Sven Dorosz

Description of hard-sphere crystals and crystal-fluid interfaces: A comparison between density functional approaches and a phase-field crystal model

In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.

On the influence of a patterned substrate on crystallization in suspensions of hard spheres

We present a computer simulation study on crystal nucleation and growth in supersaturated suspensions of mono-disperse hard spheres induced by a triangular lattice substrate. The main result is that compressed substrates are wet by the crystalline phase (the crystalline phase directly appears without any induction time), while for stretched substrates we observe heterogeneous nucleation. The shapes of the nucleated crystallites fluctuate strongly. In the case of homogeneous nucleation amorphous precursors have been observed [T. Schilling et al., Phys. Rev. Lett. 105(2), 025701 (2010)]. For heterogeneous nucleation we do not find such precursors. The fluid is directly transformed into highly ordered crystallites.

Entropy production in the nonequilibrium steady states of interacting many-body systems

Entropy production is one of the most important characteristics of nonequilibrium steady states. We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of nonequilibrium systems: transport systems and reaction-diffusion systems. The usefulness of the mean entropy production rate and of the large deviation function of the entropy production for characterizing nonequilibrium steady states of interacting many-body systems is discussed. We show that the large deviation function displays a kink-like feature at zero entropy production that is similar to that observed for a single particle driven along a periodic potential. This kink is a direct consequence of the detailed fluctuation theorem fulfilled by the probability distribution of the entropy production and is therefore a generic feature of the corresponding large deviation function.

Dynamical phase transition of a one-dimensional transport process including death.

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection alpha and death of the last particle delta . The system presents a phase transition at deltac(alpha), where the average position of the last particle L grows as sqrt[t]. For delta>deltac, a nonequilibrium stationary state exists while for delta<deltac the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.

Entropy production in nonequilibrium steady states: a different approach and an exactly solvable canonical model.

We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the systems state. This allows us to directly study entropy production in systems with microscopic irreversibility. The two sampling methods are equivalent otherwise, and the fluctuation theorem also holds for the different paths. We focus on a fully irreversible three-state loop, as a canonical model of microscopic irreversibility, finding its entropy distribution, rate of entropy production, and large deviation function in closed analytical form, and showing that the observed kink in the large deviation function arises solely from microscopic irreversibility.

Fluctuation ratios in the absence of microscopic time reversibility.

We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic time reversibility. Studying a quantity that for an equilibrium system is related to the work done to the system, we observe that under certain conditions oscillations appear on top of an exponential behavior of transient fluctuation ratios. We argue that these oscillations encode properties of the probability currents in state space.

Crystallization in glassy suspensions of hard ellipsoids.

We have carried out computer simulations of overcompressed suspensions of hard monodisperse ellipsoids and observed their crystallization dynamics. The system was compressed very rapidly in order to reach the regime of slow, glass-like dynamics. We find that, although particle dynamics become sub-diffusive and the intermediate scattering function clearly develops a shoulder, crystallization proceeds via the usual scenario: nucleation and growth for small supersaturations, spinodal decomposition for large supersaturations. In particular, we compared the mobility of the particles in the regions where crystallization set in with the mobility in the rest of the system. We did not find any signature in the dynamics of the melt that pointed towards the imminent crystallization events.

Characterizing steady-state and transient properties of reaction-diffusion systems.

In the past, the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper, we aim at characterizing the properties of diffusion-limited reactions both in their steady states and out of stationarity. Many reaction-diffusion systems have the peculiarity that microscopic reversibility is broken such that their transient behavior cannot be investigated through the study of most of the observables discussed in the literature. For this reason, we analyze the transient properties of reaction-diffusion systems through a specific work observable that remains well defined even in the absence of microscopic reversibility and that obeys an exact detailed fluctuation relation in cases where detailed balance is fulfilled. We thereby drive the systems out of their nonequilibrium steady states through time-dependent reaction rates. Using a numerical exact method and computer simulations, we analyze fluctuation ratios of the probability distributions obtained during the forward and reversed processes. We show that the underlying microscopic dynamics gives rise to peculiarities in the configuration-space trajectories, thereby, yielding prominent features in the fluctuation ratios.

Work fluctuations in quantum spin chains

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.

Dissipation by a crystallization process

We discuss crystallization as a non-equilibrium process. In a system of hard spheres under compression at a constant rate, we quantify the amount of heat that is dissipated during the crystallization process. We interpret the dissipation as arising from the resistance of the system against phase transformation. An intrinsic compression rate is identified that separates a quasi-static regime from one of rapidly driven crystallization. In the latter regime the system crystallizes more easily, because new relaxation channels are opened, at the cost of forming a higher fraction of non-equilibrium crystal structures. We rationalize the change in crystallization mechanism by analogy with shear thinning, in terms of a kinetic competition between near-equilibrium relaxation and external driving.