Density Correlation Function Research Articles

Fourier's law and many-body quantum systems

The topic of this article are transport properties of many-body quantum chains accompanying DMRG-type simulations of the Bose–Hubbard model. To set the stage, we first provide a very brief introduction to many-body quantum theory and tensor network approximations. Transport properties are studied via dynamical density correlation functions, in line with linear response theory. We observe diffusive behavior at “infinite temperature” T → ∞ . Finally, we mention other approaches to study transport, e.g., explicitly imposing a temperature gradient via thermal reservoirs at the boundary. Cet article porte sur les propriétés de transport de chaînes quantiques à n corps en s'accompagnant de simulations de type « groupe de renormalisation de matrice de densité » du modèle de Bose–Hubbard. Pour dresser une vue d'ensemble, nous présentons d'abord une très brève introduction à la théorie quantique à n corps et aux approximations des réseaux de tenseurs. Les propriétés de transport sont étudiées à l'aide de fonctions dynamiques de corrélation de densité, en suivant la théorie de la réponse linéaire. Nous observons un comportement diffusif à « température infinie » T → ∞ . Enfin, nous mentionnons d'autres approches permettant d'étudier le transport, par exemple en imposant explicitement un gradient de température via des réservoirs thermiques aux bords.

Dynamics and density correlations in matter-wave jet emission of a driven condensate

Emission of matter wave jets has been recently observed in a Bose-Einstein condensate confined by a cylindrical box potential, induced by a periodically modulated inter-particle interaction (Nature {\bf 551}, 356 (2017)). In this paper we apply the time-dependent Bogoliubov theory to study the quantum dynamics and the correlation effects observed in this highly non-equilibrium phenomenon. Without any fitting parameter, our theoretical calculations on the number of ejected atoms and the angular density correlations are in excellent quantitative agreement with the experimental measurements. The exponential growth in time of the ejected atoms can be understood in terms of a dynamical instability associated with the modulation of the interaction. We interpret the angular density correlation of the jets as the Hanbury-Brown-Twiss effect between the excited quasi-particles with different angular momenta, and our theory explains the puzzling observation of the asymmetric density correlations between the jets with the same and opposite momenta. Our theory can also identify the main factors that control the height and width of the peaks in the density correlation function, which can be directly verified in future experiments.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts.

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius , packing length p, pair correlation function , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Dipolar Bose gas with three-body interactions in weak disorder

We study effects of weak disorder with Gaussian correlation function on a dipolar Bose gas with three-body interactions using the Hartree-Fock-Bogoliubov theory. Corrections due to quantum, thermal and disorder fluctuations to the condensate depletion, the one-body density correlation function as well as to the equation of state and the ground state energy are properly calculated. We show that the intriguing interplay of the disorder, dipole-dipole interactions and three-body interactions plays a fundamental role in the physics of the system. Interestingly, we find that the three-body interactions release atoms localized in the respective minima of the random potential.

Random sequential adsorption of ellipsoids and spherocylinders

Random sequential adsorption of ellipsoids and spherocylinders is studied in order to find the shape that maximises the mean saturated packing fraction. It was found that for ellipsoids the maximum is reached for axes ratio of 0.7:1:1.6 and is equal to 0.43772±0.00051. For spherocylinders, the highest density was measured for length-to-width ratio of 1.8 and is equal to 0.42515±0.00030. The study of kinetics of packing growth shows that a packing built of more anisotropic objects grows slower. The microstructural properties of the obtained packings are analysed in terms of two-point density and order correlation functions.

Evaluation of factors affecting gully headcut location using summary statistics and the maximum entropy model: Golestan Province, NE Iran

Gully erosion is an important soil degradation process, which under climate changes is projected to increase. Therefore, better understating of factors controlling gully erosion and prediction of gully headcuts' (GHs) location is still highly relevant. This study aimed to examine the spatial distribution of GHs and to assess the importance of pedological (i.e. aggregate stability, organic matter, bulk density, silt, clay, and sand content) and topographical factors (i.e. altitude, slope length, gradient, and aspect) using summary statistics and the maximum entropy (MaxEnt) model. The study was conducted in the loess-covered region of NE Iran. The highly precise data of 287 GHs locations were obtained by extensive fieldwork and the interpretation of UAV images. The spatial distribution of GHs was evaluated by univariate pair correlation function and O-ring statistics. The spatial effect of GHs density controlling factors was assessed by the cumulative density correlation function Cm,K(r). Variable importance was analyzed using the MaxEnt model, which was also for the susceptibility modelling of GHs. The results of univariate tests showed the aggregated distribution of GHs. The Cm,K(r) analyses indicated that the areas characterized by higher values of bulk density, aggregate stability, and organic matter content have lower GHs density, whereas the areas with high silt content and higher slope gradient have higher GHs density. According to the MaxEnt, there is no one single factor responsible for GHs location, but rather the combination of topographical and pedological factors with the predominance of slope gradient (0.86) and silt content (0.57). The MaxEnt modelling of GHs susceptibility has revealed that the best accuracy (0.958) is given when all pedological and topographical factors are used in the model. The susceptibility maps prepared in the study can be used for soil conversation and land use planning and, consequently, for sustainable development in the region.

Optical signatures of Mott-superfluid transition in nitrogen-vacancy centers coupled to photonic crystal cavities

Detecting optical signatures of quantum phase transitions (QPT) in driven-dissipative systems constitutes a new frontier for many-body physics. Here we propose a practical idea to characterize the extensively studied phenomenon of photonic QPT, based on a many-body system composed of nitrogen-vacancy centers embedded individually in photonic crystal cavities, by detecting the critical behaviors of mean photon number, photon fluctuation, photon correlation, and emitted spectrum. Our results bridge these observables to the distinct optical signatures in different quantum phases and serve as good indicators and invaluable tools for studying dynamical properties of dissipative QPT.

Mode-coupling theory for the steady-state dynamics of active Brownian particles.

We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a many-particle evolution equation for the probability distribution of the particles' positions. Second, we use the projection operator technique and a mode-coupling-like factorization approximation to derive an equation of motion for the density correlation function. The nonequilibrium character of the active system manifests itself through the presence of a steady-state correlation function that quantifies spatial correlations of microscopic steady-state currents of the particles. This function determines the dependence of the short-time dynamics on the activity. It also enters into the expression for the memory matrix and thus influences the long-time glassy dynamics.

Electron-phonon cooling power in Anderson insulators

First microscopic theory for electron-phonon energy exchange in Anderson insulators is developed. The major contribution to the cooling power as a function of electron temperature is shown to be directly related to the correlation function of the local density of electron states at small energy difference argument. In Anderson insulators not far from localization transition, this correlation function is strongly enhanced by wave-function's multi-fractality and, additionally, by the presence of Mott's resonant pairs of localized states. The theory we develop explains huge enhancement of the cooling power observed in insulating Indium Oxide films as compared to predictions of the theory previously developed for disordered metals. Our results open the way to predict the conditions appropriate for the observation of Many Body Localization transition those presence in electronic insulators was advocated in the seminal paper by Basko, Aleiner and Altshuler (2006) but have not been convincingly demonstrated yet.

Topological susceptibility and η′ meson mass from Nf=2 lattice QCD at the physical point

In this paper we explore the computation of topological susceptibility and $\eta'$ meson mass in $N_f=2$ flavor QCD using lattice techniques with physical value of the pion mass as well as larger pion mass values. We observe that the physical point can be reached without a significant increase in the statistical noise. The mass of the $\eta'$ meson can be obtained from both fermionic two point functions and topological charge density correlation functions, giving compatible results. With the pion mass dependence of the $\eta'$ mass being flat we arrive at $M_{\eta'}= 772(18)\ \mathrm{MeV}$ without an explicit continuum limit. For the topological susceptibility we observe a linear dependence on $M_\pi^2$, however, with an additional constant stemming from lattice artifacts.

Slow dynamics coupled with cluster formation in ultrasoft-potential glasses.

We numerically investigate the slow dynamics of a binary mixture of ultrasoft particles interacting with the generalized Hertzian potential. If the softness parameter, α, is small, the particles at high densities start penetrating each other, form clusters, and eventually undergo the glass transition. We find multiple cluster-glass phases characterized by a different number of particles per cluster, whose boundary lines are sharply separated by the cluster size. Anomalous logarithmic slow relaxation of the density correlation functions is observed in the vicinity of these glass-glass phase boundaries, which hints the existence of the higher-order dynamical singularities predicted by the mode-coupling theory. Deeply in the cluster glass phases, it is found that the dynamics of a single particle is decoupled from that of the collective fluctuations.

First Principles Calculation of the Entropy of Liquid Aluminum.

The information required to specify a liquid structure equals, in suitable units, its thermodynamic entropy. Hence, an expansion of the entropy in terms of multi-particle correlation functions can be interpreted as a hierarchy of information measures. Utilizing first principles molecular dynamics simulations, we simulate the structure of liquid aluminum to obtain its density, pair and triplet correlation functions, allowing us to approximate the experimentally measured entropy and relate the excess entropy to the information content of the correlation functions. We discuss the accuracy and convergence of the method.

Electron density fluctuations in collisional dusty plasma with variable grain charge

The kinetic theory of electric fluctuations in a collisional weakly ionized dusty plasma is formulated with due regard to the grain charging dynamics. The correlation functions of electron and ion density are obtained by considering their collisions with neutrals described within the Bhatnagar-Gross-Krook model. The electron density correlation spectra in isothermal and nonisothermal plasma are calculated for various values of grain density, grain size, and ion collisionality.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.

Random sequential adsorption of cuboids.

The subject of this study was random sequential adsorption of cuboids of axes length ratio of a : 1 : b for a ∈ [0.3, 1.0] and b ∈ [1.0, 2.0], and the aim of this study was to find a shape that provides the highest packing fraction. The obtained results show that the densest packing fraction is 0.401 87 ± 0.000 97 and is reached for axes ratios near cuboids of 0.75:1:1.30. Kinetics of packing growth was also studied, and it was observed that its power-law character seems not to be governed by the number of cuboid degrees of freedom. The microstructural properties of obtained packings were studied in terms of density correlation function and propagation of orientational ordering.

Structure and solvation thermodynamics of asymmetric poly (acrylic acid)-b-polystyrene polyelectrolyte block copolymer micelle in water: Effect of charge density and chemical composition

Molecular structure and thermodynamic behavior of micelles formed by polyelectrolyte-neutral block copolymer chains, in particular polystyrene-b-poly(acrylic acid) (PS-b-PAA), in salt-free aqueous solution was studied via detailed explicit atomistic molecular dynamics simulations as a function of the copolymer composition (XPS) and the fractional charge (f) of ionizable PAA blocks. Micelle formation occurs via self-aggregation of PS-b-PAA copolymer chains with formation of PS core and PAA corona. The size of the PS core shows power-law dependence with respect to number of PS units per chain with an exponent 0.56 in agreement with scaling relations and experimental observations. The overall size of the micelle increases linearly with XPS. Increase in XPS results in a linear increase in micelle size and change in shape from spherical to prolate. The number of hydrogen bonds, pair correlation functions and various interatomic pair-wise energetic contributions to solvation enthalpy indicate favorable copolymer-water interaction. Micelle solvation is significantly influenced by hydrogen bonding interactions of carboxylic hydrogen atoms with water oxygens. Atom density profiles, solvation enthalpy and correlation functions of copolymer-Na+ ion pairs confirm the existence of micelle in osmotic regime, in agreement with mean-field theory.

A quantum hydrodynamical description for scrambling and many-body chaos

Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated “quantum hydrodynamics,” which is valid at finite ℏ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a “hydrodynamic cloud,” and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a “smoking gun” for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.

Novel 3-D Nonstationary MmWave Massive MIMO Channel Models for 5G High-Speed Train Wireless Communications

In fifth generation (5G) wireless communications, high-speed train (HST) communications is one of the most challenging scenarios. By adopting massive multiple-input multiple-output (MIMO) and millimeter wave (mmWave) technologies into HST communications, the underlying communication system design becomes more challenging and some new channel characteristics have to be studied, such as the non-stationarities in space, time, and frequency domains. This paper proposes a novel three-dimensional space-time-frequency non-stationary mmWave massive MIMO theoretical model, as well as a corresponding simulation model for 5G HST wireless channels based on WINNER II and Saleh–Valenzuela channel models. Cluster evolutions in space, time, and frequency domains are proposed and analyzed to ensure the models’ non-stationarities in three domains. Moreover, based on the proposed channel models, important time-variant channel statistical properties are investigated, such as the time autocorrelation function, space cross-correlation function, delay power spectrum density (PSD), angular PSD, and frequency correlation function. Results indicate that the statistical properties of the simulation model, verified by simulation results, can match well with those of the theoretical model.

Quantum Monte Carlo formalism for dynamical pions and nucleons

In most simulations of nonrelativistic nuclear systems, the wave functions found solving the many-body Schr\"odinger equations describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. In this work we present an alternative quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. We report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two-nucleon sector we show that the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and we fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. We show that the method can be readily applied to light-nuclei.