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Physical review
American Physical Society
Physical review

American Physical Society

2470-0045

Physical review/Journal Physical review
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    Coherence of oscillations in the weak-noise limit

    Benedikt RemleinVolker WeissmannUdo Seifert
    12页
    查看更多>>摘要：In a noisy environment, oscillations lose their coherence, which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional potential analytically in the weak-noise limit. With this expression, we can prove for this continuum model the analog of an upper bound that has been conjectured for the coherence of oscillations in discrete Markov network models. We show that our approach can also be adapted to motion along a noisy two-dimensional limit cycle. Specifically, we apply our scheme to the noisy Stuart-Landau oscillator and the thermodynamically consistent Brusselator as a simple model for a chemical clock. Our approach thus complements the fairly sophisticated extant general framework based on techniques from Hamilton-Jacobi theory with which we compare our results numerically.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Noise correction of large deviations with anomalous scaling

    Daniel NickelsenHugo Touchette
    13页
    查看更多>>摘要：We present a path integral calculation of the probability distribution associated with the time-integrated moments of the Ornstein-Uhlenbeck process that includes the Gaussian prefactor in addition to the dominant path or instanton term obtained in the low-noise limit. The instanton term was obtained recently [D. Nickelsen and H. Touchette, Phys. Rev. Lett. 121, 090602 (2018)] and shows that the large deviations of the time-integrated moments are anomalous in the sense that the logarithm of their distribution scales nonlinearly with the integration time. The Gaussian prefactor gives a correction to the low-noise approximation and leads us to define an instanton variance giving some insights as to how anomalous large deviations are created in time. The results are compared with simulations based on importance sampling, extending our previous results based on direct Monte Carlo simulations. We conclude by explaining why many of the standard analytical and numerical methods of large deviation theory fail in the case of anomalous large deviations.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Active random walks in one and two dimensions

    Stephy JoseDipanjan MandalMustansir BarmaKabir Ramola...
    15页
    查看更多>>摘要：We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the lattice in one and two dimensions and derive exact results in the continuum limit. Next, we compute the large deviation free-energy function in both one and two dimensions, which we use to compute the moments and the cumulants of the displacements exactly at late times. Our exact results demonstrate that the cross-correlations between the motion in the x and y directions in two dimensions persist in the large deviation function. We also demonstrate that the large deviation function of an active particle with diffusion displays two regimes, with differing diffusive behaviors. We verify our analytic results with kinetic Monte Carlo simulations of an active lattice walker in one and two dimensions.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Complete visitation statistics of one-dimensional random walks

    Léo RégnierMaxim DolgushevS. RednerOlivier Bénichou...
    15页
    查看更多>>摘要：We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that n_1, n_2, n_3, . . . distinct sites are visited at times t_1, t_a, t3, . . .. From this multiple-time distribution, we show that the visitation statistics of one-dimensional random walks are temporally correlated, and we quantify the non-Markovian nature of the process.We exploit these ideas to derive unexpected results for the two-time trapping problem and to determine the visitation statistics of two important stochastic processes, the run-and-tumble particle and the biased random walk.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Space and time correlations for diffusion models with prompt and delayed birth-and-death events

    Théophile BonnetDavide MancusiAndrea Zoia
    22页
    查看更多>>摘要：Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors and the analysis of epidemic patterns. Previous investigations of the critical regime, where births and deaths balance on average, have shown that highly non-Poissonian fluctuations might occur in the population, leading to spontaneous spatial clustering, and eventually to a "critical catastrophe," where fluctuations can result in the extinction of the population. A milder behavior is observed when the population size is kept constant: the fluctuations asymptotically level off and the critical catastrophe is averted. In this paper, we extend these results by considering the broader class of models with prompt and delayed birth-and-death events, which mimic the presence of precursors in nuclear reactor physics or incubation in epidemics. We consider models with and without population control mechanisms. Analytical or semi-analytical results for the density, the two-point correlation function, and the mean-squared pair distance will be derived and compared with Monte Carlo simulations, which will be used as a reference.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Scattering signatures of invasion percolation

    Pierre-Etienne WolfJean-Christian Anglès d'Auriac
    19页
    查看更多>>摘要：Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three-dimensional cubic lattice. Individual clusters of given size are shown to present a fractal structure up to a scale of order of their extent, even far away from the percolation threshold p_c. The influence of intercluster correlations on the structure factor of assemblies of clusters selected by an invasion phenomenon is studied in detail. For invasion from bulk germs, we show that the scattering properties are determined by three length scales, the correlation length ξ , the average distance between germs dg, and the spatial scale probed by scattering, set by the inverse of the scattering wave vector Q. At small scales, we find that the fractal structure of individual clusters is retained, the structure factor decaying as Q~(-d)_f . At large scales, the structure factor tends to a limit, set by the smaller of ξ and d_g, both below and above pc. We propose approximate expressions reproducing the simulated structure factor for arbitrary ξ , d_g, and Q, and illustrate how they can be used to avoid to resort to costly numerical simulations. For invasion from surfaces, we find that, at p_c, the structure factor behaves as Q~(-d)_f at all Q, i.e., the fractal structure is retained at arbitrarily large scales. Results away from pc are compared to the case of bulk germs. Our results can be applied to discuss light or neutrons scattering experiments on percolating systems. This is illustrated in the context of evaporation from porous materials.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Brownian motion with time-dependent friction and single-particle dynamics in liquids

    Kirit N. LadMargi K. PatelArun Pratap
    13页
    查看更多>>摘要：A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Generalized statistical mechanics of stellar systems

    Kamel Ourabah
    10页
    查看更多>>摘要：The observed distributions of stellar parameters, in particular, rotational and radial velocities, often depart from the Maxwellian (Gaussian) distribution. In the absence of a consistent statistical framework, these distributions are, in general, accounted for phenomenologically by employing power-law distributions, such as Tsallis or Kaniadakis distributions. Here we argue that the observed distributions correspond to locally Gaussian distributions, whose characteristic width is regarded as a statistical variable, in accordance with common knowledge that this parameter is mass dependent. The distributions arising within this picture correspond to superstatistics—a formalism emerging naturally in the context of self-gravitating media. We discuss in detail the distributions arising within this formalism and confront them with observational data of open clusters. We compute their moments and show that the Chandrasekhar-Münch relation remains invariant in this scenario.We also address the effect of these distributions on the thermalization of a massive body, e.g., a supermassive black hole, immersed in a stellar gas. We further discuss how the superstatistical picture clarifies certain ambiguities while offering a whole family of distributions (of which asymptotic power laws represent a special case), opening possibilities for fitting observational data.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Effects of structural inhomogeneity on equilibration processes in Langevin dynamics

    Omid MozafarColin Denniston
    10页
    查看更多>>摘要：In recent decades, computer experiments have led to an accurate and fundamental understanding of atomic and molecular mechanisms in fluids, such as different kinds of relaxation processes toward steady physical states. In this paper, we investigate how exactly the configuration of initial states in a molecular-dynamics simulation can affect the rates of decay toward equilibrium for the widely known Langevin canonical ensemble. For this purpose, we derive an original expression relating the system relaxation time τsys and the radial distribution function g(r) in the near-zero and high-density limit. We found that, for an initial state which is slightly marginally inhomogeneous in the number density of atoms, the system relaxation time τsys is much longer than that for the homogeneous case and an increasing function of the Langevin coupling constant, γ . We also found, during structural equilibration, g(r) at large distances approaches 1 from above for the inhomogeneous case and from below for the macroscopically homogeneous one.
      原文链接:
    • NSTL
    • Amer Physical Soc

    Linked cluster expansions via hypergraph decompositions

    Matthias MühlhauserKai Phillip Schmidt
    11页
    查看更多>>摘要：We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced K?nig representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.
      原文链接:
    • NSTL
    • Amer Physical Soc