA Astrophysics Data System (ADS)
Keivani, Maryam; Mardaneh, Mohamadreza; Koochi, Ali; Rezaei, Morteza; Abadyan, Mohamadreza
2016-02-01
Herein, the dynamic pull-in instability of cantilever nanoactuator fabricated from conductive cylindrical nanowire with circular cross-section is studied under the presence of Casimir force. The Gurtin-Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and size phenomenon. Using Green-Lagrange strain, the higher order surface stress components are incorporated in the governing equation. The Dirichlet mode is considered and an asymptotic solution, based on the path integral approach, is applied to consider the effect of the Casimir attraction. Furthermore, the influence of structural damping is considered in the model. The nonlinear governing equation is solved using analytical reduced order method (ROM). The effects of various parameters on the dynamic pull-in parameters, phase planes and stability threshold of the actuator are demonstrated.
Van der Waals forces in pNRQED
Shtabovenko, Vladyslav
2016-01-22
We report on the calculation of electromagnetic van der Waals forces [1] between two hydrogen atoms using non-relativistic effective field theories (EFTs) of QED for large and small momentum transfers with respect to the intrinsic energy scale of the hydrogen atom. Our results reproduce the well known London and Casimir-Polder forces.
Casimir effect for a scalar field via Krein quantization
Pejhan, H.; Tanhayi, M.R.; Takook, M.V.
2014-02-15
In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions. -- Highlights: • A modification of QFT is considered to address the vacuum energy divergence problem. • Casimir energy of a spherical shell is calculated, through this approach. • In this technique, it is shown, the theory is automatically regularized.
Casimir, gravitational, and neutron tests of dark energy
NASA Astrophysics Data System (ADS)
Brax, Philippe; Davis, Anne-Christine
2015-03-01
We investigate laboratory tests of dark energy theories which modify gravity in a way generalizing the inverse power law chameleon models. We make use of the tomographic description of such theories which captures f (R ) models in the large curvature limit, the dilaton and the symmetron. We consider their effects in various experiments where the presence of a new scalar interaction may be uncovered. More precisely, we focus on the Casimir, Eötvös-Washington and neutron experiments. We show that dilatons, symmetrons and generalized chameleon models are efficiently testable in the laboratory. For generalized chameleons, we revise their status in the light of forthcoming Casimir experiments like CANNEX in Amsterdam and show that they are within reach of detection.
Antidynamical Casimir effect as a resource for work extraction
NASA Astrophysics Data System (ADS)
Dodonov, A. V.; Valente, D.; Werlang, T.
2017-07-01
We consider the quantum Rabi model with external time modulation of the atomic frequency, which can be employed to create excitations from the vacuum state of the electromagnetic field as a consequence of the dynamical Casimir effect. Excitations can also be systematically subtracted from the atom-field system by suitably adjusting the modulation frequency, in the so-called antidynamical Casimir effect (ADCE). We evaluate the quantum thermodynamical work and show that a realistic out-of-equilibrium finite-time protocol harnessing ADCE allows for work extraction from the system, whose amount can be much bigger than the modulation amplitude, | WADCE|≫ℏ ɛΩ , in contrast to the case of very slow adiabatic modulations. We provide means to control work extraction in state-of-the-art experimental scenarios, where precise frequency adjustments or complete system isolation may be difficult to attain.
Casimir-Polder effect for a stack of conductive planes
NASA Astrophysics Data System (ADS)
Khusnutdinov, Nail; Kashapov, Rashid; Woods, Lilia M.
2016-07-01
The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the ζ -function regularization approach with zero-point energies summation. As a prototype material, each plane is represented by a graphene sheet, an atomically thin layer of carbon atoms organized in a hexagonal lattice, whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom-plane distance limit, where retardation effects are prominent, and small atom-plane distance limit, where the typical van der Waals coefficient is found to be dependent on the number of graphenes and characteristic separations. The calculated energies for different atoms and graphene conductivity models brings forward the basic science of the Casimir-Polder effect and suggests ways to manipulate this interaction experimentally.
Chern-Simons potential in models of Casimir effect
Pis'mak, Yury M.; Pis'mak, Daria Yu.
2014-07-23
In the model constructed in the framework of the proposed by Symanzik approach for description of interaction of a macroscopic material body with quantum fields the interaction of thin material film with photon field is presented by the Chern-Simons potential. All the effects of this interaction with can by described in the framework of one model. In this way, the Casimir energy for two parallel infinite planes and sphere, the Casimir-Polder potential, and characteristics of other physical phenomena have been calculated for non-ideal conducting material of film. The specific of regularization and renormalization procedures used by calculations and the physical meaning of obtained results are discussed. In the limit of infinite coupling constant one obtains the known results of models with boundary conditions. By finite value of coupling constants the model predicts unusual effects which could be important for micro-mechanics, nano-photonics, constructing of new materials.
Nonequilibrium fluctuation-induced Casimir pressures in liquid mixtures.
Kirkpatrick, T R; Ortiz de Zárate, J M; Sengers, J V
2016-03-01
In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature gradient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.
On the static Casimir effect with parity-breaking mirrors
NASA Astrophysics Data System (ADS)
Fosco, C. D.; Remaggi, M. L.
2017-03-01
We study the Casimir interaction energy due to the vacuum fluctuations of the electromagnetic (EM) field in the presence of two mirrors, described by 2+1-dimensional, generally nonlocal actions, which may contain both parity-conserving and parity-breaking terms. We compare the results with the ones corresponding to Chern-Simons boundary conditions and evaluate the interaction energy for several particular situations.
Casimir effect for a semitransparent wedge and an annular piston
Milton, Kimball A.; Wagner, Jef; Kirsten, Klaus
2009-12-15
We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by {delta}-function potentials, so-called semitransparent boundaries. A finite expression for the Casimir energy corresponding to the arc and the presence of both semitransparent potentials is obtained, from which the torque on the sidewalls can be derived. The most interesting part of the calculation is the nontrivial nature of the angular mode functions. Numerical results are obtained which are closely analogous to those recently found for a magnetodielectric wedge, with the same speed of light on both sides of the wedge boundaries. Alternative methods are developed for annular regions with radial semitransparent potentials, based on reduced Green's functions for the angular dependence, which allows calculations using the multiple-scattering formalism. Numerical results corresponding to the torque on the radial plates are likewise computed, which generalize those for the wedge geometry. Generally useful formulas for calculating Casimir energies in separable geometries are derived.
Casimir Stress on Parallel Plates in de Sitter Space with Signature Change
NASA Astrophysics Data System (ADS)
Setare, M. R.
The Casimir stress on two parallel plates in a de Sitter background corresponding to different metric signatures and cosmological constants is calculated for massless scalar fields satisfying Robin boundary conditions on the plates. Our calculation shows that for the parallel plates with false vacuum between and true vacuum outside, the total Casimir pressure leads to an attraction of the plates at very early universe.
Eigenvalues of Casimir invariants for U{sub q}[osp(m vertical bar n)
Dancer, K.A.; Gould, M.D.; Links, J.
2005-12-15
For each quantum superalgebra U{sub q}[osp(m vertical bar n)] with m>2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated.
Casimir bag energy in the stochastic approximation to the pure QCD vacuum
Fosco, C. D.; Oxman, L. E.
2007-01-15
We study the Casimir contribution to the bag energy coming from gluon field fluctuations, within the context of the stochastic vacuum model of pure QCD. After formulating the problem in terms of the generating functional of field strength cumulants, we argue that the resulting predictions about the Casimir energy are compatible with the phenomenologically required bag energy term.
Casimir effects for classical and quantum liquids in slab geometry: A brief review
NASA Astrophysics Data System (ADS)
Biswas, Shyamal
2015-05-01
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over 4He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.
EDITORIAL: The nonstationary Casimir effect and quantum systems with moving boundaries
NASA Astrophysics Data System (ADS)
Barton, Gabriel; Dodonov, Victor V.; Man'ko, Vladimir I.
2005-03-01
This topical issue of Journal of Optics B: Quantum and Semiclassical Optics contains 16 contributions devoted to quantum systems with moving boundaries. In a broad sense, the papers continue the studies opened exactly 100 years ago by Einstein in his seminal work on the electrodynamics of moving bodies and the quantum nature of light. Another jubilee which we wish to celebrate by launching this issue is the 80th anniversary of the publication of two papers, where the first solutions of the classical Maxwell equations in a one-dimensional cavity with moving boundaries were obtained, by T H Havelock (1924 Some dynamical illustrations of the pressure of radiation and of adiabatic invariance Phil. Mag. 47 754-71) and by E L Nicolai (1925 On a dynamical illustration of the pressure of radiation Phil. Mag. 49 171-7). As was shown by Einstein, studying the fluctuations of the electromagnetic field inevitably leads one to its quantum (corpuscular) nature. Many papers in this issue deal with problems where moving boundaries produce parametric excitation of vacuum fluctuations of the field, which could result in several different observable effects, like the modification of the famous Casimir force, or the creation of real quanta from the vacuum. It is worth emphasizing that these phenomena, frequently referred to as nonstationary (or dynamical) Casimir effects, are no longer the province only of pure theorists: some experimental groups have already started long-term work aimed at observing such effects in the laboratory. Of course, many difficult problems remain to be resolved before this dream becomes reality. Several papers here show both important progress in this direction, and possible difficulties still to be tackled. Problems that have been considered include, in particular, decoherence, entanglement, and the roles of geometry and polarization. Other papers deal with fundamental problems like the Unruh effect, the interaction of accelerated relativistic atoms with
Application of the proximity force approximation to gravitational and Yukawa-type forces
Decca, R. S.; Fischbach, E.; Klimchitskaya, G. L.; Krause, D. E.; Lopez, D.; Mostepanenko, V. M.
2009-06-15
We apply the proximity force approximation, which is widely used for the calculation of the Casimir force between bodies with nonplanar boundary surfaces, to gravitational and Yukawa-type interactions. It is shown that for the gravitational force in a sphere-plate configuration the general formulation of the proximity force approximation is well applicable. For a Yukawa-type interaction we demonstrate the validity of both the general formulation of the proximity force approximation and a simple mapping between the sphere-plate and plate-plate configurations. The claims to the contrary in some recent literature are thus incorrect. Our results justify the constraints on the parameters of non-Newtonian gravity previously obtained from the indirect dynamic measurements of the Casimir pressure.
The Atomic Force Microscopic (AFM) Characterization of Nanomaterials
2009-06-01
the first intramolecular field effect transistors (FETs). Additionally, the first intramolecular logic gate utilizing SWNT FETs has recently become...magnetic force microscope (MFM)), Casimir forces, solvation forces, etc. In addition to these forces, other quantities could also be simultaneously...crystals may be employed, with each responsible for scanning in the x, y and z directions. This eliminates some of the distortion effects seen with a
NASA Astrophysics Data System (ADS)
Bradonjić, K.; Swain, J. D.; Widom, A.; Srivastava, Y. N.
2009-04-01
Despite the fact that red blood cells carry negative charges, under certain conditions they form cylindrical stacks, or "rouleaux". It is shown here that a form of the Casimir effect, generalizing the more well-known van der Waals forces, can provide the necessary attractive force to balance the electrostatic repulsion. Erythrocytes in plasma are modelled as negatively charged dielectric disks in an ionic solution, allowing predictions to be made about the conditions under which rouleaux will form. The results show qualitative agreement with observations which suggest that the basic idea is worth further pursuit. In addition to revealing a mechanism which may be widespread in biology at the cellular level, it also suggest new experiments and further applications to other biological systems, colloid chemistry and nanotechnology.
Okamoto, Ryuichi; Onuki, Akira
2012-03-21
We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ(∞). Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T, the transition line ends at a capillary critical point T=T(c) (ca) slightly lower than the bulk critical temperature T(c) for the upper critical solution temperature. The Casimir amplitudes are larger than their critical point values by 10-100 times at off-critical compositions near the capillary condensation line.
Unified approach to dispersion forces within macroscopic QED
NASA Astrophysics Data System (ADS)
Raabe, Christian; Welsch, Dirk-Gunnar
2006-09-01
We outline our Lorentz-force approach to the description of dispersion forces (see also C. Raabe and D.-G. Welsch, Phys. Rev. A 71:013814, 2005; Phys. Rev. A 73:063822, 2006). It is based on the ground-state Lorentz force density that acts on the charge and current densities attributed to the polarization and magnetization in linearly, locally, and causally responding media. Application of the theory to dielectric systems yields very general formulas for the Casimir force on dielectric bodies or parts of them. It is shown that well-known expressions for the Casimir Polder force on a single atom and for the van der Waals force between atoms are also contained in our formula. The theory may thus be viewed as providing a unified basis for the calculation of dispersion forces from a macroscopic point of view.
Unified approach to dispersion forces within macroscopic QED
NASA Astrophysics Data System (ADS)
Raabe, Christian; Welsch, Dirk-Gunnar
We outline our Lorentz-force approach to the description of dispersion forces (see also C. Raabe and D.-G. Welsch, Phys. Rev. A 71:013814, 2005; Phys. Rev. A 73:063822, 2006). It is based on the ground-state Lorentz force density that acts on the charge and current densities attributed to the polarization and magnetization in linearly, locally, and causally responding media. Application of the theory to dielectric systems yields very general formulas for the Casimir force on dielectric bodies or parts of them. It is shown that well-known expressions for the Casimir-Polder force on a single atom and for the van der Waals force between atoms are also contained in our formula. The theory may thus be viewed as providing a unified basis for the calculation of dispersion forces from a macroscopic point of view.
Attractive Casimir effect in an infrared modified gluon bag model
Oxman, L.E.; Amaral, R.L.P.G.
2005-12-15
In this work, we are motivated by previous attempts to derive the vacuum contribution to the bag energy in terms of familiar Casimir energy calculations for spherical geometries. A simple infrared modified model is introduced which allows studying the effects of the analytic structure as well as the geometry in a clear manner. In this context, we show that if a class of infrared vanishing effective gluon propagators is considered, then the renormalized vacuum energy for a spherical bag is attractive, as required by the bag model to adjust hadron spectroscopy.
Critical Casimir interactions around the consolute point of a binary solvent.
Mohry, T F; Kondrat, S; Maciołek, A; Dietrich, S
2014-08-14
Spatial confinement of a near-critical medium changes its fluctuation spectrum and modifies the corresponding order parameter distribution, resulting in effective, so-called critical Casimir forces (CCFs) acting on the confining surfaces. These forces are attractive for like boundary conditions of the order parameter at the opposing surfaces of the confinement. For colloidal particles dissolved in a binary liquid mixture acting as a solvent close to its critical point of demixing, one thus expects the emergence of phase segregation into equilibrium colloidal liquid and gas phases. We analyze how such phenomena occur asymmetrically in the whole thermodynamic neighborhood of the consolute point of the binary solvent. By applying field-theoretical methods within mean-field approximation and the semi-empirical de Gennes-Fisher functional, we study the CCFs acting between planar parallel walls as well as between two spherical colloids and their dependence on temperature and on the composition of the near-critical binary mixture. We find that for compositions slightly poor in the molecules preferentially adsorbed at the surfaces, the CCFs are significantly stronger than at the critical composition, thus leading to pronounced colloidal segregation. The segregation phase diagram of the colloid solution following from the calculated effective pair potential between the colloids agrees surprisingly well with experiments and simulations.
Large-n approach to thermodynamic Casimir effects in slabs with free surfaces.
Diehl, H W; Grüneberg, Daniel; Hasenbusch, Martin; Hucht, Alfred; Rutkevich, Sergei B; Schmidt, Felix M
2014-06-01
The classical n-vector ϕ{4} model with O(n) symmetrical Hamiltonian H is considered in a ∞{2}×L slab geometry bounded by a pair of parallel free surface planes at separation L. Standard quadratic boundary terms implying Robin boundary conditions are included in H. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-n limit for temperatures T at, above, and below the bulk critical temperature T_{c}. Their n=∞ limits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first ("model A"), only the coordinate z across the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second ("model B"), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling ∝L{-1}, anomalous ones ∝L{-1}lnL should occur. They can be considerably decreased by taking an appropriate g→∞ (T_{c}→∞) limit of the ϕ{4} interaction constant g. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness L_{eff}=L+δL. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers of {4}He and Monte Carlo simulations of XY models, including a pronounced minimum of the Casimir force below T_{c}. The results are in conformity with various analytically known exact properties of the scaling functions.
Large-n approach to thermodynamic Casimir effects in slabs with free surfaces
NASA Astrophysics Data System (ADS)
Diehl, H. W.; Grüneberg, Daniel; Hasenbusch, Martin; Hucht, Alfred; Rutkevich, Sergei B.; Schmidt, Felix M.
2014-06-01
The classical n-vector ϕ4 model with O (n) symmetrical Hamiltonian H is considered in a ∞2×L slab geometry bounded by a pair of parallel free surface planes at separation L. Standard quadratic boundary terms implying Robin boundary conditions are included in H. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-n limit for temperatures T at, above, and below the bulk critical temperature Tc. Their n =∞ limits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first ("model A"), only the coordinate z across the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second ("model B"), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling ∝L-1, anomalous ones ∝L-1lnL should occur. They can be considerably decreased by taking an appropriate g →∞ (Tc→∞) limit of the ϕ4 interaction constant g. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness Leff=L+δL. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers of 4He and Monte Carlo simulations of XY models, including a pronounced minimum of the Casimir force below Tc. The results are in conformity with various analytically known exact properties of the scaling functions.
Casimir self-entropy of an electromagnetic thin sheet
NASA Astrophysics Data System (ADS)
Li, Yang; Milton, Kimball A.; Kalauni, Pushpa; Parashar, Prachi
2016-10-01
Casimir entropies due to quantum fluctuations in the interaction between electrical bodies can often be negative, caused either by dissipation or by geometry. Although generally such entropies vanish at zero temperature, consistent with the third law of thermodynamics (the Nernst heat theorem), there is a region in the space of temperature and separation between the bodies where negative entropy occurs, while positive interaction entropies arise for large distances or temperatures. Systematic studies on this phenomenon in the Casimir-Polder interaction between a polarizable nanoparticle or atom and a conducting plate in the dipole approximation have been given recently. Since the total entropy should be positive according to the second law of thermodynamics, we expect that the self-entropy of the bodies would be sufficiently positive as to overwhelm the negative interaction entropy. This expectation, however, has not been explicitly verified. Here we compute the self-entropy of an electromagnetic δ -function plate, which corresponds to a perfectly conducting sheet in the strong coupling limit. The transverse electric contribution to the self-entropy is negative, while the transverse magnetic contribution is larger and positive, so the total self-entropy is positive. However, this self-entropy vanishes in the strong-coupling limit. In that case, it is the self-entropy of the nanoparticle, which we recalculate in the perfect conducting limit, that is just sufficient to result in a non-negative total entropy.
Local Casimir energies for a thin spherical shell
Cavero-Pelaez, Ines; Milton, Kimball A.; Wagner, Jeffrey
2006-04-15
The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness {delta}, where it has height h, with the constraint h{delta}=1. In the limit of zero thickness, an ideal {delta}-function shell is recovered. In this limit, the behavior of the energy density as the surface of the shell is approached is studied in both the strong and weak coupling regimes. The former case corresponds to the well-known Dirichlet shell limit. New results, which shed light on the nature of surface divergences and on the energy contained within the shell, are obtained in the weak coupling limit, and for a shell of finite thickness. In the case of zero thickness, the energy has a contribution not only from the local energy density, but from an energy term residing entirely on the surface. It is shown that the latter coincides with the integrated local energy density within the shell. We also study the dependence of local and global quantities on the conformal parameter. In particular new insight is provided on the reason for the divergence in the global Casimir energy in third order in the coupling.
Dynamical Casimir effect in stochastic systems: Photon harvesting through noise
NASA Astrophysics Data System (ADS)
Román-Ancheyta, Ricardo; Ramos-Prieto, Irán; Perez-Leija, Armando; Busch, Kurt; León-Montiel, Roberto de J.
2017-09-01
We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold—which we referred to as a metal-insulator phase transition—between exponential growth and low photon production. The low photon production is due to Bloch-like oscillations that produce a strong localization of the initial vacuum state, thus preventing higher generation of photons. To break localization of the vacuum state and enhance the photon generation, we impose a dephasing mechanism, based on dynamic disorder, into the driving frequency of the mirror. Additionally, we explore the effects of finite temperature on the photon production. Concurrently, we propose a classical analog of the dynamical Casimir effect in engineered photonic lattices, where the propagation of classical light emulates the photon generation from the quantum vacuum of a single-mode tunable cavity.
Observation of the dynamical Casimir effect in a superconducting circuit.
Wilson, C M; Johansson, G; Pourkabirian, A; Simoen, M; Johansson, J R; Duty, T; Nori, F; Delsing, P
2011-11-16
One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. Although initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences--for instance, producing the Lamb shift of atomic spectra and modifying the magnetic moment of the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed whether it might be possible to more directly observe the virtual particles that compose the quantum vacuum. Forty years ago, it was suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. The phenomenon, later termed the dynamical Casimir effect, has not been demonstrated previously. Here we observe the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of light) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detect two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.
Effect of intermolecular force on the static/dynamic behaviour of M/NEM devices
NASA Astrophysics Data System (ADS)
Kim, Namjung; Aluru, N. R.
2014-12-01
Advances made in the fabrication of micro/nano-electromechanical (M/NEM) devices over the last ten years necessitate the understanding of the attractive force that arises from quantum fluctuations (generally referred to as Casimir effects) [Casimir H B G 1948 Proc. K. Ned. Akad. Wet. 51 793]. The fundamental mechanisms underlying quantum fluctuations have been actively investigated through various theoretical and experimental approaches. However, the effect of the force on M/NEM devices has not been fully understood yet, especially in the transition region involving gaps ranging from 10 nm to 1 μm, due to the complexity of the force. Here, we numerically calculate the Casimir effects in M/NEM devices by using the Lifshitz formula, the general expression for the Casimir effects [Lifshitz E 1956 Sov. Phys. JETP 2 73]. Since the Casimir effects are highly dependent on the permittivity of the materials, the Kramer-Kronig relation [Landau L D, Lifshitz E M and Pitaevskii L P 1984 Electrodynamics of Continuous Media (New York: Pergamon Press)] and the optical data for metals and dielectrics are used in order to obtain the permittivity. Several simplified models for the permittivity of the materials, such as the Drude and Lorentz models [Jackson J D 1975 Classical Electrodynamics (New York: Wiley)], are also used to extrapolate the optical data. Important characteristic values of M/NEM devices, such as the pull-in voltage, pull-in gap, detachment length, etc, are calculated for devices operating in the transition region. Our results show that accurate predictions for the pull-in behaviour are possible when the Lifshitz formula is used instead of the idealized expressions for Casimir effects. We expand this study into the dynamics of M/NEM devices, so that the time and frequency response of M/NEM devices with Casimir effects can be explored.
Effect of intermolecular force on the static/dynamic behaviour of M/NEM devices.
Kim, Namjung; Aluru, N R
2014-12-05
Advances made in the fabrication of micro/nano-electromechanical (M/NEM) devices over the last ten years necessitate the understanding of the attractive force that arises from quantum fluctuations (generally referred to as Casimir effects) [Casimir H B G 1948 Proc. K. Ned. Akad. Wet. 51 793]. The fundamental mechanisms underlying quantum fluctuations have been actively investigated through various theoretical and experimental approaches. However, the effect of the force on M/NEM devices has not been fully understood yet, especially in the transition region involving gaps ranging from 10 nm to 1 μm, due to the complexity of the force. Here, we numerically calculate the Casimir effects in M/NEM devices by using the Lifshitz formula, the general expression for the Casimir effects [Lifshitz E 1956 Sov. Phys. JETP 2 73]. Since the Casimir effects are highly dependent on the permittivity of the materials, the Kramer-Kronig relation [Landau L D, Lifshitz E M and Pitaevskii L P 1984 Electrodynamics of Continuous Media (New York: Pergamon Press)] and the optical data for metals and dielectrics are used in order to obtain the permittivity. Several simplified models for the permittivity of the materials, such as the Drude and Lorentz models [Jackson J D 1975 Classical Electrodynamics (New York: Wiley)], are also used to extrapolate the optical data. Important characteristic values of M/NEM devices, such as the pull-in voltage, pull-in gap, detachment length, etc, are calculated for devices operating in the transition region. Our results show that accurate predictions for the pull-in behaviour are possible when the Lifshitz formula is used instead of the idealized expressions for Casimir effects. We expand this study into the dynamics of M/NEM devices, so that the time and frequency response of M/NEM devices with Casimir effects can be explored.
Comment on ''Casimir-Polder potential in a dielectric medium out of thermal equilibrium''
Milonni, Peter W.
2011-10-15
Rodriguez and Salam [Phys. Rev. A 82, 062522 (2010)] find disagreement between their results for the temperature dependence of the Casimir-Polder potential and those of earlier publications. It is argued that the latter are correct.
Casimir-Polder interaction between an atom and a periodic nanostructure
Yannopapas, V.; Vitanov, N. V.
2010-04-15
We present a theory for the calculation of the Casimir-Polder potential experienced by an atom near the surface of a nanostructure. The potential is found by means of the electrodynamic Green's tensor based on a layer-multiple-scattering method. We calculate the distance law of the Casimir-Polder potential for a monolayer of metallic and dielectric nanospheres arranged periodically on a square lattice. We find, in particular, that the Casimir-Polder potential for a metallic nanostructure is practically independent of the type of the metal from which the nanostructure is made. Also, the Casimir-Polder potential shows an exponential decay close to the nanostructure and an inverse power-law decrease away from it wherein the exponent depends on the size of the spheres of the nanostructure.
Impact of magnetic properties on the Casimir torque between anisotropic metamaterial plates
Deng Gang; Liu Zhongzhu; Luo Jun
2009-12-15
The quantized surface mode technique is used to calculate the Casimir torque between two parallel anisotropic metamaterial plates with in-plane optical axes, and our main concern is focused on the impact of the magnetic properties of the plates on the Casimir torque. Our result shows that at small separation, the Casimir torque between the two plates with frequency dependent permeabilities is larger than that between two nonmagnetic plates, while at large separation it is smaller. This can be explained as a result of the impact of both magnetic properties and material dispersion of the plates. The impact of the Drude background in connected metallic metamaterial is also discussed. These phenomena provide us with new understanding about the Casimir effect and show great potential in application.
NASA Astrophysics Data System (ADS)
Falinejad, Hossein
2017-06-01
The three dimensional formalism of the Green function method of the electro-magnetic field quantization is extended to quantize the electromagnetic field, at the presence of two dispersive and dissipative dielectric slabs. It is shown that the system decomposes into a singlet and a doublet parts. The singlet system corresponds to the normal polarization state of the electric field and the doublet system corresponds to the sum of parallel and longitudinal polarization states. Each part is quantized separately and vector potential operator of the each part is derived in terms of rightward and leftwards annihilation and creation operators. By using the assuming commutation properties of the noise current density, the equal time canonical commutation relations between the vector potential operator and its conjugate generalized momentum are verified for each part. Finally as an application, the explicit form of field operators are used to obtain an expression for the Casimir force between the two slabs via Maxwell stress tensor.
NASA Astrophysics Data System (ADS)
Dunckle, Christopher Gregory
Time Reversal can be used to time reverse and propagate the measured scattered wave- forms to a point in both time and space, ideally to a delta function delta( r⃗ )delta(t). This is commonly referred to as time reversal focusing and has led to time reversal being applied in a wide variety of fields such as medicine, communications, nondestructive evaluation (NDE), and seismology. In practice, time reversal is not optimal for generating a delta function focus if certain conditions are not upheld. For time reversal to work perfectly, the following four conditions must be present: (1) one must record for an infinitely long period of time; (2) Green's functions must be assumed to contain infinite bandwidth; (3) attenuation must be absent within the medium; and (4) one must have full coverage of the wavefield. Due to the need for these conditions, much research is being carried out in order to enhance the time reversal process in practice. We introduce deconvolution, a simple and robust approach, in order to calculate an optimal signal for back propagation designed to give an improved focus. We demonstrate experimentally that deconvolution is able to dramatically improve the temporal focus com- pared to time reversal. Through a joint project with Los Alamos National Laboratory, we compared time reversal to deconvolution. The results showed that deconvolution was able to dramatically improve the temporal focus for a source and a receiver which were both located on the surface of our object. We then continued our experimental studies of deconvolution by doing a joint project with researcher Dr. Ernst Niederleithinger from the Federal Institute for Materials Research and Testing (BAM). For this experiment, we placed multiple sources within a concrete block and recorded the source wavefields on the surface with a single re- ceiver. This experiment was designed to further test the robust nature of deconvolution and compare its temporal focusing capability to that of time reversal. All of these experimental studies show that deconvolution was able to improve the temporal focus compared to time reversal. We continued our comparison study between time reversal and deconvolution and demon- strated theoretically, experimentally, and numerically that deconvolution also improves spa- tial focusing. We give a proof explaining why one would expect improved spatial focusing when there is improved temporal focusing for both a acoustic and elastic media. We then demonstrate in our experiments the improved spatial focus achieved using deconvolution by scanning around the source location with a laser vibrometer at the time of focus for an acoustic case. Finally, we use deconvolution to locate synthetic microseismic events to prove numerically that improved temporal focusing leads to improved spatial focusing for both acoustic and elastic media.
Casimir effects for classical and quantum liquids in slab geometry: A brief review
Biswas, Shyamal
2015-05-15
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over {sup 4}He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.
NASA Astrophysics Data System (ADS)
Mackrory, Jonathan B.; Bhattacharya, Tanmoy; Steck, Daniel A.
2016-10-01
We present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization of the electromagnetic field in planar layered media. Starting from the field theory for electromagnetism, we work with the two decoupled polarizations in planar media and develop worldline path integrals, which represent the two polarizations separately, for computing both Casimir and Casimir-Polder potentials. We then show analytically that the path integrals for the transverse-electric polarization coupled to a dielectric medium converge to the proper solutions in certain special cases, including the Casimir-Polder potential of an atom near a planar interface, and the Casimir energy due to two planar interfaces. We also evaluate the path integrals numerically via Monte Carlo path-averaging for these cases, studying the convergence and performance of the resulting computational techniques. While these scalar methods are only exact in particular geometries, they may serve as an approximation for Casimir energies for the vector electromagnetic field in other geometries.
Nernst heat theorem for the thermal Casimir interaction between two graphene sheets
NASA Astrophysics Data System (ADS)
Bezerra, V. B.; Klimchitskaya, G. L.; Mostepanenko, V. M.; Romero, C.
2016-10-01
We find analytic asymptotic expressions at low temperature for the Casimir free energy, entropy, and pressure of two parallel graphene sheets in the framework of the Lifshitz theory. The reflection coefficients of electromagnetic waves on graphene are described on the basis of first principles of quantum electrodynamics at nonzero temperature using the polarization tensor in (2+1)-dimensional space-time. The leading contributions to the Casimir entropy and to the thermal corrections to the Casimir energy and pressure are given by the thermal correction to the polarization tensor at nonzero Matsubara frequencies. It is shown that the Casimir entropy for two graphene sheets goes to zero when the temperature vanishes, i.e., the third law of thermodynamics (the Nernst heat theorem) is satisfied. At low temperature, the magnitude of the thermal correction to the Casimir pressure between two graphene sheets is shown to vary inversely proportional to the separation. The Nernst heat theorem for graphene is discussed in the context of problems occurring in Casimir physics for both metallic and dielectric plates.
Bifurcation and Stability Analysis of the Hamiltonian—Casimir Model of Liquid Sloshing
NASA Astrophysics Data System (ADS)
Salman, Ahmad; Yue, Bao-Zeng
2012-06-01
Motion stability of a spacecraft is discussed. A canonical Hamiltonian model for liquid sloshing is presented for a moving rigid body. An equivalent mechanical pendulum model is used to represent the fuel slosh inside the container. In this model sloshing is represented by the moving mass, the rest of the mass of the spacecraft is assumed to be stationary. The spacecraft structure is considered to be an elliptical rigid shape and the steady rotation along the x-axis is taken as the major-axis rotation. Motion stability for the present model is analyzed using the Lyapunov theory with Casimir energy functions. Conditions for stability and instability are derived for a steady principal axis rotation of the rigid body. Simulation results are presented to distribute the region into stable and unstable regions. Besides this, the nonlinear behavior of the system is analyzed under the influence of an external force acting periodically. Chaos is observed through a bifurcation diagram. The time history map and phase portrait are also presented to analyze the nonlinear behavior of the system.
Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions.
Venkataram, Prashanth S; Hermann, Jan; Tkatchenko, Alexandre; Rodriguez, Alejandro W
2017-06-30
We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e., between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interaction energies and forces, as well as molecular shapes deformed by vdW interactions, by orders of magnitude compared to previous treatments based on Casimir-Polder, nonretarded, or pairwise approximations, which are valid only at macroscopically large or atomic-scale separations or in dilute insulating media, respectively.
Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions
NASA Astrophysics Data System (ADS)
Venkataram, Prashanth S.; Hermann, Jan; Tkatchenko, Alexandre; Rodriguez, Alejandro W.
2017-06-01
We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e., between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interaction energies and forces, as well as molecular shapes deformed by vdW interactions, by orders of magnitude compared to previous treatments based on Casimir-Polder, nonretarded, or pairwise approximations, which are valid only at macroscopically large or atomic-scale separations or in dilute insulating media, respectively.
Symmetry reduction for central force problems
NASA Astrophysics Data System (ADS)
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier
2016-09-01
We given an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy level sets in three dimensions. These systems form a classic example of symplectic reduction which can usefully be compared to the more commonly seen case of the free rigid body. Dedicated to the memory of Jerry Marsden, 1942-2010.
Microscopic background of the Onsager-Casimir reciprocity relations
Titulaer, U.M.
1988-10-01
It has been known for some time that small deviations from the Onsager-Casimir symmetry relations are introduced when one passes from a given description of a system to a less detailed one by adiabatic elimination of fast variables. Exact validity is preserved, however, for a slightly modified form of these relations. In this paper the question is considered whether this modified Onsager symmetry is also preserved by the transition from a microscopic to a mesoscopic description, the step that introduces manifest irreversibility into the equations of motion. This question is examined in detail for a system of a few heavy oscillators coupled to a bath, a model discussed in a recent paper by van Kampen. The modified Onsager symmetry survives the transition to an irreversible description via the dense spectrum approximation. This is shown explicitly by inspection of the results obtained by van Kampen; some arguments favoring a more general validity are also briefly discussed.
Casimir effect: running Newton constant or cosmological term
NASA Astrophysics Data System (ADS)
Polonyi, Janos; Regos, Eniko
2006-01-01
We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is non-perturbative and contains a condensate of the metric tensor in a manner reminiscent of Yang Mills theories. As a simple step toward the characterization of such a vacuum the value of the 1-loop effective action is computed for Euclidean de Sitter spaces as a function of the curvature when the unstable conformal modes are held fixed. Two phases are found, one where the curvature is large and gravitons should be confined and another one which appears to be weakly coupled and tends to be flat. The induced cosmological constant is positive or negative in the strongly or weakly curved phase, respectively. The relevance of the Casimir effect in understanding the UV sensitivity of gravity is pointed out.
Speeding up the antidynamical Casimir effect with nonstationary qutrits
NASA Astrophysics Data System (ADS)
Dodonov, A. V.; Díaz-Guevara, J. J.; Napoli, A.; Militello, B.
2017-09-01
The antidynamical Casimir effect (ADCE) is a term coined to designate the coherent annihilation of excitations due to resonant external perturbation of system parameters, allowing for extraction of quantum work from nonvacuum states of some field. Originally proposed for a two-level atom (qubit) coupled to a single-cavity mode in the context of the nonstationary quantum Rabi model, it suffered from a very low transition rate and correspondingly narrow resonance linewidth. In this paper we show analytically and numerically that the ADCE rate can be increased by at least one order of magnitude by replacing the qubit by an artificial three-level atom (qutrit) in a properly chosen configuration. For the cavity thermal state we demonstrate that the dynamics of the average photon number and atomic excitation is completely different from the qubit's case, while the behavior of the total number of excitations is qualitatively similar yet significantly faster.
Rotation of a liquid crystal by the Casimir torque
NASA Astrophysics Data System (ADS)
Somers, David A. T.; Munday, Jeremy N.
2015-03-01
We present a calculation of the Casimir torque acting on a liquid crystal near a birefringent crystal. In this system, a liquid crystal bulk is uniformly aligned at one surface and is twisted at the other surface by a birefringent crystal, e.g., barium titanate. The liquid crystal is separated from the solid crystal by an isotropic, transparent material such as SiO2. By varying the thickness of the deposited layer, we can observe the effect of retardation on the torque (which differentiates it from the close-range van der Waals torque). We find that a barium titanate slab would cause 5CB (4 -cyano -4 '-pentylbiphenyl) liquid crystal to rotate by 10∘ through its bulk when separated by 35 nm of SiO2. The optical technique for measuring this twist is also outlined.