Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameter-conserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.Comment: 38 pages, 11 figure

Convergence of large deviation estimators

We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium, nonequilibrium, and manmade stochastic systems. We give conditions for the convergence of these estimators with sample size, based on the boundedness or unboundedness of the quantity sampled, and discuss how statistical errors should be defined in different parts of the convergence region. Our results shed light on previous reports of 'phase transitions' in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges.Comment: 13 pages, 6 figures. v2: corrections focusing the paper on large deviations; v3: minor corrections, close to published versio

Non-equilibrium forces following quenches in active and thermal matter

Non-equilibrium systems are known to exhibit long-ranged correlations due to conservation of quantities like density or momentum. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of non-equilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent {\it density-induced forces}. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient {\it fluctuation-induced forces} emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Finally, we propose several scenarios for their experimental observation.Comment: - Added Journal reference and DOI - Modified title - Fixed minor typos - Added plot of Eq. (32) [16 pages, 11 figures

Response of active Brownian particles to shear flow

We study the linear response of interacting active Brownian particles in an external potential to simple shear flow. Using a path integral approach, we derive the linear response of any state observable to initiating shear in terms of correlation functions evaluated in the unperturbed system. For systems and observables which are symmetric under exchange of the $x$ and $y$ coordinates, the response formula can be drastically simplified to a form containing only state variables in the corresponding correlation functions (compared to the generic formula containing also time derivatives). In general, the shear couples to the particles by translational as well as rotational advection, but in the aforementioned case of $xy$ symmetry only translational advection is relevant in the linear regime. We apply the response formulas analytically in solvable cases and numerically in a specific setup. In particular, we investigate the effect of a shear flow on the morphology and the stress of $N$ confined active particles in interaction, where we find that the activity as well as additional alignment interactions generally increase the response.Comment: 13 pages, 4 figure

Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions

In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here, we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the OP profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Our analytical results are supported by Monte Carlo simulations of the three-dimensional Ising model. We show that, in the canonical ensemble, i.e., when fixing the so-called total mass within the film, the CCF is typically repulsive instead of attractive as in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we furthermore obtain analytic expressions for the order parameter profiles and analyze the relation between the total mass in the film and the external bulk field.Comment: 22 pages, 15 figures. Version 2: minor corrections; added Journal referenc

Ballistic propagation of density correlations and excess wall forces in quenched granular media

We investigate a granular gas in a shaken quasi-two-dimensional box in molecular dynamics computer simulations. After a sudden change (quench) of the shaking amplitude, transient density correlations are observed orders of magnitude beyond the steady-state correlation length scale. Propagation of the correlations is ballistic, in contrast to recently investigated quenches of Brownian particles that show diffusive propagation [Rohwer et al., Phys. Rev. Lett., 118, 015702 (2017), Rohwer et al., Phys. Rev. E, 97, 032125 (2018)]. At sufficiently strong cooling of the fluid the effect is overlaid by clustering instability of the homogeneous cooling state with different scaling behavior. We are able to identify different quench regimes. In each regime correlations exhibit remarkably universal position dependence. In simulations performed with side walls we find confinement effects for temperature and pressure in steady-state simulations, and an additional transient wall pressure contribution upon changing the shaking amplitude. The transient contribution is ascribed to enhanced relaxation of the fluid in the presence of walls. From incompatible scaling behavior we conclude that the observed effects with and without side walls constitute distinct phenomena.Comment: 12 pages 11 figure

Additional degrees of freedom associated with position measurements in non-commutative quantum mechanics

Thesis (MSc (Physics))--University of Stellenbosch, 2010.ENGLISH ABSTRACT: Due to the minimal length scale induced by non-commuting co-ordinates, it is not clear a priori what is meant by a position measurement on a non-commutative space. It was shown recently in a paper by Scholtz et al. that it is indeed possible to recover the notion of quantum mechanical position measurements consistently on the non-commutative plane. To do this, it is necessary to introduce weak (non-projective) measurements, formulated in terms of Positive Operator-Valued Measures (POVMs). In this thesis we shall demonstrate, however, that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the aforementioned formalism entails a description that is non-local in that it requires knowledge of all orders of positional derivatives through the star product that is used ubiquitously to map operator multiplication onto function multiplication in non-commutative systems. It will be shown that there exist several equivalent local descriptions, which are arrived at via the introduction of additional degrees of freedom. Consequently non-commutative quantum mechanical position measurements necessarily confront us with some additional structure which is necessary (in addition to position) to specify quantum states completely. The remainder of the thesis, based in part on a recent publication (\Noncommutative quantum mechanics { a perspective on structure and spatial extent", C.M. Rohwer, K.G. Zloshchastiev, L. Gouba and F.G. Scholtz, J. Phys. A: Math. Theor. 43 (2010) 345302) will involve investigations into the physical interpretation of these additional degrees of freedom. For one particular local formulation, the corresponding classical theory will be used to demonstrate that the concept of extended, structured objects emerges quite naturally and unavoidably there. This description will be shown to be equivalent to one describing a two-charge harmonically interacting composite in a strong magnetic eld found by Susskind. It will be argued through various applications that these notions also extend naturally to the quantum level, and constraints will be shown to arise there. A further local formulation will be introduced, where the natural interpretation is that of objects located at a point with a certain angular momentum about that point. This again enforces the idea of particles that are not point-like. Both local descriptions are convenient, in that they make explicit the additional structure which is encoded more subtly in the non-local description. Lastly we shall argue that the additional degrees of freedom introduced by local descriptions may also be thought of as gauge degrees of freedom in a gauge-invariant formulation of the theory.AFRIKAANSE OPSOMMING: As gevolg van die minimum lengteskaal wat deur nie-kommuterende ko ordinate ge nduseer word is dit nie a priori duidelik wat met 'n posisiemeting op 'n nie-kommutatiewe ruimte bedoel word nie. Dit is onlangs in 'n artikel deur Scholtz et al. getoon dat dit wel op 'n nie-kommutatiewe vlak moontlik is om die begrip van kwantummeganiese posisiemetings te herwin. Vir hierdie doel benodig ons die konsep van swak (nie-projektiewe) metings wat in terme van 'n positief operator-waardige maat geformuleer word. In hierdie tesis sal ons egter toon dat 'n meting van slegs die posisie nie volledige inligting oor die kwantumtoestand van 'n deeltjie in 'n niekommutatiewe ruimte lewer nie. Ons formalisme behels 'n nie-lokale beskrywing waarbinne kennis oor alle ordes van posisieafgeleides in die sogenaamde sterproduk bevat word. Die sterproduk is 'n welbekende konstruksie waardeur operatorvermenigvuldiging op funksievermenigvuldiging afgebeeld kan word. Ons sal toon dat verskeie ekwivalente lokale beskrywings bestaan wat volg uit die invoer van bykomende vryheidsgrade. Dit beteken dat nie-kommutatiewe posisiemetings op 'n natuurlike wyse die nodigheid van bykomende strukture uitwys wat noodsaaklik is om die kwantumtoestand van 'n sisteem volledig te beskryf. Die res van die tesis, wat gedeeltelik op 'n onlangse publikasie (\Noncommutative quantum mechanics { a perspective on structure and spatial extent", C.M. Rohwer, K.G. Zloshchastiev, L. Gouba and F.G. Scholtz, J. Phys. A: Math. Theor. 43 (2010) 345302) gebaseer is, behels 'n ondersoek na die siese interpretasie van hierdie bykomende strukture. Ons sal toon dat vir 'n spesi eke lokale formulering die beeld van objekte met struktuur op 'n natuurlike wyse in die ooreenstemmende klassieke teorie na vore kom. Hierdie beskrywing is inderdaad ekwivalent aan die van Susskind wat twee gelaaide deeltjies, gekoppel deur 'n harmoniese interaksie, in 'n sterk magneetveld behels. Met behulp van verskeie toepassings sal ons toon dat hierdie interpretasie op 'n natuurlike wyse na die kwantummeganiese konteks vertaal waar sekere dwangvoorwaardes na vore kom. 'n Tweede lokale beskrywing in terme van objekte wat by 'n sekere punt met 'n vaste hoekmomentum gelokaliseer is sal ook ondersoek word. Binne hierdie konteks sal ons weer deur die begrip van addisionele struktuur gekonfronteer word. Beide lokale beskrywings is gerie ik omdat hulle hierdie bykomende strukture eksplisiet maak, terwyl dit in die nie-lokale beskrywing deur die sterproduk versteek word. Laastens sal ons toon dat die bykomende vryheidsgrade in lokale beskrywings ook as ykvryheidsgrade van 'n ykinvariante formulering van die teorie beskou kan word

Activated diffusiophoresis

Perturbations of fluid media can give rise to non-equilibrium dynamics, which may in turn cause motion of immersed inclusions. We consider perturbations ("activations") that are local in space and time, of a fluid density which is conserved, and study the resulting diffusiophoretic phenomena that emerge at a large distance. Specifically, we consider cases where the perturbations propagate diffusively, providing examples from passive and active matter for which this is expected to be the case. Activations can, for instance, be realized by sudden and local changes in interaction potentials of the medium, or by local changes of its activity. Various analytical results are provided for the case of confinement by two parallel walls. We investigate the possibility of extracting work from inclusions which are moving through the activated fluid. Further, we show that a time-dependent density profile, created via suitable activation protocols, allows for conveyance of inclusions along controlled and stable trajectories. In contrast, in states with a steady density, inclusions cannot be held at stable positions, reminiscent of Earnshaw's theorem of electrostatics. We expect these findings to be applicable in a range of experimental systems.Comment: 14 pages (12+2), 14 Figure