Showing papers on "Correlation function (statistical mechanics) published in 2013"

Identification of long-lived clusters and their link to slow dynamics in a model glass former

Abstract: We study the relationship between local structural ordering and dynamical heterogeneities in a model glass-forming liquid, the Wahnstrom mixture. A novel cluster-based approach is used to detect local energy minimum polyhedral clusters and local crystalline environments. A structure-specific time correlation function is then devised to determine their temporal stability. For our system, the lifetime correlation function for icosahedral clusters decays far slower than for those of similarly sized but topologically distinct clusters. Upon cooling, the icosahedra form domains of increasing size and their lifetime increases with the size of the domains. Furthermore, these long-lived domains lower the mobility of neighboring particles. These structured domains show correlations with the slow regions of the dynamical heterogeneities that form on cooling towards the glass transition. Although icosahedral clusters with a particular composition and arrangement of large and small particles are structural elements of the crystal, we find that most icosahedral clusters lack such order in composition and arrangement and thus local crystalline ordering makes only a limited contribution to this process. Finally, we characterize the spatial correlation of the domains of icosahedra by two structural correlation lengths and compare them with the four-point dynamic correlation length. All the length scales increase upon cooling, but in different ways.

Nonclassical Radiation from Thermal Cavities in the Ultrastrong Coupling Regime

Abstract: Thermal or chaotic light sources emit radiation characterized by a slightly enhanced probability of emitting photons in bunches, described by a zero-delay second-order correlation function ${g}^{(2)}(0)=2$. Here we explore photon-coincidence counting statistics of thermal cavities in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. We find that, depending on the system temperature and coupling rate, thermal photons escaping the cavity can display very different statistical behaviors, characterized by second-order correlation functions approaching zero or greatly exceeding two.

Everlasting effect of initial conditions on single-file diffusion.

Abstract: We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one-dimensional channel (a single-file model). In particular, we examine the influence of initial conditions on the dynamics of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamics, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e., a closed system that attains equilibrium independent of the initial state).

Bethe vectors of GL(3)-invariant integrable models

Abstract: We study GL(3)-invariant integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian 𝒴(gl3) on the Bethe vectors are considered. These actions are relevant for the calculation of correlation functions and form factors of local operators of the underlying quantum models.

Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: a systematic analysis of multi-point and multi-time correlations.

Abstract: We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob–Andersen, Wahnstrom, soft-sphere, and network-forming liquids. While the first three models act as fragile liquids exhibiting super-Arrhenius temperature dependence in their relaxation times, the last is a strong glass-former exhibiting Arrhenius behavior. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the four-point correlation function is extended to...

Ising interfaces and free boundary conditions

Abstract: The authors generalize the result of D. Chelkak et al. [C. R., Math., Acad. Sci. Paris 352, No. 2, 157{161 (2014; Zbl 06265643)] to the case when free boundary conditions enter the picture. The proof is related to the rigorous computation of a (dual) boundary conformal eld theory correlation function, which is obtained by using both resent results concerning the boundary correlation functions of the model and existing SLE results for dual models. The result is applied for the conformal invariance of crossing probabilities. Another application is the proof that the collection of the Ising model interfaces converges to the conformal loop ensemble.

On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation

Abstract: Differential operators derived from the explicit or implicit solution of a diffusion equation are widely used for modelling background-error correlations in geophysical applications of variational data assimilation. Key theoretical results underpinning the diffusion method are reviewed. Solutions to the isotropic diffusion problem on both the spherical space and the d-dimensional Euclidean space are considered first. In the correlation functions implied by explicit diffusion are approximately Gaussian, whereas those implied by implicit diffusion belong to the larger class of Matern functions which contains the Gaussian function as a limiting case. The Daley length-scale, defined as where ∇2 is the d-dimensional Laplacian operator and r = |r| is Euclidean distance, is used as a standard parameter for comparing the different isotropic functions c(r). Diffusion on is shown to be well approximated by diffusion on for length-scales of interest. As a result, fundamental parameters that define the correlation model on can be specified using more convenient expressions available on . Anisotropic Gaussian or Matern correlation functions on can be represented by a diffusion operator furnished with a symmetric and positive-definite diffusion tensor. For anisotropic functions c(r), the tensor where ∇ is the d-dimensional gradient operator, is a natural generalization of the (square of) the Daley length-scale for characterizing the spatial scales of the function. Relationships between this tensor, which we call the Daley tensor, and the diffusion tensor of the explicit and implicit diffusion operators are established. Methods to estimate the elements of the local Daley tensor from a sample of simulated background errors are presented and compared in an idealized experiment with spatially varying covariance parameters. Since the number of independent parameters needed to specify the local diffusion tensor is of the order of the total number of grid points N, sampling errors are inherently much smaller than those involved in the order N2 estimation problem of the full correlation function. While the correlation models presented in this paper are general, the discussion is slanted to their application to background-error correlation modelling in ocean data assimilation. Copyright © 2012 Royal Meteorological Society

Revisiting blob theory for DNA diffusivity in slitlike confinement.

Abstract: Blob theory has been widely applied to describe polymer conformations and dynamics in nanoconfinement. In slit confinement, blob theory predicts a scaling exponent of 2/3 for polymer diffusivity as a function of slit height, yet a large body of experimental studies using DNA produce a scaling exponent significantly less than 2/3. In this work, we develop a theory that predicts that this discrepancy occurs because the segment correlation function for a semiflexible chain such as DNA does not follow the Flory exponent for length scales smaller than the persistence length. We show that these short length scale effects contribute significantly to the scaling for the DNA diffusivity, but do not appreciably affect the scalings for static properties. Our theory is fully supported by Monte Carlo simulations, quantitative agreement with DNA experiments, and the results reconcile this outstanding problem for confined polymers.

Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene

Abstract: In this paper, the diffusivity in suspended monolayer graphene at low and high electric fields is investigated. The knowledge of this quantity and its dependence on the electric field is of primary importance not only for the investigation of the electronic transport properties of this material but also for the development of accurate drift-diffusion models. The results have been obtained by means of an ensemble Monte Carlo simulation. For the calculation of the diffusion coefficient, two different methods are considered, one based on the second central moment and the other one based on the Fourier analysis of velocity fluctuations, which are directly related to the noise behaviour at high frequencies. The diffusion coefficient is analyzed considering both parallel and transversal directions with regard to the applied field. Taking into account the importance of degeneracy in this material, the calculations are properly performed by considering an excess electron population obeying a linearized Boltzmann transport equation, which allows studying in an adequate fashion the diffusivity phenomena. The results show the importance of degeneracy effects at very low fields in which transport is mainly dominated by acoustic phonon scattering. Values of the diffusion coefficient larger than 40 000 cm2/Vs are obtained for a carrier concentration equal to 1012 cm−2. The correlation function of instantaneous velocity fluctuation is explained in terms of the wavevector distribution, and their power spectral density is evaluated in the THz range, showing an important dependence on the applied field and being strongly related to microscopic transport processes.

Correlation functions in the prethermalized regime after a quantum quench of a spin chain

Abstract: Results are presented for a two-point correlation function of a spin chain after a quantum quench for an intermediate time regime where inelastic effects are weak. A Callan-Symanzik-like equation for the correlation function is explicitly constructed which is used to show the appearance of three distinct scaling regimes. One is for spatial separations within a light cone, the second is for spatial separations on the light cone, and the third is for spatial separations outside the light cone. In these three regimes, the correlation function is found to decay with power laws with nonequilibrium exponents that differ from those in equilibrium, as well as from those obtained from quenches in a quadratic Luttinger liquid theory. A detailed discussion is presented on how the existence of scaling depends on the properties of the initial state before the quench.

Characterizing Magnetized Turbulence in M51

Abstract: We use previously published high-resolution synchrotron polarization data to perform an angular dispersion analysis with the aim of characterizing magnetized turbulence in M51. We first analyze three distinct regions (the center of the galaxy, and the northwest and southwest spiral arms) and can clearly discern the turbulent correlation length scale from the width of the magnetized turbulent correlation function for two regions and detect the imprint of anisotropy in the turbulence for all three. Furthermore, analyzing the galaxy as a whole allows us to determine a two-dimensional Gaussian model for the magnetized turbulence in M51. We measure the turbulent correlation scales parallel and perpendicular to the local mean magnetic field to be, respectively, δ_ǁ = 98±5 pc and δ_⊥ = 54±3 pc, while the turbulent-to-ordered magnetic field strength ratio is found to be B_t/B_0 = 1.01 ± 0.04. These results are consistent with those of Fletcher et al., who performed a Faraday rotation dispersion analysis of the same data, and our detection of anisotropy is consistent with current magnetized turbulence theories.

Height-Height Correlation Function to Determine Grain Size in Iron Phthalocyanine Thin Films

Abstract: Quasi one-dimensional iron chains are formed in thermally evaporated iron phthalocyanine (FeC32N8H16) thin films on silicon substrates. The chain length is modified by the deposition temperature during growth. Atomic force microscopy images show spherical grains at low deposition temperatures that become highly elongated at high deposition temperatures due to diffusion. The grain distributions are quantitatively characterized with a watershed-based segmentation algorithm and a height-height correlation function. The grain size distributions are found to be characteristically distinct for the α-phase and β-phase samples. The average effective grain size from the distribution is proportional to the correlation length found from the height-height correlation function and grows exponentially with deposition temperature. The long-range roughness and Hurst parameter increase only slightly with the deposition temperature.

Fluctuation and Dissipation at a Quantum Critical Point

Abstract: In non-relativistic field theories, quantum fluctuations give rise to dissipa- tive behaviour even at zero temperature. Here we use holographic methods to explore the dissipative dynamics of massive particles coupled to quantum critical theories. We present analytic expressions for correlation functions and response functions. The be- haviour changes qualitatively as the dynamical exponent passes through z = 2. In particular, for z > 2, the long time dynamics of the particle is independent of its inertial mass.

Periodic ordering of clusters in a one-dimensional lattice model

Abstract: A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J_1 between the first neighbors and repulsion J_2 between the third neighbors. The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J_2/J_1 1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J_2/J_1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J_2/J_1. Based on the exact results, for J_2/J_1>1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9

Internal protein dynamics on ps to μs timescales as studied by multi-frequency (15)N solid-state NMR relaxation.

Abstract: A comprehensive analysis of the dynamics of the SH3 domain of chicken alpha-spectrin is presented, based upon 15N T1 and on- and off-resonance T1ρ relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from 15N–1H dipole–dipole couplings. It is demonstrated that such a multi-frequency approach enables access to motional correlation times spanning about 6 orders of magnitude. We asses the validity of different motional models based upon orientation autocorrelation functions with a different number of motional components. We find that for many residues a “two components” model is not sufficient for a good description of the data and more complicated fitting models must be considered. We show that slow motions with correlation times on the order of 1–10 μs can be determined reliably in spite of rather low apparent amplitudes (below 1 %), and demonstrate that the distribution of the protein backbone mobility along the time scale axis is pronouncedly non-uniform and non-monotonic: two domains of fast (τ 10−6 s) we observe a sharp ~1 order of magnitude decrease of the apparent motional amplitudes. Such a distribution obviously reflects different nature of backbone motions on different time scales, where the slow end may be attributed to weakly populated “excited states.” Surprisingly, our data reveal no clearly evident correlations between secondary structure of the protein and motional parameters. We also could not notice any unambiguous correlations between motions in different time scales along the protein backbone emphasizing the importance of the inter-residue interactions and the cooperative nature of protein dynamics.

Spatiotemporal buildup of the Kondo screening cloud

Abstract: We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the corresponding correlation function has a tail outside the light cone. At T=0 this tail has a power law decay as a function of distance from the impurity, which we interpret as due to initial entanglement in the Fermi sea.

The origin of viscosity as seen through atomic level stress correlation function

Abstract: The atomic level origin of viscosity and of various relaxation times is of primary interest in the field of supercooled liquids and the glass transition. Previously, by starting from the Green-Kubo expression for viscosity and by decomposing it into correlation functions between local atomic level stresses, we showed that there is a connection between shear stress waves and viscosity, and that the range of propagation of shear waves is also the range that is relevant for viscosity. Here, the behavior of the atomic level stress correlation function at different temperatures is discussed in more detail. The comparison of different time scales of the system shows that the long time decay of the stress correlation function (τS) is approximately three times shorter than the long time decay of the intermediate self-scattering function (τα), while the the Maxwell relaxation time (τM) is approximately five times shorter than τα. It is demonstrated how different timescales of the stress correlation function contri...

Influence of surface roughness on the electrical conductivity of semiconducting thin films

Abstract: The Green function solution of the Boltzmann transport equation has been applied in case of no magnetic field by ignoring any volume impurities. Gaussian, exponential and power law models for the surface roughness correlation function have been studied and the results have been compared with the ones obtained by other methods. It has been found that the electrical conductivity σ increases with increasing correlation length l for the first two models, while for the third model σ value is of the same order as the first two models. Therefore we show that the shape of the surface roughness can strongly influence the electrical properties.

Communication: Long-range angular correlations in liquid water.

Abstract: At ambient conditions the intermolecular correlation in liquid water is generally believed to be short ranged as shown in the atomic pair distribution functions (PDFs) obtained from scattering experiments or from theoretical predictions. However, atom-atom PDFs provide only a partial description of the higher dimensional intermolecular correlation function that depends on both the positions and orientations of water molecules. Here we study the atomic PDFs of liquid water as well as the angular correlation function (ACF) using a classical density functional theory. We demonstrate that, different from the PDFs, the ACF exhibits long-range oscillatory decay extending up to tens of molecular diameters. The theoretical predictions are in good agreement with molecular simulations and corroborate recent experimental results from the second harmonic light scattering experiments.

Local order variations in confined hard-sphere fluids.

Abstract: Pair distributions of fluids confined between two surfaces at close distance are of fundamental importance for a variety of physical, chemical, and biological phenomena, such as interactions between macromolecules in solution, surface forces, and diffusion in narrow pores. However, in contrast to bulk fluids, properties of inhomogeneous fluids are seldom studied at the pair-distribution level. Motivated by recent experimental advances in determining anisotropic structure factors of confined fluids, we analyze theoretically the underlying anisotropic pair distributions of the archetypical hard-sphere fluid confined between two parallel hard surfaces using first-principles statistical mechanics of inhomogeneous fluids. For this purpose, we introduce an experimentally accessible ensemble-averaged local density correlation function and study its behavior as a function of confining slit width. Upon increasing the distance between the confining surfaces, we observe an alternating sequence of strongly anisotropic versus more isotropic local order. The latter is due to packing frustration of the spherical particles. This observation highlights the importance of studying inhomogeneous fluids at the pair-distribution level.

Anticorrelations from power-law spectral disorder and conditions for an Anderson transition

Abstract: We resolve an apparent contradiction between numeric and analytic results for one-dimensional disordered systems with power-law spectral correlations. The conflict arises when considering rigorous results that constrain the set of correlation functions yielding metallic states to those with nonzero values in the thermodynamic limit. By analyzing the scaling law for a model correlated disorder that produces a mobility edge, we show that no contradiction exists as the correlation function exhibits strong anticorrelations in the thermodynamic limit. Moreover, the associated scaling function reveals a size-dependent correlation with a smoothening of disorder amplitudes as the system size increases.

Periodic ordering of clusters in a one-dimensional lattice model.

Abstract: A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J1 between the first neighbors and repulsion J2 between the third neighbors. The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J2/J1 1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J2/J1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J2/J1. Based on the exact results, for J2/J1 > 1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9 < J2/J1 < 1/3 the correlation function decays monotonically below certain temperature, whereas above this temperature exponentially damped oscillatory behavior is obtained. Thus, even though macroscopic phase separation is energetically favored and appears for weak repulsion at T = 0, local spatial inhomogeneities appear for finite T. Monte Carlo simulations in canonical ensemble show that specific heat has a maximum for low density ρ that we associate with formation of living clusters, and if the repulsion is strong, another maximum for ρ = 1/2.

Nonlinear active micro-rheology in a glass-forming soft-sphere mixture.

Abstract: We present extensive molecular dynamics computer simulations of a glass-forming Yukawa mixture, investigating the nonlinear response of a single particle that is pulled through the system by a constant force. Structural changes around the pulled particle are analyzed by pair correlation functions, measured in the deeply supercooled state of the system. A regime of intermediate force strengths is found where the structural changes around the pulled particle are small, although its steady-state velocity shows a strong nonlinear response. This nonlinear response regime is characterized by a force-temperature superposition principle of a Peclet number and anisotropic diffusive behavior. In the direction parallel to the force, mean-square displacements show anomalous superdiffusion in the long time limit. We analyze this superdiffusive behavior by means of the van Hove correlation function of the pulled particle. Perpendicular to the force, the driven particle shows diffusive behavior for all considered force strengths and temperatures. We discuss the dynamics perpendicular and parallel to the force in terms of effective temperatures.

Geometrically Based Statistical Model for Polarized Body-Area-Network Channels

Abstract: A new geometry-based channel model is proposed for wide-band polarized body-area-network channels consisting of four propagation modes, ie, cylindrical surface scattering (CSS) for above-ground off-body scattering (BS), BS for body diffracted and on-BS, ground scattering (GS), and line-of-sight A conservation-of-polarization plane methodology is used for the CSS and GS propagation modes For the BS propagation mode, a geometrical theory of diffraction is used and related to CSS The channel cross-polarization discrimination (XPD) and time-frequency correlation function (TF-CF) are derived from the model Comparisons of the XPD and the TF-CF that are obtained from the model (with appropriate physical parameters) and those obtained from wide-band measurements at 13-GHz are in good agreement We observed the GS propagation mode to be the dominant mode in our experiments The azimuth angle of arrival (AAoA) of a ground reflected wave is shown in theory to have a significant effect on the XPD

Statistical properties of swarms of self-propelled particles with repulsions across the order-disorder transition

Abstract: We study dynamic self-organisation and order-disorder transitions in a two-dimensional system of self-propelled particles. Our model is a variation of the Vicsek model, where particles align the motion to their neighbours but repel each other at short distances. We use computer simulations to measure the orientational order parameter for particle velocities as a function of intensity of internal noise or particle density. We show that in addition to the transition to an ordered state on increasing the particle density, as reported previously, there exists a transition into a disordered phase at the higher densities, which can be attributed to the destructive action of the repulsions. We demonstrate that the transition into the ordered phase is accompanied by the onset of algebraic behaviour of the two-point velocity correlation function and by a non-monotonous variation of the velocity relaxation time. The critical exponent for the decay of the velocity correlation function in the ordered phase depends on particle concentration at low densities but assumes a universal value in more dense systems.

Universal Chaotic Scattering on Quantum Graphs

Abstract: We calculate the $S$-matrix correlation function for chaotic scattering on quantum graphs and show that it agrees with that of random-matrix theory. We also calculate all higher $S$-matrix correlation functions in the Ericson regime. These, too, agree with random-matrix theory results as far as the latter are known. We conjecture that our results give a universal description of chaotic scattering.

Application of p-adic analysis to time series

Abstract: Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree--like behavior and is locally constant for some time periods. It is natural to apply this kind of models for the investigation of avalanche processes and punctuated equilibrium as well as fractal-like analysis of time series generated by measurement of pressure in oil wells.

Statistical properties of swarms of self-propelled particles with repulsions across the order-disorder transition

Abstract: We study dynamic self-organisation and order-disorder transitions in a two-dimensional system of self-propelled particles. Our model is a variation of the Vicsek model, where particles align the motion to their neighbours but repel each other at short distances. We use computer simulations to measure the orientational order parameter for particle velocities as a function of intensity of internal noise or particle density. We show that in addition to the transition to an ordered state on increasing the particle density, as reported previously, there exists a transition into a disordered phase at the higher densities, which can be attributed to the destructive action of the repulsions. We demonstrate that the transition into the ordered phase is accompanied by the onset of algebraic behaviour of the two-point velocity correlation function and by a non-monotonous variation of the velocity relaxation time. The critical exponent for the decay of the velocity correlation function in the ordered phase depends on particle concentration at low densities but assumes a universal value in more dense systems.

APPLICATION OF p-ADIC ANALYSIS TO TIME SERIES

Abstract: Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree-like behavior and is locally constant for some time periods. It is natural to apply this kind of models for the investigation of avalanche processes and punctuated equilibrium as well as fractal-like analysis of time series generated by measurement of pressure in oil wells.

Non-Stationary Propagation Model for Scattering Volumes With an Application to the Rural LMS Channel

Abstract: The design of efficient positioning algorithms in navigation satellite systems, like GNSS, operating in land mobile environments demands for detailed models of the radio channel. On the one hand, the models need to accurately describe scattering and shadowing/obstruction caused by vegetation. On the other hand, they have to incorporate the steady change in the propagation constellation due to the receiver displacement. In this paper we propose a model of the non-stationary radio channel in a scenario where a mobile receiver drives past a scattering volume, such as a ball or a cuboid, while the transmitter is elevated, like in satellite positioning applications. Such a volume may represent the canopy of a single tree, the canopies of trees in a grove, or a small forest. Scattering by the volume is characterized by means of multiple point-source scatterers that are assumed to form a marked spatial point process. The system functions of the radio channel are given. An integral form of the time-frequency correlation function of the component in the system functions contributed by the scattering volume is obtained as a direct consequence of Campbell's Theorem. Furthermore, a closed-form approximation of this integral form is derived for time lags corresponding to displacements along the receiver trajectory for which the plane wave assumption holds. The approximation takes into account the steady change in the propagation constellation. The proposed model is validated by means of Monte Carlo simulations and by comparing its prediction capabilities with experimental data in a scenario where a mobile receiver drives past a roadside tree. A good agreement is observed, despite the simplicity of the model.