Universality of the thermodynamic Casimir effect

Dantchev, Daniel; Krech, M.; Dietrich, S.

doi:10.1103/physreve.67.066120

Cited by 44 publications

(73 citation statements)

References 53 publications

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“…(3) coming from the Goldstone modes in the bulk of the film. (Monte Carlo simulations with periodic boundary conditions in three dimensions yield a value of the critical amplitude which is roughly twice larger [26].) Thus, if these modes were the only cause for the thinning of the film in the superfluid phase, the height of the film would be roughly the same at the critical point and well below the λ-point.…”

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confidence: 99%

Casimir Forces, Surface Fluctuations, and Thinning of Superfluid Film

2004

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Recent experiments on the wetting of 4 He have shown that the film becomes thinner at the λ transition, and in the superfluid phase. The difference in thickness above and below the transition has been attributed to a Casimir interaction which is a consequence of a broken continuous symmetry in the bulk superfluid. However, the observed thinning of the film is larger than can be accounted by this Casimir force. We show that surface fluctuations give rise to an additional force, similar in form but larger in magnitude, which may explain the observations. PACS numbers: 46.32.+x, 82.35.Rs, 87.15.La, 85.35.Kt, 07.10.Cm Quantum fluctuations of the electromagnetic field between two conducting plates in vacuum result in longranged attractive interactions. This effect which has only recently experimentally verified by a series of high precision measurements[1], was first predicted by Casimir in 1948 [2]. Thirty years later, Fisher and de Gennes noted that the confinement of thermal fluctuations in fluids leads to similar long-ranged forces [3]. Quite generally, geometric restrictions on a fluctuating field constrain the normal modes of fluctuations and result in fluctuation-induced or Casimir forces. These forces are controlled by correlations in the fluid; when the correlations are long-ranged, corresponding to massless fields, Casimir forces decay with distance as a simple power law [4,5,6,7,8,9,10,11]. The overall strength of a Casimir interaction is typically universal. That is, it depends on symmetries of the fluctuating field, and on boundary conditions, but not on microscopic details.An important example of a Casimir force associated with thermal fluctuations in a condensed matter system is found in 4 He films at and near the superfluid phase transition [12]. The finite thickness, d, of the film constrains the fluctuations of the superfluid order parameter, which then mediate a Casimir force. Experimental demonstration of this force was reported recently by Garcia and Chan[12] (GC). To produce films of various thicknesses, a stack of copper electrodes were suspended at different heights above bulk liquid helium. The thickness of the wetting layer on each electrode as a function of temperature was monitored to gauge the strength of interactions with the substrate. Figure 1 shows the change in the film thickness ∆d = d−d 0 , as a function of reduced temperature t = T − T λ , near the superfluid transition point for the capacitor labeled "Cap 1" in Ref. [12]. The quantity d 0 is the thickness of the film well above the λ-point. As shown in the figure, there is a perceptible decrease in the thickness of the film at the transition point t = 0, followed by a substantial drop below the transition. The thinning of the film for t ≥ 0 quantitatively confirms the theoretical predictions of attractive Casimir

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confidence: 99%

Casimir Forces, Surface Fluctuations, and Thinning of Superfluid Film

2004

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“…The origin of the FIF in these systems is very different from the one leading to thermodynamic Casimir effects [4], and its behavior is distinct from, for example, equilibrium slab geometries [31,32]. It will be interesting to study the behavior of the force in other geometries.…”

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confidence: 99%

Fluctuation-Induced Forces in Nonequilibrium Diffusive Dynamics

2015

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Fluctuations in nonequilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations, in turn, experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. Our model calculations show that the force falls off with slab separation d as k B T=d (at temperature T, and in all spatial dimensions) but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is nonuniversal and explicitly depends on dynamics. The techniques introduced can be used to study pressure and fluctuation induced forces in a broad class of nonequilibrium systems. [7,8], and liquid-vapor coexistences [9]. In both cases, quantum and classical, the underlying fluctuations are long-range correlated leading to forces that fall off as power laws. In the latter (for example, in an oil-water mixture), this is achieved by tuning to a critical point, while the former is a consequence of the massless nature of the photon field. Generically, in a fluid in equilibrium, correlations (and, hence, FIF) decay exponentially and are insignificant beyond a correlation length.Nonequilibrium situations provide another route to longrange correlated fluctuations: Systems which, in equilibrium, have zero or short-ranged correlations [C eq ∼ δ s ðxÞ in s dimensions], quite generically exhibit power law correlations (C neq ∼ 1=jxj α ) with conserved dynamics when out of equilibrium [10][11][12]. Thus, it is natural to inquire about the nature (strength and range) of FIF in corresponding nonequilibrium settings (where there is no matching force in equilibrium). Indeed, such forces have been explored in a number of circumstances, including driven granular fluids [13][14][15][16], shear flow [17], active matter systems [18], and in ordinary fluids due to the Soret effect [19] or subject to a temperature gradient [20,21]. However, despite these studies, they are much less understood than other FIF.Here, we explore FIF in diffusive systems which are far from thermal equilibrium. First, we consider, in detail, possibly the simplest (and, hence, analytically tractable) example of FIF in a system of diffusing particles which are subject only to hard core exclusion. The model is commonly referred to as the symmetric simple exclusion process (SSEP) [22]. Then, we present perturbative results for general diffusive systems. The methods introduced can be used to investigate a large variety of models.The setups examined are as follows: (a) The two dimensional system shown in Fig. 1(a); infinite in the y direction and connected to two reservoirs at x ¼ 0 and x ¼ L, with densities ρð0; yÞ ¼ ρ l and ρðL; yÞ ¼ ρ r , respectively. Two slabs, a distance d from each other, span the system along the x direction. (b) The three dimensional extension of this setup is depicted in Fig. 1(b), with the two slabs replaced by a tube of square cross section. (c) A generalized setup in which the slabs (or tube in three ...

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“…In particular the former ones, frequently called "critical Casimir forces," have attracted considerable theoretical and experimental attention recently. Beginning with the seminal paper by Fisher and de Gennes [5], they have been studied theoretically for more than a decade using renormalization group (RG) [6][7][8][9][10] and conformal field theory methods [13], exact solutions of models [12], as well as Monte Carlo (MC) simulations [14][15][16]. Though their detailed experimental investigation just began, recent experiments [17][18][19][20][21] have provided clear evidence of their occurrence.…”

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confidence: 99%

Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory

Diehl¹,

Grüneberg²,

Shpot³

2006

Europhys. Lett.

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Abstract. -Systems described by n-component φ 4 models in a ∞ d−1 × L slab geometry of finite thickness L are considered at and above their bulk critical temperature Tc,∞. The renormalization-group improved perturbation theory commonly employed to investigate the fluctuation-induced forces ("thermodynamic Casimir effect") in d = 4 − ǫ bulk dimensions is re-examined. It is found to be ill-defined beyond two-loop order because of infrared singularities when the boundary conditions are such that the free propagator in slab geometry involves a zero-energy mode at bulk criticality. This applies to periodic boundary conditions and the special-special ones corresponding to the critical enhancement of the surface interactions on both confining plates. The field theory is reorganized such that a small-ǫ expansion results which remains well behaved down to Tc,∞. The leading contributions to the critical Casimir amplitudes ∆per and ∆sp,sp beyond two-loop order are ∼ (u * ) (3−ǫ)/2 , where u * = O(ǫ) is the value of the renormalized φ 4 coupling at the infrared-stable fixed point. Besides integer powers of ǫ, the small-ǫ expansions of these amplitudes involve fractional powers ǫ k/2 , with k ≥ 3, and powers of ln ǫ. Explicit results to order ǫ Fluctuations associated with long wave-length, low-energy excitations play a crucial role in determining the physical properties of many macroscopic systems. When such fluctuations are confined by boundaries, walls, or size restrictions along one or several axes, important effective forces may result. In those cases where the continuous mode spectrum that emerges as the system becomes macroscopic in all directions is not separated from zero energy by a gap, these fluctuation-induced forces are longranged, decaying algebraically as a function of the relevant confinement length L (separation of walls, thickness of the system, etc).A prominent example of such forces are the Casimir forces [1] induced by vacuum fluctuations of the electromagnetic field between two metallic bodies a distance L apart [2][3][4]. Analogous long-range effective forces occur in condensed matter systems as the result of either (i) thermal fluctuations at continuous phase transitions or else (ii) Goldstone modes and similar "massless" excitations [5][6][7][8][9][10][11][12]. In particular the former ones, frequently called "critical Casimir forces," have attracted considerable theoretical and experimental attention recently. Beginning with the seminal paper by Fisher and de Gennes [5], they have been studied theoretically for more than a decade using renormalization group (RG) [6][7][8][9][10] and conformal field theory methods [13], exact solutions of models [12], as well as Monte c EDP Sciences

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Universality of the thermodynamic Casimir effect

Cited by 44 publications

References 53 publications

Casimir Forces, Surface Fluctuations, and Thinning of Superfluid Film

Casimir Forces, Surface Fluctuations, and Thinning of Superfluid Film

Fluctuation-Induced Forces in Nonequilibrium Diffusive Dynamics

Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory

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