FLUCTUATIONS AND CASIMIR FORCESseneca.fis.ucm.es/brito/casimir/bookofabstracts.pdf · critical Casimir forces can be used to avoid stiction in micro-mechanical ... question is how

FLUCTUATIONS ANDCASIMIR FORCES

Hotel VillalbaVilaflor, Tenerife

November 4–6, 2010

Organizers:

Ricardo Brito Chris Van den Broeck

U. Complutense de Madrid Hasselt University, Belgium

Thorsten Emig Rodrigo Soto

Universite Paris Sud Universidad de Chile

PARTICIPANTS

Clemens Bechinger University of [email protected]

Ricardo Brito Universidad Complutense, [email protected]

Chris Van den Broeck Hasselt [email protected]

Antoine Canaguier-Durand Laboratoire Kastler Brossel, [email protected]

Sergio Ciliberto Ecole Normal Superieure [email protected]

David Dean Universite de [email protected]

Siegfried Dietrich MPI for Metals Research, [email protected]

Thorsten Emig Universite Paris [email protected]

Andrea Gambassi SISSA, [email protected]

Ramin Golestanian Oxford [email protected]

Davide Iannuzzi VU University [email protected]

Alberto Imparato University of [email protected]

Gert-Ludwig Ingold Universitat [email protected]

Umberto M.B. Marconi Universita di [email protected]

Ignacio Pagonabarraga Universidad de [email protected]

Juan M.R. Parrondo Universidad Complutense, [email protected]

Pablo Rodriguez-Lopez Universidad Complutense, [email protected]

Miguel Rubi Universidad de [email protected]

Rodrigo Soto Universidad de [email protected]

Fluctuations and Casimir Forces 3 Tenerife, November 4-6

ABSTRACTS

Direct measurement of critical Casimir forces

Clemens Bechinger

Physical Institute, University of Stuttgart, Germany

Similar to electromagnetic vacuum fluctuations which can induce long-ranged interactions between uncharged, conducting surfaces, a rather sim-ilar effect was predicted almost 30 years ago to occur in confined binarymixtures close to their critical point. This so-called critical Casimir effecthas attracted considerable attention because it can strongly modify theinteraction potential of colloidal particles immersed in a binary fluid.We present the first direct measurement of such critical Casimir forcesbetween a colloidal particle and a flat surface in a water – 2,6-lutidine mix-ture. With total internal reflection microscopy (TIRM) which is capable toresolve forces down to 5femto Newton, we obtain distance resolved particle-wall interaction profiles. Upon approaching the critical point we observelong-ranged interactions which are attractive or repulsive depending on thespecific boundary conditions of the walls. This behavior is in good agree-ment with recent theoretical predictions. In addition, we demonstrate, howcritical Casimir forces can be used to avoid stiction in micro-mechanicaldevices.


ABSTRACTS

Casimir Forces from Langevin Equations out of Equilibrium

Ricardo Brito

Universidad Complutense de Madrid

In this talk we will derive an expression for the Casimir force takingas starting point is the Langevin equation for the fluctuating field. TheCasimir force is calculated by solving the Langevin equation and insert-ing its solution into the stress tensor. This formalism allows to evaluateCasimir forces for systems in equilibrium as well as non equlibrium.If the system is near equilibrium, the Thermodynamics of IrreversibleProccesses provides some information about the deterministic part of theLangevin equation. Moreover, the Fluctuation–Dissipation relation tellsus how the noise intensity is related with the Onsager Matrix.On the contrary, violation of the Fluctuation-Dissipation relation puts thesystem out of equilibrium, and as a consequence, long range correlationsdevelop into the system. We will discuss how the long range correlationleads to a non vanishing Casimir force. These ingredients will be made clearby application of the formalism to a granular fluid, where its dissipativedynamics sets the system out of equilibrium, and Casimir forces appear.Emphasis will be made on the applicability to non equilibirum systems, likecolored noises, space dependent fluctuations, transients, or time dependentsystems.


ABSTRACTS

Brownian forces

Christian Van den Broeck

Hasselt University, Belgium

I will review a number of problems, such as the adiabatic piston, Brown-ian motors and noise induced transitions, in which the presence of Brownianfluctuations results in the appearance of a force.


ABSTRACTS

Thermal Casimir effect for Drude metalsin the plane-sphere geometry.

Antoine Canaguier-Durand and Serge Reynaud

Laboratoire Kastler Brossel, Campus Jussieu, Paris, France

The scattering formalism allows one to express the Casimir interactionof two distinct objects from their scattering properties. It can be applied tovarious geometries while incorporating the description of materials throughtheir dielectric functions, and the effect of temperature.We will present results obtained for the plane-sphere geometry, beyond theoften used proximity force approximation (PFA). We will also discuss thecases of the lossless plasma model and Drude model for metallic mirrors,for which a full explanation of experimental results is still missing.Our analytical and numerical results show a non-trivial interplay betweenthe effects of curvature and temperature. In some cases the thermal pho-tons even have a repulsive contribution to the force, which is never thecase within the PFA. For metallic mirrors, we find a correlation betweendissipation and curvature effects.


ABSTRACTS

Finite size effects and aging near a critical point

S. Ciliberto

Laboratoire de Physique de l’ENS 46 Allee d’Italie, 69364 Lyon, France

In this talk we will present experimental results on the measure of theorientation fluctuations of the director of a liquid crystal (LC) close to theFreedericksz transition, which is a second order transition driven by anelectric field. We show that near the critical value of the field, becauseof the divergency of the correlation length, the spatially averaged orderparameter has a generalized Gumbel distribution instead of a Gaussianone. The latter is recovered away from the critical point [1]. We also re-port experimental evidence that, because of the critical slowing down, theLC presents several properties of an aging system after the quench, suchas power law scaling in times of correlation and response functions. Dur-ing this slow relaxation, a well defined effective temperature, much largerthan the heat bath temperature, can be measured using the fluctuationdissipation relation [2].

References

[1] Experimental evidence of non-Gaussian fluctuations near a criticalpoint. S. Joubaud, A. Petrosyan, S. Ciliberto, N. Garnier, Phys. Rev.Lett. 100, 180601 (2008)

[2] Aging and effective temperatures near a critical point, S. Joubaud, B.Percier, A. Petrosyan, S. Ciliberto, Phys. Rev. Lett. 102, 130601 (2009).


ABSTRACTS

Out of equilibrium fluctuation induced interactions

David Dean

Classical fields driven by thermal fluctuations exhibit the pseudo orcritical Casimir effect first predicted by Fisher and de Gennes. There exista number of simple models for the dynamics of these fields and a naturalquestion is how do thermal Casimir forces evolve in time ? Rather thanimposing boundary conditions one can introduce an energy of interactionof a surface with the fluctuating field and via this energy one can writedown an expression for the instantaneous force acting on the surface. Thisenables one to derive expressions for the force in a number of out of equi-librium situations. I will examine the evolution of the Casimir force to itsequilibrium value for parallel plate geometries and also discuss the Casimirdrag on a test particle moving through a fluctuating free field at constantvelocity.


ABSTRACTS

Critical Casimir Forces

S Dietrich

Max Planck Institute for Metals Research, Stuttgart, Germany, andInstitute for Theoretical and Applied Physics, University of Stuttgart, Germany

Long-ranged correlations in a fluid near its critical point lead to clearlyidentifiable effective forces acting on confining walls. The correspondinguniversal scaling functions are discussed for different boundary conditionsand geometries. The theoretical predictions are compared with high pre-cision experimental data for He4 and He3/He4 wetting films near the su-perfluid phase transition as well as with synchrotron scattering data fromclassical binary liquid mixtures. Direct measurements and applications forcollidal suspensions are discussed.


ABSTRACTS

Casimir Forces: Geometry and Material dependence

Thorsten Emig

Universite Paris Sud

The properties of fluctuation induced interactions like van der Waalsand Casimir-Lifshitz forces are of interest in a plethora of fields rangingfrom biophysics to nanotechnology. Recent high precision experiments andemerging micro-electromechanical applications have generated great inter-est in the properties and the selective manipulation of these interactions.In this talk, I will present a powerful method to compute Casimir forcesand torques between various shapes and materials. The approach is basedon a combination of methods from statistical physics and scattering theory.


ABSTRACTS

Steering the Casimir effect: lateral forces, levitation, and dynamics

Andrea Gambassi

SISSA, Trieste

The critical Casimir effect results from the confinement of the pro-nounced fluctuations occurring upon approaching a second-order phasetransition such as the demixing of a binary liquid mixture. The spatialdirection of the force acting on the confining surfaces can be controlledby suitably patterning them. For a colloid close to a patterned substrateand immersed in a critical solvent a spatially confining potential can bereversibly generated, which also allows a temperature-controlled stable lev-itation of the particle. External perturbations affect the strength of thecritical Casimir force, the time-dependence of which displays interestingfeatures. I will present the results of the theoretical investigation of thesevarious aspects, comparing them with the available experimental data.


ABSTRACTS

Stochastic Low Reynolds Number Swimmers

Ramin Golestanian

The Rudolf Peierls Centre for Theoretical Physics, University of Oxford1 Keble Road, Oxford OX1 3NP, United Kingdom

The directed propulsion of small scale objects in water is problematicbecause of the combination of low Reynolds number and Brownian mo-tion on these length scales. One possibility for designing propulsion is todevise non-reciprocal deformation strategies that are simple enough to berealizable. This opens up the discussion of what is the minim number ofdegrees of freedom that we can use in our design strategies for objects thatcan swim at low Reynolds numbers. As technological advances allow us tofabricate smaller and smaller autonomous self-propelled devices, it is clearthat at some point directed propulsion could not come from pre-specifieddeterministic periodic deformation of the swimmer’s body and we need todevelop strategies to extract a net directed motion from a series of randomtransitions in the conformation space of the swimmer.Using the simple three-sphere microswimmer model [1, 2, 3], which is madeof three spheres in a row connected by two rigid rods that undergo a non-reciprocal stroke cycle, we introduce the notion of stochastic propulsion[4, 5]. The model is used to study the physical properties of molecular-scale swimmers, such as their force–velocity response [4], as well as theconcept of coherence between stochastic swimmers that are coupled viahydrodynamic interactions [6].Using the same formalism, a new minimal low Reynolds number swimmermodel is introduced that could take advantage of an electrostatic stochasticactuation mechanism to induce conformational changes on the device [7].The swimmer has two enzymes on board that catalyze chemical reactionsthat involve ionic products. When the ions are still attached to the en-zymes, electrostatic interaction between them and other charged elementsof the swimmer can lead to conformational changes. The design proposeshow one can take advantage of these stochastically temporary charged com-ponents of the system and achieve net propulsion at low Reynolds number.Another strategy to achieve propulsion at low Reynolds numbers could beto take advantage of various phoretic phenomena. We propose a simplemodel for the reaction-driven propulsion of a small device is proposed asa model for a molecular swimmer in aqueous media [8]. It is shown thatthe stochastic motion of such active colloids is anomalous due the mem-ory effect of the concentration profile of the solute molecules and densityfluctuations [9].


ABSTRACTS

Finally, a number of recent experimental realizations of such mi-croswimmers are discussed, including the works of experimental groupsin Sheffield [10, 11] and Barcelona [12].

References

[1] A. Najafi and R. Golestanian, Phys. Rev. E 69, 062901 (2004).

[2] R. Golestanian and A. Ajdari, Phys. Rev. E 77, 036308 (2008).

[3] R. Golestanian, Eur. Phys. J. E 25, 1 (R) (2008).

[4] R. Golestanian and A. Ajdari, Phys. Rev. Lett. 100, 038101 (2008).

[5] R. Golestanian and A. Ajdari, J. Phys.: Condens. Matter 21, 204104 (2009).

[6] A. Najafi and R. Golestanian, Europhys. Lett. 90, 68003 (2010).

[7] R. Golestanian, Phys. Rev. Lett. 105, 018103 (2010).

[8] R. Golestanian, T.B. Liverpool, and A. Ajdari, Phys. Rev. Lett. 94, 220801(2005); New J. Phys. 9, 126 (2007).

[9] R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009).

[10] J.R. Howse, R.A.L. Jones, A.J. Ryan, T. Gough, R. Vafabakhsh, and R.Golestanian, Phys. Rev. Lett. 99, 048102 (2007).

[11] S. Ebbens, R. A. L. Jones, A. J. Ryan, R. Golestanian, and J. R. Howse, Phys.Rev. E 82, 015304 (R) (2010).

[12] P. Tierno, R. Golestanian, I. Pagonabarraga, and F. Sagues, Phys. Rev. Lett.101, 218304 (2008).


ABSTRACTS

From 100 nm to the edge of the Universewith Casimir force experiments

S. de Man, K. Heeck, J.H. Rector, R. Sedmik, P. Zuurbier, G. Gruca, R.J.Wijngaarden

Department of Physics and Astronomy and LaserLaB, VU University AmsterdamDe Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

Ph. BraxInstitut de Physique Theorique, CEA, IPhT, CNRS, URA 2306

F-91191Gif/Yvette Cedex, France

C. van de BruckDepartment of Applied Mathematics, University of Sheffield Hounsfield Road

Shieffield S3 7RH, United Kingdom

A. C. DavisDepartment of Applied Mathematics and Theoretical Physics

Centre for Mathematical Sciences, Cambridge CB3 0WA, United Kingdom

D. J. ShawQueen Mary University of London, Astronomy Unit, Mile End Road

London E1 4NS, United Kingdom

D. [email protected]

Department of Physics and Astronomy and LaserLaB, VU University AmsterdamDe Boelelaan 1081, 1081 HV Amsterdam, The Netherlands.

The first part of the talk will be focused on the description of the Amster-dam Casimir force setup. After an in-depth introduction on the measurementmethod, I will use a few examples extracted from our most recent works toillustrate the possibilities offered by our setup as well as its limitations.In the second part of the talk I will present a new approach to explore theexistence of chameleon fields in table-top Casimir-like experiments. The idea isto bring two metallic plates at a separation of a few tens of microns and thenmeasure the force between them as a function of the density of a gas allowedin the gap. At low densities, chameleons are nearly massless, giving rise toan attractive force. Unfortunately, this force can not be detected via directmeasurements, as it is largely dominated by other interaction mechanisms. Athigher gas densities, however, chameleons become heavier and the force thatthey generate becomes much weaker. One can show that the change of thechameleon force is then larger than the change of any other force. A precisecomparison of the experimental results at low and high gas densities shouldthus allow one to claim whether the chameleon force has decreased with theincrease of the gas density, and, therefore, whether chameleons exist or not.


ABSTRACTS

Work and Heat Probability Distribution of a Driven Brownian Particle

Imparato

University of Aarhus

I will first introduce the differential equations governing the time evo-lution of the probability distributions of the work and heat exchanged bya driven Brownian particle with the surrounding environment. I will thenshow that the explicit solutions of such equations can be obtained in thesimple case of a particle dragged by an harmonic potential. The theoreticalresults will be compared with the outcomes of manipulation experiments,where a micron-sized colloidal particle is dragged through water with alaser trap. Finally I will consider the more complex case of a Brownianparticle trapped in a double well potential periodically modulated by anexternal driving force. Also in this case I will compare experimental out-comes with the predicted distributions of the work and heat exchanged bythe particle.


ABSTRACTS

Casimir effect and quantum Brownian motion

Gert-Ludwig Ingold

Institut fur Physik, Universitat Augsburg, Germany

If the interaction of a system with its environment is not negligible, inthe quantum regime the thermodynamic quantities pertaining to the sys-tem degree of freedom alone are in general no longer uniquely defined [1].Furthermore, choosing the reduced partition function as a starting point,one finds that under certain conditions the specific heat of a free Brown-ian particle may even become negative [2]. This at first surprising resultcan be explained in terms of differences of specific heats of system plusenvironment and of the environment alone [3]. While the free Brownianparticle may seem like a very particular system, it can be shown that itbears close analogy to the Casimir effect where a negative entropy is foundif the electrons in two parallel plane mirrors are described within the Drudemodel [4].

[1] P. Hanggi, G.-L. Ingold, Acta Phys. Pol. B 37, 1537 (2006)[2] P. Hanggi, G.-L. Ingold, P. Talkner, New J. Phys. 10, 115008 (2008)[3] G.-L. Ingold, P. Hanggi, P. Talkner, Phys. Rev. E 79, 061105 (2009)[4] G.-L. Ingold, A. Lambrecht, S. Reynaud, Phys. Rev. E 80, 041113(2009)


ABSTRACTS

Fluctuation-induced interactions between solid inclusions in adissipative fluid

I. Pagonabarraga

Universidad de Barcelona

Granular gases are materials which are intrinsically out of equilibrium.They can develop long range spatial correlations which lead to strong den-sity fluctuations. As a result, solid inclusions in such materials can expe-rience long range interactions due to the disturbance they induce in theintrinsic fluctuations of these systems.In this contribution I will introduce a dissipative fluid model which doesnot exhibit any intrinsic structure in equilibrium. After characterizing thecorrelations which the system intrinsically develops when homogeneouslyagitated, I will describe the effective interactions measured between solidparticles suspended in such a fluid.


ABSTRACTS

Non-Equilibrium Fluctuation-Dissipation Theorem

Juan MR Parrondo


The fluctuation-dissipation theorem is a central result of statisticalphysics, which applies to any system at thermodynamic equilibrium. Its vi-olation is a strong signature of nonequilibrium behavior. We show that forany system with Markovian dynamics, in a nonequilibrium steady state, aproper choice of observables restores a fluctuation-response theorem iden-tical to a suitable version of the equilibrium fluctuation-dissipation

[J. Prost, J.-F. Joanny, J. M. R. Parrondo. Phys. Rev. Lett. 103, 090601(2009)]


ABSTRACTS

Some results of Casimir energy

Pablo Rodriguez-Lopez


By the use of the multiscattering formalism of Emig et. al. [Phys. Rev.Lett. 99, 170403, 2007.], I will present two different results. First I presentthe Casimir energy between crossed cylinders. Casimir energy betweenparallel cylinders is a known result. we could not say the same for theenergy between crossed cylinders. Contrary to the parallel case, energy donot scale with the lenght of the cylinders. Asymptotic results will be givenat zero and high Temperature limits. The dependence with the angle willbe discussed and numerical results will be showed. I will also present thederivation of PSA for electromagnetic Casimir energy. Taking the soft di-electric and soft diamagnetic limit, this formalism let us to obtain generalresults of PSA. In particular the Pairwise Summation Approximation forthe complete electromagnetic field valid for any temperature is obtained.Then it is possible to obtain corrections to high and low T energies. Inadittion to that, the regime in which Casimir interaction is a superpo-sition interaction will be derived. In the asymptotic distance limit theN-points potential formalism of Power and Thirunamachandran [Proc. R.Soc. London, Ser. A 401, 267, 1985.] will be generalized with the inclussionof magnetic contribution effects. Finally, the first correction term to PSAis discussed.


ABSTRACTS

Thermodynamics and stochastic dynamics of transportin confined media

Miguel Rubi

University of Barcelona

We show how a probabilistic interpretation of non-equilibrium thermo-dynamics, based on the assumption of local equilibrium at the mesoscale,can be used to analyze the stochastic dynamics of entropy driven diffusionprocesses characterized by the presence of entropic barriers. This approachsets up a systematic method to study the effect of confinement on the trans-port properties, providing a derivation of a generalized FickJacobs equationfor the constrained dynamics of the mesoscopic degrees of freedom. It isshown that confinement originates an entropic bias which gives rise to ageometric rectification of non-equilibrium fluctuations and that entropiceffects in transport can be controlled by means of the application of anexternal force.


ABSTRACTS

Fluctuation-induced self-force in a nonequilibrium steady state fluid

Rodrigo Soto

Universidad de Chile

We show that the fluctuations of a fluid driven out of equilibrium caninduce a net force on a single asymmetric object immersed in it. The forceoriginates in the restriction of the fluid’s fluctuations at the object’s bound-aries, as in the Casimir effect. In contrast to the equilibrium situation, itsemergence on a single obstacle is not ruled out by the second law of ther-modynamics since the fluid is in a nonequilibrium state. We explicitly cal-culate this self-force on a deformed circle embedded in a fluid whose densityfluctuations obey stochastic reaction–diffusion equation. When two objectsare considered, the presence of self-forces can violate the action–reactionprinciple. We illustrate this by calculating the internal Casimir-type forcesbetween a circle and a plate. Their sum, instead of vanishing, provides theself-force exerting on the circle–plate assembly.


INFORMATION

Venue:

Hotel Spa Villalba

Carretera San Roque, S/N

38613 Vilaflor de Chasna, Tenerife

E-mail: [email protected]

Phone: (+34) 922 709 930

Fax: (+34) 922 709 341

Wifi: Villalba (no password required)

Airport Information: 902 404 704 or (+34) 913 211 000

Taxi: (+34) 922 397 475 or (+34) 922 315 555

Bus service between Airports:

Lines: L340 or L343. Price: 6,50 e . About 1 hour.

Tenerife North to Tenerife South: 6:55, 9:25, 11:25, 15:45, 17:40, 22:10

Tenerife South to Tenerife North: 8:45, 12:00, 13:00 16:00, 18:30, 19:45


PROGRAM


FLUCTUATIONS AND CASIMIR FORCESseneca.fis.ucm.es/brito/casimir/bookofabstracts.pdf · critical Casimir forces can be used to avoid stiction in micro-mechanical ... question is how

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