Showing papers on "Correlation function (statistical mechanics) published in 2017"
20 Nov 2017
TL;DR: In this paper, a generalized Langevin equation with regularized Prabhakar derivative operator is considered and the mean square displacement, time-dependent diffusion coefficient and velocity autocorrelation function are analyzed.
Abstract: We consider a generalized Langevin equation with regularized Prabhakar derivative operator. We analyze the mean square displacement, time-dependent diffusion coefficient and velocity autocorrelation function. We further introduce the so-called tempered regularized Prabhakar derivative and analyze the corresponding generalized Langevin equation with friction term represented through the tempered derivative. Various diffusive behaviors are observed. We show the importance of the three parameter Mittag-Leffler function in the description of anomalous diffusion in complex media. We also give analytical results related to the generalized Langevin equation for a harmonic oscillator with generalized friction. The normalized displacement correlation function shows different behaviors, such as monotonic and non-monotonic decay without zero-crossings, oscillation-like behavior without zero-crossings, critical behavior, and oscillation-like behavior with zero-crossings. These various behaviors appear due to the friction of the complex environment represented by the Mittag-Leffler and tempered Mittag-Leffler memory kernels. Depending on the values of the friction parameters in the system, either diffusion or oscillations dominate.
68 citations
TL;DR: In this article, the relation of particle number cumulants and correlation functions is discussed, and it is argued that measuring couplings of the genuine multiparticle correlation functions could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions.
Abstract: In this paper we discuss the relation of particle number cumulants and correlation functions. It is argued that measuring couplings of the genuine multiparticle correlation functions could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions. We extract integrated multiproton correlation functions from the presently available experimental data on proton cumulants. We find that the STAR data contain significant four-proton correlations, at least at the lower energies, with indication of changing dynamics in central collisions. We also find that these correlations are rather long ranged in rapidity. Finally, using the Ising model, we demonstrate how the signs of the multiproton correlation functions may be used to exclude certain regions of the phase diagram close to the critical point.
58 citations
TL;DR: In this paper, a generalized Langevin equation for a free particle in the presence of a truncated power-law and Mittag-Leffler memory kernel is studied, and it is shown that the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit.
Abstract: We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.
55 citations
TL;DR: In this article, a single ultracold caesium atom is trapped in a periodic potential and measured its diffusion, and the particle-environment interaction is used to fully control motion over a broad range of diffusion constants and timescales.
Abstract: Drawing microscopic information out of the diffusive dynamics of complex processes often requires an assumption of ergodicity. Precision experiments on a single atom in a periodic potential suggest that this may be too simplistic in many cases. Diffusion can be used to infer the microscopic features of a system from the observation of its macroscopic dynamics. Brownian motion accurately describes many diffusive systems, but non-Brownian and nonergodic features are often observed on short timescales. Here, we trap a single ultracold caesium atom in a periodic potential and measure its diffusion1,2,3. We engineer the particle–environment interaction to fully control motion over a broad range of diffusion constants and timescales. We use a powerful stroboscopic imaging method to detect single-particle trajectories and analyse both non-equilibrium diffusion properties and the approach to ergodicity4. Whereas the variance and two-time correlation function exhibit apparent Brownian motion at all times, higher-order correlations reveal strong non-Brownian behaviour. We additionally observe the slow convergence of the exponential displacement distribution to a Gaussian and—unexpectedly—a much slower approach to ergodicity5, in perfect agreement with an analytical continuous-time random-walk model6,7,8. Our experimental system offers an ideal testbed for the detailed investigation of complex diffusion processes.
51 citations
TL;DR: In this article, the correlation functions related to topological phase transitions in inversion-symmetric lattice models described by Dirac Hamiltonians are discussed and the scaling laws that constrain the critical exponents are revealed, and are predicted to be satisfied even in interacting systems.
Abstract: The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\ifmmode\times\else\texttimes\fi{}2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows us to extract a correlation length that diverges at topological phase transitions. The correlation length and the curvature function that defines the topological invariants are shown to have universal critical exponents, allowing the notion of universality classes to be introduced. Particularly in two dimensions, the universality class is determined by the orbital symmetry of the Dirac model. The scaling laws that constrain the critical exponents are revealed, and are predicted to be satisfied even in interacting systems, as demonstrated in an interacting topological Kondo insulator.
47 citations
TL;DR: A stochastic optimization procedure is employed to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest.
Abstract: A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.
45 citations
TL;DR: In this article, the integrability-based quench dynamics of a one-dimensional anyonic gas was studied, and it was shown that the system evolves from an initial state where the local momentum distribution function is nonsymmetric to a steady state where it becomes symmetric.
Abstract: We study the nonequilibrium quench dynamics of a one-dimensional anyonic gas We focus on the integrable anyonic Lieb-Liniger model and consider the quench from noninteracting to hard-core anyons We study the dynamics of the local properties of the system By means of integrability-based methods, we compute analytically the one-body density matrix and the density-density correlation function at all times after the quench and in particular at infinite time Our results show that the system evolves from an initial state where the local momentum distribution function is nonsymmetric to a steady state where it becomes symmetric Furthermore, while the initial momentum distribution functions (and the equilibrium ones) explicitly depend on the anyonic parameter, the final ones do not This is reminiscent of the dynamical fermionization observed in the context of free expansions after release from a confining trap
42 citations
TL;DR: The results reveal that along short links only the intensity correlation function captures the anisotropic information of turbulence, corresponding to the refractive index anisotropy ellipse of atmospheric fluctuations.
Abstract: An experimental study has been performed of a laser beam propagating horizontally through the near-ground atmosphere above a grassy field at the University of Miami (UM) Coral Gables campus. The average intensity, scintillation index, and intensity correlation function are measured in the receiver plane for three channels with different turbulent conditions and at three different heights above the ground. Our results reveal that along short links (210 m) only the intensity correlation function captures the anisotropic information of turbulence, corresponding to the refractive index anisotropy ellipse of atmospheric fluctuations. In addition, we report an interesting phenomenon relating to turbulence eddy orientation near the ground. We confirmed that the experimental results are in agreement with the numerical simulations based on the multiple phase-screen method. Our findings provide an efficient method of determining the anisotropic parameters of atmospheric turbulence.
38 citations
TL;DR: In this article, the authors analyzed the minimum resolvable separation between two points under partially coherent beam illumination and found that the image resolution of two points can overcome the classic Rayleigh diffraction limit through manipulating the correlation function of a partially coherent source.
Abstract: In classical optical imaging, the Rayleigh diffraction limit dR is defined as the minimum resolvable separation between two points under incoherent light illumination. In this paper, we analyze the minimum resolvable separation between two points under partially coherent beam illumination. We find that the image resolution of two points can overcome the classic Rayleigh diffraction limit through manipulating the correlation function of a partially coherent source, and the image resolution, which independent of the specified positions of two points in the object plane, can in principle reach the value of 0.17dR. Furthermore, we carry out an experimental demonstration of sub-Rayleigh imaging of a 1951 USAF resolution target via engineering the correlation function of the illuminating beam. Our experimental results are in agreement with our theoretical predictions.
36 citations
TL;DR: Two ways to analyse two-time correlation functions and the implications for the evaluation of the correlation times and functional shape of the correlations for equilibrium and non-equilibrium systems are discussed.
Abstract: Multi-time correlation functions are especially well suited to study non-equilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.
35 citations
TL;DR: A theoretical prediction for the functional space and time dependence of the velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the Navier-Stokes equation with stochastic forcing is provided.
Abstract: Turbulence is a ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular, deriving the properties of turbulent flows from a mesoscopic description, that is, from the Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the functional space and time dependence of the velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the Navier-Stokes equation with stochastic forcing. This prediction, which goes beyond Kolmogorov theory, is the analytical fixed point solution of nonperturbative renormalization group flow equations, which are exact in the limit of large wave numbers. This solution is compared to two-point two-times correlation functions computed in direct numerical simulations. We obtain a remarkable agreement both in the inertial and in the dissipative ranges.
TL;DR: In this article, the anomalous Hall effect is shown to be sensitive to the correlation properties of the random potential, such as the correlation length, while it remains independent of the integral disorder strength.
Abstract: Both longitudinal and anomalous Hall conductivities are computed in the model of two-dimensional Dirac fermions with a mass in the presence of weak Gaussian spin-independent disorder with an arbitrary correlation function. The anomalous Hall conductivity is shown to be highly sensitive to the correlation properties of the random potential, such as the correlation length, while it remains independent of the integral disorder strength. This property extends beyond the Dirac model making the anomalous Hall effect an interesting tool to probe disorder correlations.
TL;DR: In this paper, the authors consider several cases in the solid state and find that if the real motion is more complex than the assumed model, then model fitting is biased towards correlation times where the relaxation data is most sensitive.
Abstract: Relaxation data in NMR is often used for dynamics analysis, by modeling motion in the sample with a correlation function consisting of one or more decaying exponential terms, each described by an order parameter, and correlation time. This method has its origins in the Lipari-Szabo model-free approach, which originally considered overall tumbling plus one internal motion and was later expanded to several internal motions. We consider several of these cases in the solid state, and find that if the real motion is more complex than the assumed model, then model fitting is biased towards correlation times where the relaxation data is most sensitive. This leads to unexpected distortions in the resulting dynamics description. We propose using dynamics detectors, which each characterize a range of correlation times, and can be used to give an analysis of protein motion without assuming a specific model of the correlation function.
TL;DR: This work establishes a clear link between the microscopic structure of the material and the frequency correlation function of LDOS accessed by a near-field hyperspectral imaging technique and paves a way towards complete control of statistical properties of disordered photonic systems, allowing for designing materials with predefined correlations ofLDOS.
Abstract: We present experimental evidence for the different mechanisms driving the fluctuations of the local density of states (LDOS) in disordered photonic systems. We establish a clear link between the microscopic structure of the material and the frequency correlation function of LDOS accessed by a near-field hyperspectral imaging technique. We show, in particular, that short- and long-range frequency correlations of LDOS are controlled by different physical processes (multiple or single scattering processes, respectively) that can be-to some extent-manipulated independently. We also demonstrate that the single scattering contribution to LDOS fluctuations is sensitive to subwavelength features of the material and, in particular, to the correlation length of its dielectric function. Our work paves a way towards complete control of statistical properties of disordered photonic systems, allowing for designing materials with predefined correlations of LDOS.
26 Sep 2017
TL;DR: In this article, a growing standing density wave and a checkerboard feature in the density-density correlation function were observed in an analog black/white hole pair, consisting of a region of supersonic flow, using an elongated Bose-Einstein condensate.
Abstract: Analog black/white hole pairs, consisting of a region of supersonic flow, have been achieved in a recent experiment by J. Steinhauer using an elongated Bose-Einstein condensate. A growing standing density wave, and a checkerboard feature in the density-density correlation function, were observed in the supersonic region. We model the density-density correlation function, taking into account both quantum fluctuations and the shot-to-shot variation of atom number normally present in ultracold-atom experiments. We find that quantum fluctuations alone produce some, but not all, of the features of the correlation function, whereas atom-number fluctuation alone can produce all the observed features, and agreement is best when both are included. In both cases, the density-density correlation is not intrinsic to the fluctuations, but rather is induced by modulation of the standing wave caused by the fluctuations.
TL;DR: In this article, a number of statistical tests are applied: nearest neighbor analysis, fractal dimension, dipole and quadrupole moments of the distribution function decomposed into spherical harmonics, binomial test, and two point angular correlation function.
Abstract: Gamma-ray bursts (GRBs) were confirmed to be of extragalactic origin due to their isotropic angular distribution, combined with the fact that they exhibited an intensity distribution that deviated strongly from the $-3/2$ power law. This finding was later confirmed with the first redshift, equal to at least $z=0.835$, measured for GRB970508. Despite this result, the data from $CGRO$/BATSE and $Swift$/BAT indicate that long GRBs are indeed distributed isotropically, but the distribution of short GRBs is anisotropic. $Fermi$/GBM has detected 1669 GRBs up to date, and their sky distribution is examined in this paper. A number of statistical tests is applied: nearest neighbour analysis, fractal dimension, dipole and quadrupole moments of the distribution function decomposed into spherical harmonics, binomial test, and the two point angular correlation function. Monte Carlo benchmark testing of each test is performed in order to evaluate its reliability. It is found that short GRBs are distributed anisotropically on the sky, and long ones have an isotropic distribution. The probability that these results are not a chance occurence is equal to at least 99.98\% and 30.68\% for short and long GRBs, respectively. The cosmological context of this finding and its relation to large-scale structures is discussed.
TL;DR: In this article, the authors studied the dependence of multiproton correlation functions and cumulants on the acceptance in rapidity and transverse momentum and found that rapidity correlations which moderately increase with rapidity separation between protons are slightly favored.
Abstract: The dependence of multiproton correlation functions and cumulants on the acceptance in rapidity and transverse momentum is studied. We find that the preliminary data of various cumulant ratios are consistent, within errors, with rapidity and transverse momentum-independent correlation functions. However, rapidity correlations which moderately increase with rapidity separation between protons are slightly favored. We propose to further explore the rapidity dependence of multiparticle correlation functions by measuring the dependence of the integrated reduced correlation functions as a function of the size of the rapidity window.
TL;DR: Direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution.
Abstract: Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. We report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four point space-time intensity correlation function demonstrates a growing dynamic correlation length, $\xi$, upon cooling of the liquid toward the glass transition temperature. $\xi$ as a function of the relaxation time $\tau$ data are in the good agreement with the Adam-Gibbs, inhomogeneous mode coupling theory and random first order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near surface layer with order of magnitude shorter relaxation time than inside the bulk.
TL;DR: A direct procedure for determining the parameters of a discrete harmonic bath modeling the influence of a complex condensed phase environment on the system of interest using directly the classical correlation function as input, avoiding numerical computation of the spectral density by means of an discrete Fourier transform.
Abstract: We present a direct procedure for determining the parameters of a discrete harmonic bath modeling the influence of a complex condensed phase environment on the system of interest. The procedure employs an efficient discretization of the spectral density into modes that correspond to equal fractions of the reorganization energy. The new procedure uses directly the classical correlation function (available from molecular dynamics calculations) as input, avoiding numerical computation of the spectral density by means of a discrete Fourier transform. Convergence is obtained using a shorter time length of the correlation function, leading to significant computational savings. © 2016 Wiley Periodicals, Inc.
TL;DR: Uhrich et al. as mentioned in this paper measured dynamic correlation functions using noninvasive measurement of dynamic correlation function and showed that non-invasive measurements can be more accurate than invasive measurements. But,
Abstract: CITATION: Uhrich, P., et al. 2017. Noninvasive measurement of dynamic correlation functions. Physical Review A, 96(2):022127, doi:10.1103/PhysRevA.96.022127.
TL;DR: The results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.
Abstract: We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales We study in detail the two-point static structure factor at low wave vectors in Fourier space We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor This implies that the direct correlation function is short ranged, as we also demonstrate directly Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior
TL;DR: The relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function is obtained, highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average.
Abstract: In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ^{2}[over ¯]〉∼2D_{ν}t^{β}Δ^{ν-β}, where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x^{2}〉∼t^{ν}, while β≥-1 marks the growth or decline of the kinetic energy 〈v^{2}〉∼t^{β}. Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant D_{ν}. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β=0, the time scaling of 〈δ^{2}[over ¯]〉 and 〈x^{2}〉 are identical; however, the time-averaged transport coefficient D_{ν} is not identical to the corresponding ensemble-averaged diffusion constant.
TL;DR: The overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation, including a long time ballistic one.
Abstract: Via molecular dynamics simulations, we study kinetics in a Vicsek-like phase-separating active matter model. Quantitative results, for isotropic bicontinuous pattern, are presented on the structure, growth, and aging. These are obtained via the two-point equal-time density-density correlation function, the average domain length, and the two-time density autocorrelation function. Both the correlation functions exhibit basic scaling properties, implying self-similarity in the pattern dynamics, for which the average domain size exhibits a power-law growth in time. The equal-time correlation has a short distance behavior that provides reasonable agreement between the corresponding structure factor tail and the Porod law. The autocorrelation decay is a power-law in the average domain size. Apart from these basic similarities, the overall quantitative behavior of the above-mentioned observables is found to be vastly different from those of the corresponding passive limit of the model which also undergoes phase separation. The functional forms of these have been quantified. An exceptionally rapid growth in the active system occurs due to fast coherent motion of the particles, mean-squared-displacements of which exhibit multiple scaling regimes, including a long time ballistic one.
19 Mar 2017
TL;DR: A novel geometrical model for non-wide-sense stationary uncorrelated scattering (non-WSSUS) M2M channels that incorporates variations following a plane wave propagation approach is proposed and a general expression for the four-dimensional TF correlation function (TFCF) of the proposed channel model is derived.
Abstract: This paper aims to characterize the effects that the velocity variations of the mobile stations (MSs) produce on the correlation properties of non-stationary time-frequency (TF) dispersive mobile- to-mobile (M2M) fading channels. Toward that end, we propose a novel geometrical model for non-wide-sense stationary uncorrelated scattering (non-WSSUS) M2M channels that incorporates such variations following a plane wave propagation approach. Capitalizing on the mathematical simplicity of this approach, we derive a general expression for the four-dimensional (4D) TF correlation function (TFCF) of the proposed channel model. From this expression, we analyze the influence of the MSs' acceleration#x002F;deceleration on the channel's correlation properties. Some simulation examples illustrating our findings are presented for the particular case of the geometrical one-ring scattering model. The proposed channel model can be used as a reference to study the performance of emerging vehicular communication systems in safety-threatening scenarios, such as when a MS is forced to break suddenly.
TL;DR: In this article, the amplitudes of the leading oscillating terms in the dimer correlation functions are determined with high accuracy as functions of the exchange anisotropy parameter and the external magnetic field through the combined use of bosonization and density-matrix renormalization-group methods.
Abstract: Correlation functions of dimer operators, the product operators of spins on two adjacent sites, are studied in the spin-$\frac{1}{2}$ XXZ chain in the critical regime. The amplitudes of the leading oscillating terms in the dimer correlation functions are determined with high accuracy as functions of the exchange anisotropy parameter and the external magnetic field through the combined use of bosonization and density-matrix renormalization-group methods. In particular, for the antiferromagnetic Heisenberg model with SU(2) symmetry, logarithmic corrections to the dimer correlations due to the marginally irrelevant operator are studied, and the asymptotic form of the dimer correlation function is obtained. The asymptotic form of the spin-Peierls excitation gap including logarithmic corrections is also derived.
TL;DR: In this article, boundary correlation functions for higher spin gravity duals of O(N) or U(N ) symmetric field theories have been studied and shown to be consistent with propagation through a bulk thermal anti de Sitter space and the emergence of localized black hole like objects in the bulk.
Abstract: Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N ) or U(N ) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at finite temperature and large N phase transitions even at vanishing ’t Hooft coupling. At low temperature, the leading behavior of boundary two-point functions is consistent with propagation through a bulk thermal anti de Sitter space. Above the phase transition, the two-point function shows significant departure from thermal AdS space and the emergence of localized black hole like objects in the bulk. In adjoint models, these objects appear at length scales of order of the AdS radius, consistent with a Hawking-Page transition, but in vector models they are parametrically larger than the AdS scale. In low dimensions, we find another crossover at large distances beyond which the correlation function again takes a thermal AdS form, albeit with a temperature dependent normalization factor.
TL;DR: The zero-temperature spin-boson model for five different cutoff functions of the spectral density is inspected, and the hierarchy equation of motion is reliably extended to each spectral density under investigation.
Abstract: Following a recently proposed decomposition technique [C. R. Duan et al., Phys. Rev. B 95, 214308 (2017)], we inspect the zero-temperature spin-boson model for five different cutoff functions of the spectral density. With oscillatory and non-oscillatory exponentially decaying functions to decompose the bath correlation function, the hierarchy equation of motion is reliably extended to each spectral density under our investigation. The predicted spin dynamics is gradually converged with the increase of the hierarchic expansion order and the number of decomposing basis functions. Our systematic study of different cutoff functions expands previous results of the delocalized-localized phase transition with the exponential and sudden cutoffs in the spectral density.
TL;DR: It is demonstrated that the structure factor, even though it has only pair correlation information of the liquid structure, can shed light on three-body correlations in liquid water through its isothermal pressure derivative term.
Abstract: Despite very significant developments in scattering experiments like X-ray and neutron diffraction, it has been challenging to elucidate the nature of tetrahedral molecular configurations in liquid water. A key question is whether the pair correlation functions, which can be obtained from scattering experiments, are sufficient to describe the tetrahedral ordering of water molecules. In our previous study (Dhabal et al., J. Chem. Phys., 2014, 141, 174504), using data-sets generated from reverse Monte Carlo and molecular dynamics simulations, we showed that the triplet correlation functions contain important information on the tetrahedrality of water in the liquid state. In the present study, X-ray scattering experiments and molecular dynamics (MD) simulations are used to link the isothermal pressure derivative of the structure factor with the triplet correlation functions for water. Triplet functions are determined for water up to 3.3 kbar at 298 K to display the effect of pressure on the water structure. The results suggest that triplet functions ((q)) obtained using a rigid-body TIP4P/2005 water model are consistent with the experimental results. The triplet functions obtained in experiment as well as in simulations evince that in the case of tetrahedral liquids, exertion of higher pressure leads to a better agreement with the Kirkwood superposition approximation (KSA). We further validate this observation using the triplet correlation functions (g(3)(r,s,t)) calculated directly from simulation trajectory, revealing that both (q) in q-space and g(3)(r,s,t) in real-space contain similar information on the tetrahedrality of liquids. This study demonstrates that the structure factor, even though it has only pair correlation information of the liquid structure, can shed light on three-body correlations in liquid water through its isothermal pressure derivative term.
TL;DR: It is shown that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity, and the generality of this scaling theory is confirmed using Monte Carlo simulations of two distinct models of anomalous diffusion.
Abstract: In this Letter, we present a measurement of the phase-space density distribution (PSDD) of ultracold $^{87}\mathrm{Rb}$ atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function ${C}_{xv}(t)$ builds up on a time scale related to the initial conditions of the ensemble and then decays asymptotically as a power law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte Carlo simulations of two distinct models of anomalous diffusion.
TL;DR: In this article, the authors investigated sub-AdS scale locality in a weakly coupled toy model of the AdS3/CFT2 correspondence, and showed that this simple model has the correct density of states at low and high energies to be dual to Einstein gravity coupled to matter in AdS 3.
Abstract: We investigate sub-AdS scale locality in a weakly coupled toy model of the AdS3/CFT2 correspondence. We find that this simple model has the correct density of states at low and high energies to be dual to Einstein gravity coupled to matter in AdS3. The bulk correlation functions also have the correct behavior at leading order in the large N expansion, but deviations appear at order 1/N . We interpret this as evidence for non-locality of the theory, which is consistent with the presence of an infinite tower of massless higher-spin fields. Finally, we conjecture that any large N CFT2 that is both modular invariant, and exhibits the correct low-energy density of states, is dual to a gravitational theory with sub-AdS scale locality.