No Arabic abstract
Most theories of homogeneous nucleation are based on a Fokker-Planck-like description of the behavior of the mass of clusters. Here we will show that these approaches are incomplete for a large class of nucleating systems, as they assume the effective dynamics of the clusters to be Markovian, i.e., memoryless. We characterize these non-Markovian dynamics and show how this influences the dynamics of clusters during nucleation. Our results are validated by simulations of a three-dimensional Ising model with locally conserved magnetization.
Recent experiments using fluorescence spectroscopy have been able to probe the dynamics of conformational fluctuations in proteins. The fluctuations are Gaussian but do not decay exponentially, and are therefore, non-Markovian. We present a theory where non-Markovian fluctuation dynamics emerges naturally from the superposition of the Markovian fluctuations of the normal modes of the protein. A Rouse-like dynamics of the normal modes provides very good agreement to the experimentally measured correlation functions. We provide simple scaling arguments rationalising our results.
The persistence exponent theta for the global order parameter, M(t), of a system quenched from the disordered phase to its critical point describes the probability, p(t) sim t^{-theta}, that M(t) does not change sign in the time interval t following the quench. We calculate theta to O(epsilon^2) for model A of critical dynamics (and to order epsilon for model C) and show that at this order M(t) is a non-Markov process. Consequently, theta is a new exponent. The calculation is performed by expanding around a Markov process, using a simplified version of the perturbation theory recently introduced by Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].
The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $ntoinfty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $ntoinfty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.
Non-Markovian dynamics pervades human activity and social networks and it induces memory effects and burstiness in a wide range of processes including inter-event time distributions, duration of interactions in temporal networks and human mobility. Here we propose a non-Markovian Majority-Vote model (NMMV) that introduces non-Markovian effects in the standard (Markovian) Majority-Vote model (SMV). The SMV model is one of the simplest two-state stochastic models for studying opinion dynamics, and displays a continuous order-disorder phase transition at a critical noise. In the NMMV model we assume that the probability that an agent changes state is not only dependent on the majority state of his neighbors but it also depends on his {em age}, i.e. how long the agent has been in his current state. The NMMV model has two regimes: the aging regime implies that the probability that an agent changes state is decreasing with his age, while in the anti-aging regime the probability that an agent changes state is increasing with his age. Interestingly, we find that the critical noise at which we observe the order-disorder phase transition is a non-monotonic function of the rate $beta$ of the aging (anti-aging) process. In particular the critical noise in the aging regime displays a maximum as a function of $beta$ while in the anti-aging regime displays a minimum. This implies that the aging/anti-aging dynamics can retard/anticipate the transition and that there is an optimal rate $beta$ for maximally perturbing the value of the critical noise. The analytical results obtained in the framework of the heterogeneous mean-field approach are validated by extensive numerical simulations on a large variety of network topologies.
The classical Hall effect resulting from the impact of external magnetic and electric fields on the non-Markovian dynamics of charge carriers is studied. The dependence of the tangent of the Hall angle on the magnetic field is derived and compared with the experimental data for Zn. The method is proposed to determine experimentally the memory time in a system.