Classically the kinetic theory for a perfect gas has zero spatial number density correlation between separate points because the particles are independent. But the joint spatial and temporal correlation is non-zero (and easily calculable) because each individual particle moves in a straight line. The same holds for particle flux density correlation. The equivalent 'quantum kinetic theory' correlations are evaluated here via Feynman paths with their direct access to geometry and topology. The calculation is exact, yielding known special functions, but it is quite primitive physically. No heat bath, and no multi-particle statistics are invoked (the gas is thus 'Boltzmann'). Formally it reduces to path analysis of Brownian motion, in fact, of Brownian loops (suitably analytically continued). A check of the results is their correct classical limit. Attention is paid to the all-time-integral of the flux density correlation, with its topological significance. A particle's random path, in the presence of a fixed hypothetical hoop of arbitrary shape, accumulates a random linking number by repeatedly passing through it, positively or negatively. The mean is zero and the mean square is infinite, uninformatively. The interest lies in two separate arbitrary hoops: the linking numbers are correlated, their average product grows linearly, and is calculated from the flux density correlation. For a charged particle this would produce a correlation the induced Ampere magnetic circulation around the hoops.
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in fluctuations at `external drive' time scales. As an example, we consider a class of sandpile models displaying non-trivial correlations. Employing the scaling methods, we demonstrate the computation of spatial correlation by establishing a link between local and global temporal correlations.
The standard kinetic path integral for all spatially closed Brownian paths (loops) of duration t weighted by the product mn is evaluated, where m and n are the linking numbers of the Brownian loop with two arbitrary curves in 3D space. The path integral thus indicates the extent to which these two linking numbers are correlated, ranging from the value zero for far apart curves when it is unlikely that the Brownian loop links with both, to (plus or minus) infinity for nearly coincident curves. The result takes a form that loosely resembles that for the mutual inductance of two current carrying …
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically. At the gelation point, the typical length of paths and cycles, l, scales with the component size k as l ~ k^{1/2}. Dynamic and finite-size scaling laws for the behavior at and near the gelation point are obtained. Finite-size scaling laws are verified using numerical simulations.
We propose an analytic formula for the non-local Fisher information functional, or electronic kinetic correlation term, appearing in the expression of the kinetic density functional. Such an explicit formula is constructed on the basis of well-founded physical arguments and a rigorous mathematical prescription.
A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green's function formalism. The method is applicable to a wide range of correlated initial states described by nonequilibrium statistical thermodynamics. Initial correlations and the real-time evolution are treated by a unified technique employing many-component ``mixed'' Green's functions. The Dyson equation for the mixed Green's function leads to a set of equations for real-time Green's functions and new (cross) components linking initial correlations with dynamical proce…
We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation functions and, at odds with modeling based on Poisson statistics, it is formulated in terms of actual nucleation rate. It is shown that truncation of the series up to second order terms in correlation functions provides a very good approximation of the kinetics. The time evolution of both total amount of growing phase and surface coverage by the new phase have been determined. The theory is applied to desc…
The Kolmogorov-Johnson-Mehl-Avrami model, which is a nucleation and growth poissonian process in space, has been implemented by taking into account spatial correlation among nuclei. This is achieved through a detailed study of a system of distinguishable and correlated dots (nuclei). The probability that no dots be in a region of the space has been evaluated in terms of correlation functions. The theory has been applied to describe nucleation and growth in two dimensions under constant nucleation rate, where correlation among nuclei depends upon the size of the nucleus. We propose a simple for…
A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle distribution function and the mean interaction energy are treated as independent nonequilibrium state parameters. The density operator method is used to derive a kinetic equation in second-order non-Markovian Born approximation and an evolution equation for the nonequilibrium quasi-temperature which is thermodynamically conjugated to the mean interaction en…
Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive numerical simulations of the (1+1)- and (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth system in the presence of temporally correlated noise, and compare our results with previous theoretical predictions and numerical simulations. We find that surface morphologies are obviously affected with long-range temporal correlations, and as the temporal correlation…
The presence of knots has been observed in a small fraction of single-domain proteins and related to their thermodynamic and kinetic properties. The exchanging of identical structural elements, typical of domain-swapped proteins, make such dimers suitable candidates to validate the possibility that mutual entanglement between chains may play a similar role for protein complexes. We suggest that such entanglement is captured by the linking number. This represents, for two closed curves, the number of times that each curve winds around the other. We show that closing the curves is not necessary,…
We derive expressions for the critical density for jamming in a hyper-rhomboid system of arbitrary shape in any dimension for the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models. We find that changing the system's shape without altering its total volume or particle density may induce jamming. We also find a transition between shapes in which the correlation length between jammed particles is infinite, and shapes that have a finite correlation length.
The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimension) and by solving the meanfield dynamical equation of motion for the average magnetization. The temperature variations of hysteretic loss (loop area) and the dynamic correlation have been studied near the transition point. The transition point has been identified as the minimum-correlation point. The hysteretic loss becomes maximum above the transition point. An analytical formulation has been developed to analyse …
A ring-kinetic theory for Vicsek-style models of self-propelled agents is derived from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle pre-collisional correlations and cluster formation which both seem important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small density expansion of the collision operator and derive the first two equations of the BBGKY-hierarchy. An algorithm is presented that numerically solves …
A diagrammatic kinetic theory of density fluctuations in simple dense liquids at long times, described in the preceding paper, is applied to a high density Lennard-Jones liquid to calculate various equilibrium time correlation functions. The calculation starts from the general theory and makes two approximations. 1. The general diagrammatic expression for an irreducible memory kernel is approximated using a one-loop approximation. 2. The generalized Enskog projected propagator, which is required for the calculation, is approximated using a simple kinetic model for the hard sphere memory functi…
If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly oscillating periodic field with enough strength to compete with the spin-spin interaction. By analyzing correlation functions and the distribution of domain lengths both analytically and numerically, we observe nontrivial correlation with more than one length scale at the threshold field strength.
We study the time evolution of the two-dimensional kinetic Ising model in finite systems with a non-conserved order parameter, considering nearest-neighbour interactions on the square lattice with periodic and open boundary conditions. Universal data collapse in spin product correlation functions is observed which, when expressed in rescaled units, is valid across the entire time evolution of the system at all length scales, not just within the time regime usually considered in the dynamical scaling hypothesis. Consequently, beyond rapidly decaying finite size effects, the evolution of correla…
We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining different scaling relationships among the involved critical exponents depending on how far from or close to a critical point the system is. Our scaling arguments are very general and connect local and global magnitudes through several scaling relationships. We expect our results to be applicable in a wide range of systems exhibiting interface kinetic roughe…
Non-local twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which, in the limits n -> 0 (resp. Q -> 1) count the numbers of self-avoiding loops (resp. percolation clusters) surrounding a given point. This yields many results, for example the distribution of the number of percolation clusters which must be crossed to connect a given point to an infinitely distant boundary. These twist operators correspond to (1,2) in the Kac classification of conformal field theory, so that their higher-point correlations, which describe linking numbers around multiple point…
It has been established in nineteen seventies that in nonequilibrium case the pair collisions generate non-zero two-particle correlations which are non-diagonal in momentum space and give the essential contribution to the current fluctuations of hot electrons. It is shown here that this correlations give also a contribution to the collision integral, i.e., to kinetic properties of nonequilibrium gas. The expression for electron energy loss rate P via phonons is re-derived in detail from this point of view. The contribution of the non-diagonal part of the nonequilibrium pair correlator to phono…
In recent work we developed a description of cosmic large scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial Gaussian correlations between particles have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate th…
The dynamics of an asymmetric kinetic Ising model is studied. Two schemes for improving the existing mean-field description are proposed. In the first scheme, we derive the formulas for instantaneous magnetization, equal-time correlation, and time-delayed correlation, considering the correlation between different local fields. To derive the time-delayed correlation, we emphasize that the small correlation assumption adopted in previous work [M. Mézard and J. Sakellariou, J. Stat. Mech., L07001 (2011)] is in fact not required. To confirm the inference efficiency of our method, we perform extens…
We investigate the influences of quantum many-body effects, such as criticality and the existence of factorisation fields, in the thermodynamic cost of establishing a bonding link between two independent quantum spin chains. We provide a physical interpretation of the behavior of irreversible work spent in such process by linking the phenomenology of such quantities to the properties of the spectrum of the system
The melting of ultrathin lubricant film is studied by friction between atomically flat surfaces. The fluctuations of lubricant temperature are taken into account defined by Ornstein-Uhlenbeck process. The phase diagrams and portraits are calculated for the cases of second-order and first-order transitions -- the melting of amorphous and crystalline lubricants. It is shown that in the first case the stick-slip friction domain appears, dividing the regions of dry and sliding friction. In the second case the three stick-slip friction domains arise characterized by transitions between dry, metasta…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or epidemics. After reviewing the assumptions and mean-field type approximations involved in the construction of chemical rate equations for uniform reactant densities, we first discuss spatial clustering in birth-death systems, where non-linearities are introduced through either density-limiting pair reactions, or equivalently via local imposition of finite ca…
We consider the link between fragility and elasticity that follows from analysis of the data for a set of soft-colloid materials consisting of deformable spheres reported by Mattsson et. al., in Nature vol 462, 83 (2009). Fragility index for a soft-colloid is obtained from the density dependence of the long time relaxation near a so-called glass transition point. In addition, we fit data for the high frequency shear modulus for the respective soft-colloid to a corresponding theoretical expression for the same modulus. This expression for the elastic constant is in terms of the corresponding pa…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence of correlations of particle states at initial time, for instance, correlations characterizing the condensed states.
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fix univocally the entropy of the system, which turn out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the rela…
