Casimir-like Effect Research Articles

Playing with active matter

In the past 20 years, active matter has been a very successful research field, bridging the fundamental physics of nonequilibrium thermodynamics with applications in robotics, biology, and medicine. Active particles, contrary to Brownian particles, can harness energy to generate complex motions and emerging behaviors. Most active-matter experiments are performed with microscopic particles and require advanced microfabrication and microscopy techniques. Here, we propose some macroscopic experiments with active matter employing commercially available toy robots (the Hexbugs). We show how they can be easily modified to perform regular and chiral active Brownian motion and demonstrate through experiments fundamental signatures of active systems such as how energy and momentum are harvested from an active bath, how obstacles can sort active particles by chirality, and how active fluctuations induce attraction between planar objects (a Casimir-like effect). These demonstrations enable hands-on experimentation with active matter and showcase widely used analysis methods.

The Casimir-like effect induced by active nematics

We consider an active nematic phase and use hydrodynamical equations of it to model the activity as an internal field. The interaction of this field with the nematic director in a confined geometry is included in the Hamiltonian of the system. Based on this model Hamiltonian and the standard field theoretical approach, the Casimir-like force induced between the boundaries of such a confined film is discussed. The force depends on the geometrical shape and the dynamical character of the constituents of our active phase, as well as the anchoring conditions. For homeotropically aligned rod-like particles which in principle tend to align along a planar flow field, extensile activity enhances the attraction present in a thin nematic film. As the film thickness increases the force reduces. Beyond a critical thickness, a planar flow field instantaneous to a bend distortion sets in. Near but below the threshold of this activity-induced instability, the force crosses zero and repulsively diverges right at the critical threshold of this so-called flow instability. For contractile rods, in the same geometry as above, the structure is stable and the Casimir-like force diminishes by an exponential factor as a function of the film thickness. On the other side for a planar director alignment, rod-like contractile particles can induce opposite shear flows at the boundaries creating a splay distortion for the director between the plates. In this configuration, we obtain the same universal pretransitional behavior for the force as above. Vice versa, for extensile rod-like particles in this geometry, the director fluctuations become massive and the Casimir-like force diminishes again by an exponential factor as the film thickness increases. The effect of the active field on thermal fluctuations of the director and the fluctuation-induced Casimir force per area is derived through a "semi"-dynamical approach as well. However, the results of the calculation due to a mathematical sum over the fluctuating modes do not lead to an approved closed form.

Quantum Vacuum Sagnac Effect.

We report on the quantum electrodynamical analog of a Sagnac phase induced by the fast rotation of a neutral nanoparticle onto atomic waves propagating in its vicinity. The quantum vacuum Sagnac phase is a geometric Berry phase proportional to the angular velocity of rotation. The persistence of a noninertial effect into the inertial frame is also analogous to the Aharonov-Bohm effect. Here, a rotation confined to a restricted domain of space gives rise to an atomic phase even though the interferometer is at rest with respect to an inertial frame. By taking advantage of a plasmon resonance, we show that the magnitude of the induced phase can be close to the sensitivity limit of state of the art interferometers. The quantum vacuum Sagnac atomic phase is a geometric footprint of a dynamical Casimir-like effect.

Casimir-Like Effect from Thermal Field Fluctuations

Landau-Ginzburg ϕ4 field theory is usually applied to systems for understanding continuous phase transitions at critical points. Here, we analyse thermal field using similar free energy description in statistical field theory perspective, and study fluctuations in such a field with particular focus on realizing thermal Casimir effect. Initially, we qualitatively describe emergence of Casimir-like effect using mean-field approximation and further derive it using coarse-graining of perturbative renormalization procedure in the vicinity of Gaussian-fixed point. These results may lead to further the understanding of Casimir effect from scalar fields without employing the concept of zero-point energy in a cosmological sense.

On the Casimir-Like Effect in System of Two Segregated Bose–Einstein Condensates Restricted by Two Hard Walls

The Casimir-like effect in the system of two segregated Bose–Einstein condensates restricted by two hard walls (optical walls) is studied by means of the Gross–Pitaevskii theory in the double-parabola approximation. After determining the boundary conditions (BCs) at hard walls, we obtain the analytical expressions for both condensates and the interface tensions corresponding, respectively, to the Neumann, Robin and Dirichlet BCs. We discover two finite-size effects which closely connect with interface tensions: (a) Beside the conventional Casimir force caused by the zero-point energy there still emerges in the system a new type of long-range forces associated with different interface tensions. They are called the Casimir-like forces. (b) The second finite-size effect is directly associated with the BCs, it claims that the Neumann BC leads to stable state while the two other BCs provide unstable states of the underlying system. Therefore, the Casimir-like force derived from the Neumann BC is the dominant one in the system since it is present in the stable state. As a by-product, we conjecture that the above-mentioned effects could be present in all two-components systems confined by two walls.

The Casimir-like effect in a one-dimensional Bose gas

The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross–Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is a classical result that can be understood using the mean-field Gross–Pitaevskii equation. We find that at larger distances, the induced interaction crosses over into a power law dependence due to the quantum fluctuations. We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization.

Correlated Partial Disorder in a Weakly Frustrated Quantum Antiferromagnet.

Partial disorder-the microscopic coexistence of long-range magnetic order and disorder-is a rare phenomenon that has been experimentally and theoretically reported in some Ising- or easy plane-spin systems, driven by entropic effects at finite temperatures. Here, we present an analytical and numerical analysis of the S=1/2 Heisenberg antiferromagnet on the sqrt[3]×sqrt[3]-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180° Néel ordered honeycomb subsystem coexisting with disordered spins at the hexagon center sites. These central spins are ferromagnetically aligned at short distances, as a consequence of a Casimir-like effect originated by the zero-point quantum fluctuations of the honeycomb lattice.

Interaction and structuration of membrane-binding and membrane-excluding colloidal particles in lamellar phases.

Within the framework of a discrete Gaussian model, we present analytical results for the interaction induced by a lamellar phase between small embedded colloidal particles. We consider the two limits of particles strongly adherent to the adjacent membranes and of particles impenetrable to the membranes. Our approach takes into account the finite size of the colloidal particles, the discrete nature of the layers, and includes the Casimir-like effect of fluctuations, which is very important for dilute phases. Monte Carlo simulations of the statistical behavior of the membrane-interacting colloidal particles account semi-quantitatively, without any adjustable parameters, for the experimental data measured on silica nanospheres inserted within lyotropic smectics. We predict the existence of finite-size and densely packed particle aggregates originating from the competition between attractive interactions between colloidal particles in the same layer and repulsion between colloidal particles one layer apart.

Is zero-point energy physical? A toy model for Casimir-like effect

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.

Domain wall interactions due to vacuum Dirac field fluctuations in2+1dimensions

We evaluate quantum effects due to a $2$-component Dirac field in $2+1$ space-time dimensions, coupled to domain-wall like defects with a smooth shape. We show that those effects induce non trivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode, corresponding to the Callan-Harvey mechanism, by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a non trivial, Casimir-like effect between them, and provide an exact expression for that interaction in the case of two straight-line parallel defects. As is the case for the Casimir interaction energy, the result is finite and unambiguous.

Generating Net Forces from Backgrounds of Randomly Created Waves

We examine the possibility of generating net forces on concave isolated objects from backgrounds consisting of randomly created waves carrying momentum. This issue is examined first for waves at the surface of a liquid, and second for quantum vacuum electromagnetic waves, both in relation with a one-side-open rectangular structure whose interior embodies a large number of parallel reflecting plates. Using known results about the Casimir-like effect and the original Casimir effect for parallel plates, we explain why and how such rectangular hollow structures should feel net oriented forces. We briefly describe real systems that would allow testing these theoretical results.

Hydrophobic force, a Casimir-like effect due to hydrogen-bond fluctuations

Hydrophobic force, interfacial tension, and transverse density profile in a confined water system are addressed from first principles of statistical mechanics in a lattice model for water. Using the molecular mean field theory technique we deduce explicit expressions for each of the above mentioned phenomena and show that hydrophobic force is a manifestation of a Casimir-like effect due to hydrogen-bond fluctuations in confined water. It is largely influenced by the long range correlations of orientational fluctuations. Furthermore, the temperature dependence of hydrophobic force between large non-polar surfaces is suggested to be different from that between small solutes. The mechanisms contributing to characteristic behavior in each case are identified. In the case of large surfaces, the prevalence of discrete fluctuation modes in the confinement direction and their entropic contribution to the overall free energy dominate the temperature dependence. Mode discretization is also implicated in the variation of interfacial tension with separation distance between confining surfaces and characteristic density profile of the confined fluid. All the computations are parameter free and compare favorably with results of molecular dynamics simulations and experiments.

Can dark energy emerge from quantum effects in a compact extra dimension?

The origin of the observed acceleration of the expansion of the universe is a major problem of modern cosmology and theoretical physics. Simple estimations of the contribution of vacuum to the density energy of the universe in quantum field theory are known to lead to catastrophic large values compared to observations. Such a contribution is therefore generally not regarded as a viable source for the acceleration of the expansion. In this letter we propose that the vacuum contribution actually provides a small positive value to the density energy of the universe. The underlying mechanism is a manifestation of the quantum nature of the gravitational field, through a Casimir-like effect from an additional compact dimension of space. A key ingredient is to assume that only modes with wavelength shorter than the Hubble length contribute to the vacuum. Such a contribution gives a positive energy density, has a Lorentz invariant equation of state in the usual 4D spacetime and hence can be interpreted as a cosmological constant. Its value agrees with observations for a radius of a 5th extra dimension given by $35\,\mu$m. This implies a modification of the gravitational inverse square law around this scale, close but below existing limits from experiments testing gravity at short range.

Simulation of a Casimir-like effect in a granular pile with avalanches

Using a modified Bak-Tang-Wiesenfeld model for sand piles, we simulate a Casimir-like effect in a granular pile with avalanches. Results obtained in the simulation are in good agreement with results previously acquired experimentally: two parallel walls are attracted to each other at small separation distances, with a force decreasing with increasing distance. In the simulation only, at medium distances a weak repulsion exists. Additionally, with the aim of avalanche prevention, the possibility of suppressing self-organized criticality with an array of walls placed on the slope of the pile is investigated, but the prevention effect is found to be negligible.

Casimir-like effect on a granular pile

We investigate experimentally a Casimir-like effect in a three-dimensional pile of rice, which has a power-law avalanche size distribution. We observe the change in distance between two Plexiglas sheets placed on the pile parallel to each other and parallel to the mean avalanche flow direction, while rice grains are continuously and uniformly falling on top of the pile. The resulting avalanches are fluctuations, confinement of which is found to drive the two plates together. During 25-h experimental runs, for initial intersheet distances ranging from 20.0 to 90.0 mm we observe changes in the range from 6.0 mm to less than 1.0 mm. A similar distance dependence is obtained from a simple analytical model.

Gauge gravity in noncommutative de Sitter space and pair creation

From the invariance of the generalized space-time non-commutative commutation relations, local Poincaré and general coordinate transformations are derived. Moreover, a generalized Dirac equation is obtained. Applied to the de Sitter universe, it is shown that the space-time non-commutativity contributes to the particle creation process and induces a Casimir-like effect.