Many-body Correlation Functions Research Articles

MemHC: An Optimized GPU Memory Management Framework for Accelerating Many-body Correlation

The many-body correlation function is a fundamental computation kernel in modern physics computing applications, e.g., Hadron Contractions in Lattice quantum chromodynamics (QCD). This kernel is both computation and memory intensive, involving a series of tensor contractions, and thus usually runs on accelerators like GPUs. Existing optimizations on many-body correlation mainly focus on individual tensor contractions (e.g., cuBLAS libraries and others). In contrast, this work discovers a new optimization dimension for many-body correlation by exploring the optimization opportunities among tensor contractions. More specifically, it targets general GPU architectures (both NVIDIA and AMD) and optimizes many-body correlation’s memory management by exploiting a set of memory allocation and communication redundancy elimination opportunities: first, GPU memory allocation redundancy : the intermediate output frequently occurs as input in the subsequent calculations; second, CPU-GPU communication redundancy : although all tensors are allocated on both CPU and GPU, many of them are used (and reused) on the GPU side only, and thus, many CPU/GPU communications (like that in existing Unified Memory designs) are unnecessary; third, GPU oversubscription: limited GPU memory size causes oversubscription issues, and existing memory management usually results in near-reuse data eviction, thus incurring extra CPU/GPU memory communications. Targeting these memory optimization opportunities, this article proposes MemHC, an optimized systematic GPU memory management framework that aims to accelerate the calculation of many-body correlation functions utilizing a series of new memory reduction designs. These designs involve optimizations for GPU memory allocation, CPU/GPU memory movement, and GPU memory oversubscription, respectively. More specifically, first, MemHC employs duplication-aware management and lazy release of GPU memories to corresponding host managing for better data reusability. Second, it implements data reorganization and on-demand synchronization to eliminate redundant (or unnecessary) data transfer. Third, MemHC exploits an optimized Least Recently Used (LRU) eviction policy called Pre-Protected LRU to reduce evictions and leverage memory hits. Additionally, MemHC is portable for various platforms including NVIDIA GPUs and AMD GPUs. The evaluation demonstrates that MemHC outperforms unified memory management by \( 2.18\times \) to \( 10.73\times \) . The proposed Pre-Protected LRU policy outperforms the original LRU policy by up to \( 1.36\times \) improvement. 1

Bridging the quartet and pair pictures of isovector proton-neutron pairing

The formal implications of a quartet coherent-state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many-body correlation functions. The intrinsic structure of the quartet coherent state is detailed as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

Many-body correlations from integral geometry.

In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid-state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalization of scaled-particle theory, and we derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory that is particularly suited to the treatment of many-body correlation functions in the hard-sphere liquid, which we demonstrate by numerical tests against simulation.

Theory of resonant Raman scattering: Towards a comprehensive ab initio description

We develop a general, fully quantum mechanical theory of Raman scattering from first principles in terms of many-body correlation functions. In order to arrive at expressions that are practically useful in the context of condensed matter physics, we adopt the Lehmann-Symanzik-Zimmermann reduction formula from high-energy physics and formulate in the modern language of many-body perturbation theory. This enables us to derive a general and practically useful expression for the Raman scattering rate in terms of quantities that can be computed \textit{ab initio}. Our work paves the way toward a comprehensive computational approach to the calculation of Raman spectra that goes beyond the current state of the art by capturing both excitonic and non-adiabatic effects.

Structural and Collective Dynamics of Bi50Zn50 of binary metallic glass

In the present paper, structural properties, collective dynamics and elastic properties have been studied of Bi50Zn50 liquid metallic glass at a wide range of temperatures. Ashcroft and Langreth binary structure factor have been used to study for static structure factor and pair correlation function for present alloy. The collective excitation has been studied for longitudinal and transverses phonon modes based on our well-established model potential along with Hubbard and Beeby (HB) approach. These frequencies are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential. The important ingredients in the present study are the pair-potential and pair-correlation functions. The local field correlation functions due to Hartree (H) and Farid et al (F) are employed to investigate the influence of the screening effects on the vibrational dynamics of Bi50Zn50 liquid metallic glass. The results for bulk modulus (BT), modulus of rigidity (G), Poisson’s ratio (ξ), Young’s modulus (Y), Debye temperature (ƟD), the propagation velocity of elastic waves and dispersion curves are reported. Good agreement with the experiment is observed for the structure factors and elastic properties results are consistent and confirm the applicability of model potential and self-consistent phonon theory for such studies.

Interaction-induced light scattering in thin neon film confined between graphite slabs: MD study

The dynamics of ultrathin neon layer located between parallel graphite walls have been investigated by the classical molecular dynamics simulations. The interaction-induced Rayleigh light scattering spectra of neon layer and the corresponding many-body correlation functions for three layer's thicknesses have been calculated. The calculations have been performed at the constant temperature and for the constant number of neon atoms. The mean square displacement and diffusion coefficient of neon atom in the confined space has been also calculated and discussed. The substantial dependence of the interaction-induced light scattering correlation functions on the separation distance between graphite walls has been observed. Moreover, the structural features of the thin layer have been studied by calculating the neon density profile, perpendicular to the graphite walls. In the innermost region of confined neon layer the increase mobility of neon atoms has been observed.

Molecular theory of solvation: Methodology summary and illustrations

Integral equation theory of molecular liquids based on statistical mechanics is quite promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. Beginning with a molecular interaction potential force field, it uses diagrammatic analysis of the solvation free energy to derive integral equations for correlation functions between molecules in solution in the statistical-mechanical ensemble. The infinite chain of coupled integral equations for many-body correlation functions is reduced to a tractable form for 2- or 3-body correlations by applying the so-called closure relations. Solving these equations produces the solvation structure with accuracy comparable to molecular simulations that have converged but has a critical advantage of readily treating the effects and processes spanning over a large space and slow time scales, by far not feasible for explicit solvent molecular simulations. One of the versions of this formalism, the three-dimensional reference interaction site model (3D-RISM) integral equation complemented with the Kovalenko-Hirata (KH) closure approximation, yields the solvation structure in terms of 3D maps of correlation functions, including density distributions, of solvent interaction sites around a solute (supra)molecule with full consistent account for the effects of chemical functionalities of all species in the solution. The solvation free energy and the subsequent thermodynamics are then obtained at once as a simple integral of the 3D correlation functions by performing thermodynamic integration analytically.

Collision-induced light scattering in a thin xenon layer between graphite slabs – MD study

The collision-induced light scattering many-body correlation functions and their spectra in thin xenon layer located between two parallel graphite slabs have been investigated by molecular dynamics computer simulations. The results have been obtained at three different distances (densities) between graphite slabs. Our simulations show the increased intensity of the interaction-induced light scattering spectra at low frequencies for xenon atoms in confined space, in comparison to the bulk xenon sample. Moreover, we show substantial dependence of the interaction-induced light scattering correlation functions of xenon on the distances between graphite slabs. The dynamics of xenon atoms in a confined space was also investigated by calculating the mean square displacement functions and related diffusion coefficients. The structural property of confined xenon layer was studied by calculating the density profile, perpendicular to the graphite slabs. Building of a fluid phase of xenon in the innermost part of the slot was observed. The nonlinear dependence of xenon diffusion coefficient on the separation distance between graphite slabs has been found.

Depolarised Rayleigh light scattering in argon layer confined between graphite plains: MD simulation

The interaction-induced light scattering many-body correlation functions and their spectra in a thin argon layer located between two parallel graphite walls have been investigated by molecular dynamics simulation method. The calculations have been performed for three different distances between graphite plates. Our simulations show the increased intensity of the interaction-induced light scattering spectra at low frequencies for argon atoms in confined space, in comparison to the bulk (unconfined) sample. Moreover, we show a substantial dependence of the interaction-induced light scattering correlation functions of argon on the distances between graphite walls, that is, on the density of argon layer. The mean square displacement and related diffusion coefficient of argon atom in the confined space has been also investigated. Moreover, the structural feature of the thin layer has been studied by calculating the argon density profile, perpendicular to the graphite walls. An interesting observation is the development of a fluid phase in the innermost region of the confined argon layer.

Study of Collective Modes and Elastic Constants of Zr<sub>57</sub>Ti<sub>5</sub>Cu<sub>20</sub>Ni<sub>8</sub>Al<sub>10</sub> Bulk Metallic Glass

The methodical expressions for the phonon frequencies of Zr57Ti5Cu20Ni8Al10 bulk metallic glass (BMG) both for longitudinal and transverse phonon modes are computed for the first time using Hubbard-Beeby (HB) approach and our well recognized model potential. The self-consistent phonon scheme given by Takeno-Goda, involving multiple scattering and phonon Eigen frequencies expressed in terms of many-body correlation functions of atoms as well as of interatomic potential in the solids, has been used to generate the collective modes in the Zr57Ti5Cu20Ni8Al10 BMG. In the present paper, the local field correction functions due to Hartree (H), Farid et al (F), Sarkar et al (S) and Hubbard Sham (HS) are used to examine the influence of screening effects on the vibrational properties. Further, from the long wavelength limit of phonon frequencies, various elastic constants have been calculated and are found to be in good agreement with experimental and other available data.

Importance of many-body correlations in glass transition: An example from polydisperse hard spheres

Most of the liquid-state theories, including glass-transition theories, are constructed on the basis of two-body density correlations. However, we have recently shown that many-body correlations, in particular, bond orientational correlations, play a key role in both the glass transition and the crystallization transition. Here we show, with numerical simulations of supercooled polydisperse hard spheres systems, that the length-scale associated with any two-point spatial correlation function does not increase toward the glass transition. A growing length-scale is instead revealed by considering many-body correlation functions, such as correlators of orientational order, which follows the length-scale of the dynamic heterogeneities. Despite the growing of crystal-like bond orientational order, we reveal that the stability against crystallization with increasing polydispersity is due to an increasing population of icosahedral arrangements of particles. Our results suggest that, for this type of systems, many-body correlations are a manifestation of the link between the vitrification and the crystallization phenomena. Whether a system is vitrified or crystallized can be controlled by the degree of frustration against crystallization, polydispersity in this case.

Collective Modes and Elastic Constants of Liquid Al83Cu17 Binary Alloy

The collective dynamics (longitudinal and transverse phonon modes) are studied for aluminum-copper (Al-Cu) binary alloy in terms of the eigen-frequencies of the localized collective excitations. The model pseudopotential formalism is employed using a self-consistent phonon scheme by involving multiple scattering and phonon eigen-frequencies. These frequencies are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential. The important ingredients in the present study are the pair-potential and pair-correlation functions. The most recent and sparingly used local field correlation functions are employed to investigate the influence of the screening effects on the vibrational dynamics of non-crystalline Al83Cu17 binary alloy. The results for the elastic constants like bulk modulus BT, rigidity modulus G, Poisson's ratio ζ, Young's modulus Y, Debye temperature θD, propagation velocity of elastic waves and dispersion curves are reported based on the collective modes of this binary alloys. The present results are consistent and confirm the applicability of model potential and self-consistent phonon theory for such studies.

Teleportation-Induced Correlated Quantum Channels

Quantum teleportation of an n-qubit state performed using as an entangled resource a general bipartite state of 2n qubits instead of n Bell states is equivalent to a correlated Pauli channel. This yields a new characterization of such channels in terms of many-body correlation functions of the teleporting media. It provides a relatively simple method for determining whether a correlated quantum channel is able to reliably convey quantum messages by studying the entanglement properties of the teleportation mediating system. Our model is then generalized to the continuous-variable case.

Study of collective dynamics of a non-crystalline aluminum–nickel binary alloy using pseudopotential theory

The phonon dynamics of a transition metal–aluminum alloy, i.e. the Al0.75Ni0.25 binary non-crystalline system, has been studied in terms of the eigenfrequencies of the localized collective excitations using model potential formalism. The self-consistent phonon scheme given by Takeno and Goda, involving multiple scattering and phonon eigenfrequencies that are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential in the solids, has been used to generate the collective modes in the non-crystalline Al0.75Ni0.25 alloy. The pair potential is obtained in Wills Harrison (WH) form from the well-recognized model potential of Ashcroft as a test case. The local field correlation functions due to Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Sarkar et al (S) and Farid (F) are used to investigate the influence of the screening effects on the vibrational properties. Results for the bulk modulus BT are obtained using the aforesaid local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio (σ), Young modulus (Y), propagation velocity of elastic waves and phonon dispersion curves using model potential are reported here and good agreement with available experimental results was achieved.

Many-body correlations versus mode-coupling effects in the dynamics of dense gases

Time dependent contributions due to the triplet and quadruplet correlation functions have been combined with microscopically determined contribution due to the pair correlation function for the transverse stress correlation function. Comparison of the results with simulation data shows that contributions due to two- and three-body static correlation functions are sufficient to understand the viscous dynamics of dense gases. However, close to the triple point, it becomes necessary to include the contribution due to the four-body correlation function. The contribution due to the mode coupling effect has been contrasted with the contribution due to three- and four-body correlation functions. It is noted that the mode coupling contribution plays a similar role as that due to many-body correlation functions.

Realizability issues for iso-g (2) processes

Iso-g (2) processes in the equilibrium regime concern density-dependent interactions that identically cancel the usual density variation of many-body pair correlation functions. This paper considers the formal density expansion for effective pair potentials with this iso-g (2) property, showing how successive terms in that expansion can be determined iteratively. Explicit results through second density order have been obtained for two types of ‘target’ pair correlation functions: (a) a unit step function (hard core), and (b) unity augmented by an origin-centred Gaussian profile with numerical multiplier A. For the unit step function and the −1 ≤ A<0 Gaussian cases, realizability appears to be attainable up to a finite terminal density. However, when the Gaussian A>0, the terminal density diverges to infinity while the effective pair interaction series is non-convergent, though possibly valid as an asymptotic expansion.

Random walk beyond Hartree–Fock

We give a brief discussion of the recently developed Constrained-Path Monte Carlo method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The elimination is accomplished by trading an exact procedure for an approximate one that has been demonstrated to give very accurate estimates of energies and many-body correlation functions. We also give a short review of its applications, a discussion of several strategies for parallelizing it, and some speculation of its future extensions.

Collective modes in Ca70Mg30 glass

The self-consistent phonon scheme given by Takeno and Goda, involving multiple scattering and phonon eigen frequencies which are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential in the solids, has been used to generate the collective modes in the Ca70Mg30 glass. A model potential is proposed to describe the effective interaction in the glass. Three different forms of the local field correction functions viz. Hartree, Taylor and Ichimaru and Utsumi are used to examine relative influence of exchange and correlation effects. The phonon frequencies of the longitudinal and transverse modes are computed employing the theoretical formulation of Hubbard and Beeby. The elastic property of the glassy system is then studied using the long wavelength limits of the phonon modes. The theoretical computations reproduce much better dispersion curves (both for the longitudinal and transverse phonons) compared to earlier reports and are found to be in good agreement with the available experimental results due to neutron scattering.

Interfacial reaction kinetics

We study irreversible A{B reaction kinetics at a xed interface separating two immiscible bulk phases, A and B. Coupled equations are derived for the hierarchy of many-body correlation functions. Postulating physically motivated bounds, closed equations result without the need for ad hoc decoupling approximations. We consider general dynamical exponent z ,w herext t 1=z is the rms diusion distance after time t. At short times the number of reactions per unit area, Rt ,i s2nd order in the far-eld reactant densities n 1 ;n 1 . For spatial dimensions d above a critical value dc = z 1, simple mean eld (MF) kinetics pertain, Rt Qbtn 1 n 1 where Qb is the local reactivity. For low dimensions d Q b (n 1 ) (z (d+1))=d . Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs:Rt xtn 1 . A density depletion hole grows on the more dilute A side. In the symmetric case (n 1 = n 1 ), when d d c fluctuations are unimportant: local mean eld theory applies at the interface (joint density distribution approximating the product of A and B densities) and n s t (1 z)=(2z) . We apply our results to simple molecules (Fickian diusion, z = 2) and to several

From snakes to stars: the statistics of collapsed objects -- I.Lower order clustering properties

The highly non-linear regime of gravitational clustering is characterized by the presence of scale-invariance in the hierarchy of many-body correlation functions. Although the exact nature of this correlation hierarchy can only be obtained by solving the full set of BBGKY equations, useful insights can be obtained by investigating the consequences of a generic scaling ansatz. Extending earlier studies by Bernardeau & Schaeffer, we calculate the detailed consequences of such scaling for the implied behaviour of a number of statistical descriptors, including some new ones, developed to provide useful diagnostics of scale-invariance. We generalize the two-point cumulant correlators (now familiar in the literature) to a hierarchy of multipoint cumulant correlators (MCCs) and introduce the concept of reduced cumulant correlators (RCCs) and their related generating functions. The description of these quantities in diagrammatic form is particularly attractive. We show that every new vertex of the tree representation of higher order correlations has its own reduced cumulant associated with it, and, in the limit of large separations, MCCs of arbitrary order can be expressed in terms of RCCs of the same and lower order. The generating functions for these RCCs are related to the generating functions of the underlying tree vertices for matter distribution. Relating the generating functions of RCCs to the statistics of collapsed objects suggests a scaling ansatz of a very general form for the many-body correlation functions which, in turn, induces a similar hierarchy for the correlation functions of overdense regions. In this vein, we compute the lower order SN parameters and two-point cumulant correlators CNM for overdense regions and study how they vary as a function of the initial power spectrum of primordial density fluctuations. These are especially important results because they are model-independent, at least within the class of models considered here. We also show that our results match those obtained by the extended Press–Schechter formalism (which is based on entirely different arguments) in the limit of large mass.