Particle dynamics in two-dimensional random-energy landscapes: experiments and simulations

Deep learning for optical tweezers

Optical tweezers exploit light-matter interactions to trap particles ranging from single atoms to micrometer-sized eukaryotic cells. For this reason, optical tweezers are a ubiquitous tool in physics, biology, and nanotechnology. Recently, the use of deep learning has started to enhance optical tweezers by improving their design, calibration, and real-time control as well as the tracking and analysis of the trapped objects, often outperforming classical methods thanks to the higher computational speed and versatility of deep learning. In this perspective, we show how cutting-edge deep learning approaches can remarkably improve optical tweezers, and explore the exciting, new future possibilities enabled by this dynamic synergy. Furthermore, we offer guidelines on integrating deep learning with optical trapping and optical manipulation in a reliable and trustworthy way.

Single-file diffusion in spatially inhomogeneous systems

We study the effect of spatially varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Noninteracting particles in such a system exhibit normal diffusion at late times, which is characterized by an effective diffusion constant D_{eff}. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially homogeneous system with constant diffusivity D_{eff}. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.

Electric Fields in Liquid Water Irradiated with Protons at Ultrahigh Dose Rates

We study the effects of irradiating water with 3 MeV protons at high doses by observing the motion of charged polystyrene beads outside the proton beam. By single-particle tracking, we measure a radial velocity of the order of microns per second. Combining electrokinetic theory with simulations of the beam-generated reaction products and their outward diffusion, we find that the bead motion is due to electrophoresis in the electric field induced by the mobility contrast of cations and anions. This work sheds light on the perturbation of biological systems by high-dose radiations and paves the way for the manipulation of colloid or macromolecular dispersions by radiation-induced diffusiophoresis.

Fickian yet non-Gaussian diffusion of a quasi-2D colloidal system in an optical speckle field: experiment and simulations

We investigate a quasi-2D suspension of Brownian particles in an optical speckle field produced by holographic manipulation of a laser wavefront. This system was developed to study, in a systematic and controllable way, a distinctive instance of diffusion, called Fickian yet Non Gaussian diffusion (FnGD), observed, during the last decade, for colloidal particles in a variety of complex and biological fluids. Our setup generates an optical speckle field that behaves like a disordered set of optical traps. First, we describe the experimental setup and the dynamics of the particles, focusing on mean square displacements, displacement distributions and kurtosis. Then, we present Brownian Dynamics simulations of point-like particles in a complex energy landscape, mimicking that generated by the optical speckle field. We show that our simulations can capture the salient features of the experimental results, including the emergence of FnGD, also covering times longer than the ones so far achieved in experiments. Some deviations are observed at long time only, with the Gaussian restoring being slower in simulations than in experiments. Overall, the introduced numerical model might be exploited to guide the design of upcoming experiments targeted, for example, to fully monitor the recovery of Gaussianity.

Comparison of Physicochemical Properties of Native Mucus and Reconstituted Mucin Gels

Simulating native mucus with model systems such as gels made from reconstituted mucin or commercially available polymers presents experimental advantages including greater sample availability and reduced inter- and intradonor heterogeneity. Understanding whether these gels reproduce the complex physical and biochemical properties of native mucus at multiple length scales is critical to building relevant experimental models, but few systematic comparisons have been reported. Here, we compared bulk mechanical properties, microstructure, and biochemical responses of mucus from different niches, reconstituted mucin gels (with similar pH and polymer concentrations as native tissues), and commonly used commercially available polymers. To evaluate gel properties across these length scales, we used small-amplitude oscillatory shear, single-particle tracking, and microaffinity chromatography with small analytes. With the exception of human saliva, the mechanical response of mucin gels was qualitatively similar to that of native mucus. The transport behavior of charged peptides through native mucus gels was qualitatively reproduced in gels composed of corresponding isolated mucins. Compared to native mucus, we observed substantial differences in the physicochemical properties of gels reconstituted from commercially available mucins and the substitute carboxymethylcellulose, which is currently used in artificial tear and saliva treatments. Our study highlights the importance of selecting a mucus model system guided by the length scale relevant to the scientific investigation or disease application.

Anomalous diffusion and long-range memory in the scaled voter model

We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the scaled voter model reduces to the usual noisy voter model, but it is driven by the scaled Brownian motion. We derive analytical expressions for the time evolution of the first and second moments of the scaled voter model. In addition, we have derived an analytical approximation of the first passage time distribution. By numerical simulation, we confirm our analytical results as well as showing that the model exhibits long-range memory indicators despite being a Markov model. The proposed model has steady-state distribution consistent with the bounded fractional Brownian motion, thus we expect it to be a good substitute model for the bounded fractional Brownian motion.

First-passage statistics of colloids on fractals: Theory and experimental realization

In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.

A model-system of Fickian yet non-Gaussian diffusion: light patterns in place of complex matter

Fickian yet non-Gaussian Diffusion (FnGD), widely observed for colloidal particles in a variety of complex and biological fluids, emerges as a most intriguing open issue in Soft Matter. To fully monitor FnGD and advance its understanding, recording many trajectories over a large time range is crucial, which makes experiments challenging. Here we exploit a recently introduced experimental model of finely tunable FnGD: a quasi-2d system of Brownian beads in water moving in a heterogeneous energy landscape generated by a static and spatially random optical force field (speckle pattern). By performing experiments at different optical power, we succeed in monitoring the evolution as well as the precursors of FnGD. Fickian scaling of the mean square displacement is always attained after a subdiffusive regime while the displacement distributions keep on being non-Gaussian, which allows for measuring a characteristic length- and time-scale for the onset of FnGD, ξ_f and t_f. We find that ξ_f stays constant, whereas t_f grows as the inverse of the long-time diffusion coefficient t_f ∝ D^-1 for increasing the optical power. Deviations from the standard Gaussian shape of the displacement distribution are neatly characterized on a broad range of times, focusing on the excess probability at small displacements and on the decay-length of the distinctive exponential tails. Such deviations are fully built in the subdiffusive regime and, at the FnGD onset, grow with the optical power. As time goes on, the small-displacement probability narrows and the exponential tails progressively break up, with a tendency to recover the Gaussian behaviour. Overall, both subdiffusion and FnGD become more marked and persistent on increasing the optical power, suggesting a strict relation between these two regimes. As clearly demonstrated by our results, the adopted model-system represents a privileged stage for in-depth study of FnGD and opens the way to unveil the nature of this phenomenon through finely tuned and well-controlled experiments.

Anomalous diffusion in nonlinear transformations of the noisy voter model

Voter models are well known in the interdisciplinary community, yet they have not been studied from the perspective of anomalous diffusion. In this paper, we show that the original voter model exhibits a ballistic regime. Nonlinear transformations of the observation variable and time scale allow us to observe other regimes of anomalous diffusion as well as normal diffusion. We show that numerical simulation results coincide with derived analytical approximations describing the temporal evolution of the raw moments.

Rapid Fickian Yet Non-Gaussian Diffusion after Subdiffusion

The recently discovered Fickian yet non-Gaussian diffusion (FnGD) is here finely tuned and investigated over a wide range of probabilities and timescales using a quasi-2D suspension of colloidal beads under the action of a static and spatially random optical force field. This experimental model allows one to demonstrate that a "rapid" FnGD regime with a diffusivity close to that of free suspension can originate from earlier subdiffusion. We show that these two regimes are strictly tangled: as subdiffusion deepens upon increasing the optical force, deviations from Gaussianity in the FnGD regime become larger and more persistent in time. In addition, the distinctive exponential tails of FnGD are quickly built up in the subdiffusive regime. Our results shed new light on previous experimental observations and suggest that FnGD may generally be a memory effect of earlier subdiffusive processes.

Dense hard disk ordering: influence of bidispersity and quenched disorder

Using Monte Carlo simulations, the impact on structural ordering in two-dimensional systems via the interplay of size bidispersity and quenched disorder in the form of an externally applied spatially random potential, is studied for a system of hard disks. By scanning across a wide range of dense packing fractions, size ratios and roughness of the applied potential, the phase diagram is constructed, which demonstrates that both quenched and size disorders shift the onset of translational order to higher packings, while maintaining the presence of the intermediate hexatic phase. At larger disorder strengths, the signatures of structural order are absent within the range of investigated packing fractions. Further, the dynamics with increasing potential strength is analysed for the mono-component system to obtain a spatio-temporal description of the melting process. Finally, the influence of the externally rough field on the Mermin-Wagner fluctuations, characteristic to two-dimensional systems, is investigated.

Collective Dynamics of Model Pili-Based Twitcher-Mode Bacilliforms

Pseudomonas aeruginosa, like many bacilliforms, are not limited only to swimming motility but rather possess many motility strategies. In particular, twitching-mode motility employs hair-like pili to transverse moist surfaces with a jittery irregular crawl. Twitching motility plays a critical role in redistributing cells on surfaces prior to and during colony formation. We combine molecular dynamics and rule-based simulations to study twitching-mode motility of model bacilliforms and show that there is a critical surface coverage fraction at which collective effects arise. Our simulations demonstrate dynamic clustering of twitcher-type bacteria with polydomains of local alignment that exhibit spontaneous correlated motions, similar to rafts in many bacterial communities.

Overdamped Brownian dynamics in piecewise-defined energy landscapes

We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(-aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusion coefficient 〈D_{eff}〉 is introduced to characterize the diffusive motion: 〈x^{2}〉=2〈D_{eff}〉t. A general expression for 〈D_{eff}〉 in terms of U(x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a=1, and a reduction to free diffusion as a→∞. The behavior of 〈D_{eff}〉 around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.

Long-time self-diffusion in quasi-two-dimensional colloidal fluids of paramagnetic particles

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r^{3}, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D_{L}^{★}=D_{L}/(D_{0}Γ^{1/2}), with D_{0} the self-diffusion coefficient at infinite dilution and D_{L} the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r^{3} long-ranged DI, the reduced quantity D_{L}^{★} is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.

Glass forming liquids in a quenched random potential

The response of a model two-dimensional colloidal glass former to an externally imposed spatially random potential, which acts as a quenched disorder, is investigated using numerical simulations, motivated by recent experiments and also mean field predictions. The external potential induces the onset of the glassy dynamics at increasingly smaller field roughness, with increasing packing fraction of the particulate assembly, and the existence of aging processes within the glassy regime is also observed. Furthermore, along the axis of increasing field roughness, the dynamical slowdown is not correlated to the hexatic order within the supercooled regime.

Energy landscape of colloidal dumbbells in a periodic distribution of light

Using a ray tracing calculation, the energy landscape of dumbbells, made of spherical colloidal particles, interacting with a periodic distribution of light is calculated. As shown previously [E. Sarmiento-Gomez, J. A. Rivera-Moran and J. L. Aruaz-Lara, Soft Matter, 2018, 14, 3684], planar aggregates of spherical particles adopt discrete configurations in such light distribution. Here we focus on the case of colloidal dumbbells both symmetric and asymmetric from an experimental and theoretical point of view. It has been shown that the direct calculation using the ray tracing approximation is in excellent agreement with the experiment in spite of the fact that the particles size and the wavelength of the trapping light are comparable. We also corroborate, at least for the more simple case of a single particle in a parabolic light distribution, that the simple method used here provides the same results as the more complex and general Lorenz-Mie approach giving a more simple yet reliable method for the calculation of the energy landscape of colloidal aggregates in periodic light distributions.

A Rheological Study of the Association and Dynamics of MUC5AC Gels

The details of how a mucus hydrogel forms from its primary structural component, mucin polymers, remain incompletely resolved. To explore this, we use a combination of macrorheology and single-particle tracking to investigate the bulk and microscopic mechanical properties of reconstituted MUC5AC mucin gels. We find that analyses of thermal fluctuations on the length scale of the micrometer-sized particles are not predictive of the linear viscoelastic response of the mucin gels, and that taken together, the results from both techniques help to provide complementary insight into the structure of the network. In particular, we show that macroscopic stiffening of MUC5AC gels can be brought about in different ways by targeting specific associations within the network using environmental triggers such as modifications to the pH, surfactant, and salt concentration. Our work may be important for understanding how environmental factors, including pathogens and therapeutic agents, alter the mechanical properties of fully constituted mucus.

Dynamics of fluids in quenched-random potential energy landscapes: a mode-coupling theory approach

Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the mode-coupling theory, based on the simple model of the hard-sphere fluid in a Gaussian random field. The possible dynamical arrest scenarios driven by an increase of the disorder strength and/or of the fluid density are mapped, and the corresponding evolutions of time-dependent quantities typically used for the characterization of anomalous self-diffusion are illustrated with detailed computations. Overall, a fairly reasonable picture of the dynamics of the system at hand is outlined, which in particular involves a non-monotonicity of the self-diffusion coefficient with fluid density at fixed disorder strength, in agreement with experiments. The disorder correlation length is shown to have a strong influence on the latter feature.

Colloidal diffusion over a quenched two-dimensional random potential

A two-layer colloidal system is developed for the study of diffusion over a quenched two-dimensional random potential. A mixture of bidisperse silica spheres is used to form a randomly packed colloidal monolayer on the bottom substrate. The corrugated surface of the bottom colloidal monolayer provides a gravitational potential field for the dilute diffusing particles in the top layer. The population probability histogram P(x,y) of the diffusing particles is obtained to fully characterize the random potential landscape U(x,y) via the Boltzmann distribution. The dynamical properties of the top diffusing particles, such as their mean square displacement (MSD), histogram of the escape time, and long-time self-diffusion coefficient, are simultaneously measured from the particle trajectories. A quantitative relationship between the long-time diffusion coefficient and the random potential is obtained, which is in good agreement with the theoretical prediction. The measured MSD reveals a wide region of subdiffusion resulting from the structural disorders. The crossover from subdiffusion to normal diffusion is explained by the Lorentz model for tracer diffusion through a heterogeneous space filled with a set of randomly distributed obstacles.

Self-diffusion in two-dimensional binary colloidal hard-sphere fluids

We present a systematic experimental study of the dynamic behavior of monodisperse and bidisperse two-dimensional colloidal hard-sphere fluids. We consider the diffusive behavior of the two types of particles for systems with a variety of compositions and total area fractions. In particular, we measure the short- and long-time diffusion coefficients for both species independently. We find that the short-time self-diffusion coefficients show an approximately linear dependence on the area fraction and that the long-time self-diffusion coefficients are well described by an expression dependent upon only the area fraction and contact value of the radial distribution function. Finally, we consider the effect of composition change and find some variation in the long-time self-diffusion coefficients, which we ascribe to the complex packing effects exhibited by binary systems.

Influence of external potentials on heterogeneous diffusion processes

In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. The heterogeneous diffusion processes can yield subdiffusion as well as superdiffusion, depending on the behavior of the diffusion coefficient. We assume that not only the diffusion coefficient but also the external force has a power-law dependence on the position. We obtain analytic expressions for the transition probability in two cases: when the power-law exponent in the external force is equal to 2η-1, where 2η is the power-law exponent in the dependence of the diffusion coefficient on the position, and when the external force has a linear dependence on the position. We found that the power-law exponent in the dependence of the mean square displacement on time does not depend on the external force; this force changes only the anomalous diffusion coefficient. In addition, the external force having the power-law exponent different from 2η-1 limits the time interval where the anomalous diffusion occurs. We expect that the results obtained in this paper may be relevant for a more complete understanding of anomalous diffusion processes.

Time- and ensemble-averages in evolving systems: the case of Brownian particles in random potentials

Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general.

Active dynamics of colloidal particles in time-varying laser speckle patterns

Colloidal particles immersed in a dynamic speckle pattern experience an optical force that fluctuates both in space and time. The resulting dynamics presents many interesting analogies with a broad class of non-equilibrium systems like: active colloids, self propelled microorganisms, transport in dynamical intracellular environments. Here we show that the use of a spatial light modulator allows to generate light fields that fluctuate with controllable space and time correlations and a prescribed average intensity profile. In particular we generate ring-shaped random patterns that can confine a colloidal particle over a quasi one-dimensional random energy landscape. We find a mean square displacement that is diffusive at both short and long times, while a superdiffusive or subdiffusive behavior is observed at intermediate times depending on the value of the speckles correlation time. We propose two alternative models for the mean square displacement in the two limiting cases of a short or long speckles correlation time. A simple interpolation formula is shown to account for the full phenomenology observed in the mean square displacement across the entire range from fast to slow fluctuating speckles.

Tuning protein-protein interactions using cosolvents: specific effects of ionic and non-ionic additives on protein phase behavior

Cosolvents are routinely used to modulate the (thermal) stability of proteins and, hence, their interactions with proteins have been studied intensely. However, less is known about their specific effects on protein-protein interactions, which we characterize in terms of the protein phase behavior. We analyze the phase behavior of lysozyme solutions in the presence of sodium chloride (NaCl), guanidine hydrochloride (GuHCl), glycerol, and dimethyl sulfoxide (DMSO). We experimentally determined the crystallization boundary (XB) and, in combination with data on the cloud-point temperatures (CPTs), the crystallization gap. In agreement with other studies, our data indicate that the additives might affect the protein phase behavior through electrostatic screening and additive-specific contributions. At high salt concentrations, where electrostatic interactions are screened, both the CPT and the XB are found to be linear functions of the additive concentration. Their slopes quantify the additive-specific changes of the phase behavior and thus of the protein-protein interactions. While the specific effect of NaCl is to induce attractions between proteins, DMSO, glycerol and GuHCl (with increasing strength) weaken attractions and/or induce repulsions. Except for DMSO, changes of the CPT are stronger than those of the XB. Furthermore, the crystallization gap widens in the case of GuHCl and glycerol and narrows in the case of NaCl. We relate these changes to colloidal interaction models, namely square-well and patchy interactions.

Effect of Hydrodynamic Interactions on Self-Diffusion of Quasi-Two-Dimensional Colloidal Hard Spheres

We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient D(S) scaled by the diffusion coefficient at infinite dilution, D(0), strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient D(L)/D(0) is in quantitative agreement with D(L)/D(0) obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of D(L)/D(0) on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.

Controlling dispersion forces between small particles with artificially created random light fields

Appropriate combinations of laser beams can be used to trap and manipulate small particles with optical tweezers as well as to induce significant optical binding forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir–Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theoretically and experimentally, that dispersion forces between small colloidal particles can also be induced and controlled using artificially created fluctuating light fields. Using optical tweezers as a gauge, we present experimental evidence for the predicted isotropic attractive interactions between dielectric microspheres induced by laser-generated, random light fields. These light-induced interactions open a path towards the control of translationally invariant interactions with tuneable strength and range in colloidal systems.

Natural dispersion forces acting between molecules and particles arise from electromagnetic fields generated by quantum and thermal fluctuations. Here, Brügger et al. show that isotropic dispersion forces between colloidal particles can be induced, controlled and tuned with artificial, fluctuating laser light fields.

Run-and-tumble particles in speckle fields

The random energy landscapes developed by speckle fields can be used to confine and manipulate a large number of micro-particles with a single laser beam. By means of molecular dynamics simulations, we investigate the static and dynamic properties of an active suspension of swimming bacteria embedded into speckle patterns. Looking at the correlation of the density fluctuations and the equilibrium density profiles, we observe a crossover phenomenon when the forces exerted by the speckles are equal to the bacteria's propulsion.

Realization of nonequilibrium thermodynamic processes using external colored noise

We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey the Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen.

Speckle optical tweezers: micromanipulation with random light fields

Current optical manipulation techniques rely on carefully engineered setups and samples. Although similar conditions are routinely met in research laboratories, it is still a challenge to manipulate microparticles when the environment is not well controlled and known a priori, since optical imperfections and scattering limit the applicability of this technique to real-life situations, such as in biomedical or microfluidic applications. Nonetheless, scattering of coherent light by disordered structures gives rise to speckles, random diffraction patterns with well-defined statistical properties. Here, we experimentally demonstrate how speckle fields can become a versatile tool to efficiently perform fundamental optical manipulation tasks such as trapping, guiding and sorting. We anticipate that the simplicity of these "speckle optical tweezers" will greatly broaden the perspectives of optical manipulation for real-life applications.

Brownian particles on rough substrates: relation between intermediate subdiffusion and asymptotic long-time diffusion

Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or simulations. For the case of one-dimensional random potentials with Gaussian distributed energies, we present a detailed analysis of experimental and simulation data. It is shown that the asymptotic long-time diffusion coefficient can be related to the behavior at intermediate times, namely, the minimum of the exponent that characterizes subdiffusion and hence corresponds to the maximum degree of subdiffusion. As a consequence, investigating only the dynamics at intermediate times is sufficient to predict the order of magnitude of the long-time diffusion coefficient and the time scale at which the crossover from subdiffusion to diffusion occurs, i.e., when the long-time diffusive regime and hence thermal equilibrium is established. Inversely, theoretical predictions derived for the asymptotic long-time behavior can be used to quantitatively characterize the intermediate behavior, which hardly has been studied so far.

Transport and diffusion of overdamped Brownian particles in random potentials

We present a numerical study of the anomalies in transport and diffusion of overdamped Brownian particles in totally disordered potential landscapes in one and in two dimensions. We characterize and analyze the effects of three different disordered potentials. The anomalous regimes are characterized by the time exponents that exhibit the statistical moments of the ensemble of particle trajectories. The anomaly in the transport is always of the subtransport type, but diffusion presents a greater variety of anomalies: Both subdiffusion and superdiffusion are possible. In two dimensions we present a mixed anomaly: subdiffusion in the direction perpendicular to the force and superdiffusion in the parallel direction.