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The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear many-body system in a Galilean-invariant fashion, thereby avoiding spurious center-of-mass contributions to observables, it is necessary to express these operators with respect to the translational intrinsic frame. Several commonly-encountered operators in nuclear many-body calculations, including the magnetic dipole and electric quadrupole operators (in the impulse approximation) and generators of U(3) and symmetry groups, are bilinear in the coordinates and momenta of the nucleons and, when expressed in intrinsic form, become two-body operators. To work with such operators in a second-quantized many-body calculation, it is necessary to relate three distinct forms: the defining intrinsic-frame expression, an explicitly two-body expression in terms of two-particle relative coordinates, and a decomposition into one-body and separable two-body parts. We establish the relations between these forms, for general (non-scalar and non-isoscalar) operators bilinear in coordinates and momenta. [ABSTRACT FROM AUTHOR]

We study within the many-body Green's function GW and Bethe-Salpeter formalisms the excitation energies of a paradigmatic model dipeptide, focusing on the four lowest-lying local and charge-transfer excitations. Our GW calculations are performed at the self-consistent level, updating first the quasiparticle energies, and further the single-particle wavefunctions within the static Coulomb-hole plus screened-exchange approximation to the GW self-energy operator. Important level crossings, as compared to the starting Kohn-Sham LDA spectrum, are identified. Our final Bethe-Salpeter singlet excitation energies are found to agree, within 0.07 eV, with CASPT2 reference data, except for one charge-transfer state where the discrepancy can be as large as 0.5 eV. Our results agree best with LC-BLYP and CAM-B3LYP calculations with enhanced long-range exchange, with a 0.1 eV mean absolute error. This has been achieved employing a parameter-free formalism applicable to metallic or insulating extended or finite systems. [ABSTRACT FROM AUTHOR]

We present an efficient method for reproducing CCSD(T) (i.e., the coupled-cluster method with single, double and perturbative connected triple excitations) optimized geometries and harmonic vibrational frequencies for molecular clusters with the N-body:Many-body QM:QM technique. In this work, all 1-body through N-body interactions are obtained from CCSD(T) computations, and the higher-order interactions are captured at the MP2 level. The linear expressions from the many-body expansion facilitate a straightforward evaluation of geometrical derivative properties (e.g., gradients and Hessians). For (H2O)n clusters (n = 3-7), optimized structures obtained with the 2-body:Many-body CCSD(T):MP2 method are virtually identical to CCSD(T) optimized geometries. Harmonic vibrational frequencies calculated with this 2-body:Many-body approach differ from CCSD(T) frequencies by at most a few cm-1. These deviations can be systematically reduced by including more terms from the many-body expansion at the CCSD(T) level. Maximum deviations between CCSD(T) and 3-body:Many-body CCSD(T):MP2 frequencies are typically only a few tenths of a cm-1 for the H2O clusters examined in this work. These results are obtained at a fraction of the wall time of the supermolecular CCSD(T) computation, and the approach is well-suited for parallelization on relatively modest computational hardware. [ABSTRACT FROM AUTHOR]

We derive a dynamic Ornstein-Zernike equation for classical fluids undergoing overdamped Brownian motion and driven out of equilibrium. Inhomogeneous two-time correlation functions are obtained from functional differentiation of the one-body density and current with respect to an appropriately chosen external field. Functional calculus leads naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a space- and time-nonlocal power dissipation functional. We propose an excess (over ideal gas) dissipation functional that both generates mode-coupling theory for the two-body correlations and extends dynamical density functional theory for the one-body fields, thus unifying the two approaches. [ABSTRACT FROM AUTHOR]

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems. [ABSTRACT FROM AUTHOR]

We present a mean-field model for the description of transition or noble metal nano-objects interacting with an environment. It includes a potential given by the second-moment approximation to the tight-binding Hamiltonian for metal-metal interactions, and an additional many-body potential that depends on the local atomic coordination for the metal-environment interaction. The model does not refer to a specific type of chemical conditions, but rather provides trends as a function of a limited number of parameters. The capabilities of the model are highlighted by studying the relative stability of semi-infinite gold surfaces of various orientations and formation energies of a restricted set of single-faceted gold nanoparticles. It is shown that, with only two parameters and in a very efficient way, it is able to generate a great variety of stable structures and shapes, as the nature of the environment varies. It is thus expected to account for formation energies of nano-objects of various dimensionalities (surfaces, thin films, nano-rods, nano-wires, nanoparticles, nanoribbons, etc.) according to the environment. [ABSTRACT FROM AUTHOR]

Kohn and Luttinger [Phys. Rev. 118, 41 (1960)] showed that the conventional finite-temperature extension of the second-order many-body perturbation theory had the incorrect zero-temperature limit in metals and, on this basis, argued that the theory was incorrect. We show that this inconsistency arises from the noninclusion of the temperature effect in the energies of the zeroth-order eigenstates of the perturbation theory, which causes not only the Kohn-Luttinger conundrum but also another inconsistency with the zero-temperature many-body perturbation theory, namely, the different rates of divergence of the correlation energy in a homogeneous electron gas (HEG). We propose a renormalized many-body perturbation theory derivable from the finite-temperature extension of the normal-ordered second quantization applied to the denominators of the energy expression, which involves the energies of the zeroth-order states, as well as to the numerators. The renormalized theory is shown to have the correct zero-temperature limit and the same rate of divergence in a HEG as the zero-temperature counterpart, and is, therefore, the correct finite-temperature many-body perturbation theory. [ABSTRACT FROM AUTHOR]

The attosecond, time-resolved X-ray double-quantum-coherence four-wave mixing signals of formamide at the nitrogen and oxygen K-edges are simulated using restricted excitation window time-dependent density functional theory and the excited core hole approximation. These signals, induced by core exciton coupling, are particularly sensitive to the level of treatment of electron correlation, thus providing direct experimental signatures of electron and core-hole many-body effects and a test of electronic structure theories. [ABSTRACT FROM AUTHOR]

High level ab initio investigations on molecular clusters are generally restricted to those of small size essentially due to the nonlinear scaling of corresponding computational cost. Molecular tailoring approach (MTA) is a fragmentation-based method, which offers an economical and efficient route for studying larger clusters. However, due to its approximate nature, the MTA-energies carry some errors vis-à-vis their full calculation counterparts. These errors in the MTA-energies are reduced by grafting the correction at a lower basis set (e.g., 6-31+G(d)) onto a higher basis set (e.g., aug-cc-pvdz or aug-cc-pvtz) calculation at MP2 level of theory. Further, better estimates of energies are obtained by making use of many-body interaction analysis. For this purpose, R-goodness (Rg) parameters for the three- and four-body interactions in a fragmentation scheme are proposed. The procedure employing grafting and many-body analysis has been tested out on molecular clusters of water, benzene, acetylene and carbon dioxide. It is found that for the fragmentation scheme having higher three- and four-body Rg-values, the errors in MTA-grafted energies are reduced typically to ∼0.2 mH at MP2 level calculation. Coupled with the advantage in terms of computational resources and CPU time, the present method opens a possibility of accurate treatment of large molecular clusters. [ABSTRACT FROM AUTHOR]

We study to what extent dielectric nanoparticles prefer to self-assemble into linear chains or into more compact structures. To calculate the Van der Waals (VdW) attraction between the clusters we use the Coupled Dipole Method (CDM), which treats each atom in the nanoparticle as an inducible oscillating point dipole. The VdW attraction then results from the full many-body interactions between the dipoles. For non-capped nanoparticles, we calculate in which configuration the VdW attraction is maximal. We find that in virtually all cases we studied, many-body effects only result in local potential minima at the linear configuration, as opposed to global ones, and that these metastable minima are in most cases rather shallow compared to the thermal energy. In this work, we also compare the CDM results with those from Hamaker-de Boer and Axilrod-Teller theory to investigate the influence of the many-body effects and the accuracy of these two approximate methods. [ABSTRACT FROM AUTHOR]

We present a linear-scaling method based on self-consistent charge non-orthogonal tight-binding. Linear scaling is achieved using a many-body expansion, which is adjusted dynamically to the instantaneous molecular configuration of a liquid. The method is capable of simulating liquids over large length and time scales, and also handles reactions correctly. Benchmarking on typical carbonate electrolytes used in Li-ion batteries displays excellent agreement with results from full tight-binding calculations. The decomposition slightly breaks the Hellmann-Feynman theorem, which is demonstrated by application to water. However, an additional correction also enables dynamical simulation in this case. [ABSTRACT FROM AUTHOR]

In this article, we present the extension of the exchange-hole dipole moment model (XDM) of dispersion interactions to the calculation of two-body and three-body dispersion energy terms to any order, 2l-pole oscillator strengths, and polarizabilities. By using the newly-formulated coefficients, we study the relative importance of the higher-order two-body and the leading non-additive three-body (triple-dipole) interactions in gas-phase as well as in condensed systems. We show that the two-body terms up to R-10, but not the terms of higher-order, are essential in the correct description of the dispersion energy, while there are a number of difficulties related to the choice of the damping function, which precludes the use three-body triple-dipole contributions in XDM. We conclude that further study is required before the three-body term can be used in production XDM density-functional calculations and point out the salient problems regarding its use. [ABSTRACT FROM AUTHOR]

The purpose is to fit an accurate smooth function of the many-body expansion type to a multidimensional large data set using a basis-set type method. By adopting a combined-hyperbolic-inverse-power-representation for the basis, the novel approach is tested in detail for the ground electronic state of tri-hydrogen and hydroperoxyl systems, assuming that their potential energy surfaces are single-sheeted representable. It is also shown that the method can be easily applicable to potential energy curves by considering as prototypes molecular oxygen and the hydroxyl radical. [ABSTRACT FROM AUTHOR]

The purpose is to fit an accurate smooth function of the many-body expansion type to a multidimensional large data set using a basis-set type method. By adopting a combined-hyperbolic-inverse-power-representation for the basis, the novel approach is tested in detail for the ground electronic state of tri-hydrogen and hydroperoxyl systems, assuming that their potential energy surfaces are single-sheeted representable. It is also shown that the method can be easily applicable to potential energy curves by considering as prototypes molecular oxygen and the hydroxyl radical. [ABSTRACT FROM AUTHOR]

We consider the strictly correlated electron (SCE) limit of the fermionic quantum many-body problem in the second-quantized formalism. This limit gives rise to a multimarginal optimal transport (MMOT) problem. Here the marginal state space for our MMOT problem is the binary set { 0, 1}, and the number of marginals is the number L of sites in the model. The costs of storing and computing the exact solution of the MMOT problem both scale exponentially with respect to L. We propose an efficient convex relaxation to the MMOT which can be solved by semidefinite programming (SDP). In particular, the semidefinite constraint is only of size 2L \times 2L. We further prove that the SDP has dual attainment, in spite of the lack of Slater's condition (i.e., the primal SDP does not have any strictly feasible point). In the context of determining the lowest energy of electrons via density functional theory, such dual attainment implies the existence of an effective potential needed to solve a nonlinear Schr\"odinger equation via self-consistent field iteration. We demonstrate the effectiveness of our methods on computing the ground state energy of spinless and spinful Hubbard-type models. Numerical results indicate that our SDP formulation yields comparable results when using the unrelaxed MMOT formulation. We also describe how our relaxation methods generalize to arbitrary MMOT problems with pairwise cost functions. [ABSTRACT FROM AUTHOR]

In the full quantum theory, the energy of a many-body quantum system with a given one-body density is described by the Levy–Lieb functional. It is exact but very complicated to compute. For practical computations, it is useful to introduce the local density approximation that is based on the local energy of constant densities. The aim of this paper is to make a rigorous connection between the Levy–Lieb functional theory and the local density approximation. Our justification is valid for fermionic systems with a general class of smooth short range interaction potentials, in the regime of slowly varying densities. We follow a general approach developed by Lewin, Lieb, and Seiringer for Coulomb potential [M. Lewin et al., Pure Appl. Anal. 2(1), 35–73 (2020)] but avoid using any special properties of the potential including the scaling property and screening effects for the localization of the energy. [ABSTRACT FROM AUTHOR]

This work considers the gravitational N-body problem and introduces global time-renormalization functions that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate time-renormalization. In the new fictitious time \tau, it is then proved that any solution exists for all \tau \in R and that it is uniquely extended as a holomorphic function to a strip of fixed width. As a by-product, a global power series representation of the solutions of the N-body problem is obtained. Notably, our global time-renormalizations remain valid in the limit when one of the masses vanishes. Finally, numerical experiments show the efficiency of the new time-renormalization functions for the numerical integration of some N-body problems with close encounters. [ABSTRACT FROM AUTHOR]

In the present work, projection methods employed to restore the spontaneously broken symmetry in the mean-field approach to many-body problem are reviewed. The symmetry restoration is important to include correlations going beyond the mean-field approximation. Further, in order to cause a direct comparison with the experimental quantities, quantum states must have sharp values of the desired quantum numbers. For Hamiltonian based approaches, projection methods have been developed and applied for restoration of symmetries. Symmetry projected Hartree–Fock–Bogoliubov (HFB) equations have been derived in the Hamiltonian based approach, which have a similar structure to those of bare HFB equations. The explicit expressions for the projected Hartree-Fock (HF) and pairing fields are derived in the present work for a generalized projection operator. Approximations to the projection method, based on the work of Lipkin and Kamlah, are discussed with some technical details. Finally, problems associated in the application of the projection technique to the energy density functional approaches are highlighted. [ABSTRACT FROM AUTHOR]

Here the buckling of inextensible rods due to axial body forces is mapped to 1D, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2D, three simple and physically realizable applications of the mapping are given in detail; the quantum counterparts of these are particle in a box, particle in a delta-function well, and particle in a triangular well. A fourth application examines the buckling counterpart of a quantum many-body problem (in the Hartree approximation). Through a fifth application, given in the form of an exercise, the reader can explore the surprising consequences of adding a second transverse dimension to the rod buckling problem and imposing periodic boundary conditions. [ABSTRACT FROM AUTHOR]

A mathematical model of the early stage of the formation of interstellar clouds resulting from the interaction of oppositely directed cosmic particle flows and evolution of the clouds into planetary systems is proposed. An important role in the evolution is played by mechanical energy dissipation caused mainly by particle collisions. The simulation is based on the classical n-body problem and the Newtonian theory of instantaneous collisions of rigid bodies with a relative velocity recovery factor smaller than unity. The performed computations suggest that this model is applicable in cosmogonic theories of planetary system formation. [ABSTRACT FROM AUTHOR]

We study chaos and Lévy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density |$\mathcal {S}$| and the Lévy flight (LF) index |$\mathcal {L}$|⁠ , that are derived from the Agekyan–Anosova maps and homology radius |$R_{\mathcal {H}}$|⁠. Based on these metrics, we develop detailed procedures to isolate the ergodic interactions and Lévy flight interactions. This enables us to study the three-body lifetime distribution in more detail by decomposing it into the individual distributions from the different kinds of interactions. We observe that ergodic interactions follow an exponential decay distribution similar to that of radioactive decay. Meanwhile, Lévy flight interactions follow a power-law distribution. Lévy flights in fact dominate the tail of the general three-body lifetime distribution, providing conclusive evidence for the speculated connection between power-law tails and Lévy flight interactions. We propose a new physically motivated model for the lifetime distribution of three-body systems and discuss how it can be used to extract information about the underlying ergodic and Lévy flight interactions. We discuss ejection probabilities in three-body systems in the ergodic limit and compare it to previous ergodic formalisms. We introduce a novel mechanism for a three-body relaxation process and discuss its relevance in general three-body systems. [ABSTRACT FROM AUTHOR]

Dynamical mean-field theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered p-spin interactions, we show how to incorporate the mean-field theory of aging within DMFT. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking phase, and cases with an infinite number of slow time-scales, corresponding statically to the full replica symmetry breaking (FRSB) phase. For the former, we show that the effective temperature of the slow degrees of freedom is fixed by requiring critical dynamical behavior on short time-scales, i.e. marginality. For the latter, we find that aging on an infinite number of slow time-scales is governed by a stochastic equation where the clock for dynamical evolution is fixed by the change of the effective temperature, hence obtaining a dynamical derivation of the stochastic equation at the basis of the FRSB phase. Our results extend the realm of the mean-field theory of aging to all situations where DMFT holds. [ABSTRACT FROM AUTHOR]

We study the effects produced by interactions among neutrinos upon extra-galactic neutrino-fluxes. We have assumed a separable type of pair interactions and performed a transformation to a quasi-particle mean field followed by a Tamm–Damcoff diagonalization. In doing so, we have adopted techniques originated in the quantum many-body problem, and adapted them to this specific case. The solutions of the associated eigenvalue problem provide us with energies and amplitudes which are then used to construct the neutrino response functions at finite density and temperature. The formalism is applied to the description of neutrinos produced in a SN environment. [ABSTRACT FROM AUTHOR]

We prove that equally spaced choreographic solutions of a large class of n-body problems, including the classical n-body problem and a subset of quasi-homogeneous n-body problems, have equal masses if the dimension of the space spanned by the point masses is n − 1, n − 2, or, if n is odd, if the dimension is n − 3. If n is even and the dimension is n − 3, then all masses with an odd label are equal and all masses with an even label are equal. Additionally, we prove that the same results hold true for any solution of an n + 1-body problem for which n of the point masses behave like an equally spaced choreography and the n + 1th point mass is fixed at the origin. Furthermore, we deduce that if the curve along which the point masses of a choreography move has an axis of symmetry, the masses have to be equal if n = 3 and that if n = 4, if three of the point masses behave as stated and the fourth mass is fixed at a point, the masses of the first three point masses are all equal. Finally, we prove for the n-body problem in spaces of negative constant Gaussian curvature that if n < 6, n ≠ 4, equally spaced choreographic solutions should have equal masses, and for n = 4, the even labeled masses are equal and the odd labeled masses are equal and that the same holds true for the n-body problem in spaces of positive constant Gaussian curvature, as long as the point masses do not move along a great circle. Additionally, we show that these last two results are also true for any solution to the n + 1-body problem in spaces of negative constant Gaussian curvature and the n + 1-body problem in spaces of positive constant Gaussian curvature, respectively, for the case that n of the point masses behave like an equally spaced choreography and the n + 1 is fixed at a point. [ABSTRACT FROM AUTHOR]

The authors consider non-autonomous N-body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity. Using Ljusternik-Schnirelmann theory, the authors prove the existence of unbounded sequences of critical values for the Lagrangian action corresponding to non-collision periodic solutions. [ABSTRACT FROM AUTHOR]

We investigate via molecular dynamics simulations the propagation of solitons in a two‐dimensional many‐body system characterized by Yukawa interaction potential. The solitons are created in an equilibrated system by the application of electric field pulses. Such pulses generate pairs of solitons, which are characterized by a positive and negative density peak, respectively, and which propagate into opposite directions. At small perturbation, the features propagate with the longitudinal sound speed, from which an increasing deviation is found at higher density perturbations. An external magnetic field is found to block the propagation of the solitons, which can, however, be released upon the termination of the magnetic field and can propagate further into directions that depend on the time of trapping and the magnetic field strength. [ABSTRACT FROM AUTHOR]

We examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-layer quasi-geostrophic model. We consider the special case of N-fold symmetry in which the original system of 4N ordinary differential equations reduces to just two equations for the so-called "equivalent" heton. We perform a qualitative analysis to classify the possible types of vortex motions for the case N = 2. We identify the regions of the parameter space corresponding to unbounded motion and to different types of bounded, or localized, motions. We focus on the properties of localized, in particular periodic, motion. We identify classes of absolute and relative "choreographies" first introduced by Simó ["New families of solutions to the N-body problems," in Proceedings of the European 3rd Congress of Mathematics, Progress in Mathematics Vol. 201, edited by C. Casacuberta, R. M. Miró-Roig, J. Verdera, and S. Xambó-Descamps (Birkhäuser, Basel, Barcelona, 2000), pp. 101–115]. We also study the forms of vortex trajectories occurring for unbounded motion, which are of practical interest due to the associated transport of heat and mass over large distances. [ABSTRACT FROM AUTHOR]

We propose a method to construct a reduced order model with machine learning for unsteady flows. The present machine-learned reduced order model (ML-ROM) is constructed by combining a convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM), which are trained in a sequential manner. First, the CNN-AE is trained using direct numerical simulation (DNS) data so as to map the high-dimensional flow data into low-dimensional latent space. Then, the LSTM is utilized to establish a temporal prediction system for the low-dimensionalized vectors obtained by CNN-AE. As a test case, we consider flows around a bluff body whose shape is defined using a combination of trigonometric functions with random amplitudes. The present ML-ROMs are trained on a set of 80 bluff body shapes and tested on a different set of 20 bluff body shapes not used for training, with both training and test shapes chosen from the same random distribution. The flow fields are confirmed to be well reproduced by the present ML-ROM in terms of various statistics. We also focus on the influence of two main parameters: (1) the latent vector size in the CNN-AE, and (2) the time step size between the mapped vectors used for the LSTM. The present results show that the ML-ROM works well even for unseen shapes of bluff bodies when these parameters are properly chosen, which implies great potential for the present type of ML-ROM to be applied to more complex flows. [ABSTRACT FROM AUTHOR]

We study the quantum mechanical many-body problem of N ≥ 1 non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and K ≥ 0 static nuclei. We model the dynamics of the electrons and their self-generated electromagnetic field with the so-called many-body Maxwell–Pauli equations. Here we construct time global, finite-energy, weak solutions to the many-body Maxwell–Pauli equations under the assumption that the fine structure constant α and the nuclear charges are not too large. The particular assumptions on the size of α and the nuclear charges ensure that we have energetic stability of the many-body Pauli Hamiltonian, i.e., the ground state energy is finite and uniformly bounded below with lower bound independent of the magnetic field and the positions of the nuclei. This work serves as an initial step towards understanding the connection between the energetic stability of matter and the well-posedness of the corresponding dynamical equations. [ABSTRACT FROM AUTHOR]

We prove that for various impurity models, in both classical and quantum settings, the self-energy matrix is a sparse matrix with a sparsity pattern determined by the impurity sites. In the quantum setting, such a sparsity pattern has been known since Feynman. Indeed, it underlies several numerical methods for solving impurity problems, as well as many approaches to more general quantum many-body problems, such as the dynamical mean field theory. The sparsity pattern is easily motivated by a formal perturbative expansion using Feynman diagrams. However, to the extent of our knowledge, a rigorous proof has not appeared in the literature. In the classical setting, analogous considerations lead to a perhaps less known result, i.e., that the precision matrix of a Gibbs measure of a certain kind differs only by a sparse matrix from the precision matrix of a corresponding Gaussian measure. Our argument for this result mainly involves elementary algebraic manipulations and is in particular non-perturbative. Nonetheless, the proof can be robustly adapted to various settings of interest in physics, including quantum systems (both fermionic and bosonic) at zero- and finite-temperature, non-equilibrium systems, and superconducting systems. [ABSTRACT FROM AUTHOR]

Rock breakdown due to diurnal thermal cycling has been hypothesized to drive boulder degradation and regolith production on airless bodies. Numerous studies have invoked its importance in driving landscape evolution, yet morphological features produced by thermal fracture processes have never been definitively observed on an airless body, or any surface where other weathering mechanisms may be ruled out. The Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) mission provides an opportunity to search for evidence of thermal breakdown and assess its significance on asteroid surfaces. Here we show boulder morphologies observed on Bennu that are consistent with terrestrial observations and models of fatigue-driven exfoliation and demonstrate how crack propagation via thermal stress can lead to their development. The rate and expression of this process will vary with asteroid composition and location, influencing how different bodies evolve and their apparent relative surface ages from space weathering and cratering records. In their study, the authors discuss the potential of thermal weathering on airless bodies. As a case study, they use boulder and fracture morphologies on asteroid Bennu. [ABSTRACT FROM AUTHOR]

The properties of the wake generated by a porous body fully immersed in a turbulent boundary layer are experimentally assessed. The body consists of an array of cylinders, with diameter $d$ , covering a circular patch of diameter $D$. For fixed $d$ and $D$ , by increasing the number of cylinders, $N_{c}$ , within the patch, the wake properties are systematically tested under different levels of density ($\unicode[STIX]{x1D719}$   $=$ covered planar area per total surface) and compared to the flow past a solid body of equivalent diameter and height ($H$). Some insights on the complex flow developing in the wake are captured: $\unicode[STIX]{x1D719}$ varying in the range 2 %–24 % results in the flow meandering among the cylinders and bleeding from the top, the sides and the trailing edge of the patch. The interplay between trailing edge and top bleeding prevents wake entrainment, locking the wake longitudinal extent to 5–7 patch diameters, regardless of the density level. Due to the finite body vertical extent, a third shear layer develops from the top of the patch. The interaction between the top shear layer and the lateral ones leads to a mutual alteration, namely a nonlinear growth not captured by the classical mixing layer theory. Nevertheless, on the horizontal plane at the patch mid-height, the mean flow recovers, exhibiting a self-similar decay. Surprisingly, the recovery is well described by the classical planar wake theory and the characteristic scales, namely the maximum velocity deficit and the wake half-width, evolve linearly as proposed by Wygnanski et al. (J. Fluid Mech., vol. 168, 1986, pp. 31–71). [ABSTRACT FROM AUTHOR]

Entanglement helps in understanding diverse phenomena, going from quantifying complexity to classifying phases of matter. Here we study the influence of conservation laws on entanglement growth. Focusing on systems with U(1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of entanglement, as quantified by the Rényi entropy, in lattice systems in any spatial dimension d and for any local Hilbert space dimension q (qudits). We find that the growth depends both on d and q, and is in generic case first linear in time, similarly as for systems without any conservation laws. Exception to this rule are chains of 2-level systems where the dependence is a square-root of time at all times. Predictions are numerically verified by simulations of diffusive Clifford circuits with upto ~ 105 qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems. Entanglement is one of the most fascinating quantum properties, being a resource in quantum computation and an obstacle in classical simulations. The author analyses entanglement growth in terms of purity, and verifies the results by introducing a class of random Clifford circuits that conserve magnetization, finding that for systems with diffusive dynamics that entanglement growth differs depending on the dimension as well as between qubits or qutrits. [ABSTRACT FROM AUTHOR]

Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a "hard" kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a "soft" constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure. Quantum many-body scarring, a peculiar phenomenon whereby a system thermalizes whilst it keeps returning to its initial state during the time evolution, has recently been observed in experiments on arrays of Rydberg atoms. The authors theoretically investigate the spectral properties of three Hamiltonians using a chain of bosons with density-dependent hopping, providing new insight in the phenomenon of many-body quantum scarring. [ABSTRACT FROM AUTHOR]

A new family of high order one-step symplectic integration schemes for separable Hamiltonian systems with Hamiltonians of the form T (p) + U (q) is presented. The new integration methods are defined in terms of an explicitly defined generating function (of the third kind). They are implicit in q (but explicit in p and the internal states), and require the evaluation of the gradients of T(p) and U(q) and the actions of their Hessians on vectors (the later being relatively cheap in the case of many-body problems). A time-symmetric symplectic method is constructed that has order 10 when applied to Hamiltonian systems with quadratic kinetic energy T(p). It is shown by numerical experiments that the new methods have the expected order of convergence. [ABSTRACT FROM AUTHOR]

Introduction: Dental care is an extremely important part of leading a healthy life. Bad oral hygiene can cause many problems in the body, which can lead to painful and harmful diseases. Pregnancy involves complex physical and hormonal changes that have a significant impact on almost every organ system, including the oral cavity. They need to maintain their oral hygiene as any infection in them can transfer to their fetus. Materials and Methods: A questionnaire which consisted of 20 questions was prepared to enhance the knowledge of pregnant women on the aspects of dental health during pregnancy period. The survey was conducted with the help of a digital platform such as survey planet and was transmitted to 100 pregnant women with the help of social media. Results and Discussion: Result shows that 53% of pregnant women are aware of the fact that maintaining proper oral hygiene prevents complications in child development. About 41% knows that the right period of undergoing dental treatment is the second trimester. About 44% agrees that improper oral hygiene leads to premature birth and low birth weight. Conclusion: The obtained results show that majority do not know how to maintain oral hygiene during pregnancy. They also do not know salient facts about oral health during pregnancy. This calls for an awareness program which will impart knowledge to them, for their and their baby's healthy future. [ABSTRACT FROM AUTHOR]

We provide an exact construction of particular Hamitonians on a one-dimensional lattice as matrix product operators, a type of tensor network. Namely, we consider Hamiltonians describing interactions between degrees of freedom at lattice sites whose strength grows with the lattice site separation as a polynomial multiplied by an exponential. We show that the bond dimension is (k + 3) for a polynomial of order k, independent of the system size and the number of particles. Our construction is manifestly translationally invariant, and so may be used in finite- or infinite-size variational matrix product state algorithms. Our results provide new insight into the correlation structure of many-body quantum operators, and may also be practical in simulations of many-body systems whose interactions are exponentially screened at large distances, but may have complex short-distance structure. [ABSTRACT FROM AUTHOR]

The unique‐continuation property from sets of positive measure is here proven for the many‐body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger equation vanishes on a set of positive measure, then it is identically zero. We explicitly consider potentials written as sums of either one‐body or two‐body functions, typical for Hamiltonians in many‐body quantum mechanics. As a special case, we are able to treat atomic and molecular Hamiltonians. The unique‐continuation property plays an important role in density‐functional theories, which underpins its relevance in quantum chemistry. [ABSTRACT FROM AUTHOR]

Purpose: Monte Carlo (MC) simulation of radiation interactions with water medium at physical, physicochemical, and chemical stages, as well as the computation of biologically relevant quantities such as DNA damages, are of critical importance for the understanding of microscopic basis of radiation effects. Due to the large problem size and many‐body simulation problem in the chemical stage, existing CPU‐based computational packages encounter the problem of low computational efficiency. This paper reports our development on a GPU‐based microscopic Monte Carlo simulation tool gMicroMC using advanced GPU‐acceleration techniques. Methods: gMicroMC simulated electron transport in the physical stage using an interaction‐by‐interaction scheme to calculate the initial events generating radicals in water. After the physicochemical stage, initial positions of all radicals were determined. Simulation of radicals' diffusion and reactions in the chemical stage was achieved using a step‐by‐step model using GPU‐accelerated parallelization together with a GPU‐enabled box‐sorting algorithm to reduce the computations of searching for interaction pairs and therefore improve efficiency. A multi‐scale DNA model of the whole lymphocyte cell nucleus containing ~6.2 Gbp of DNA was built. Results: Accuracy of physical stage simulation was demonstrated by computing stopping power and track length. The results agreed with published data and the data produced by GEANT4‐DNA (version 10.3.3) simulations with 10 ‐20% difference in most cases. Difference of yield values of major radiolytic species from GEANT4‐DNA results was within 10%. We computed DNA damages caused by monoenergetic 662 keV photons, approximately representing 137Cs decay. Single‐strand break (SSB) and double‐strand break (DSB) yields were 196 ± 8 SSB/Gy/Gbp and 7.3 ± 0.7 DSB/Gy/Gbp, respectively, which agreed with the result of 188 SSB/Gy/Gbp and 8.4 DSB/Gy/Gbp computed by Hsiao et al. Compared to computation using a single CPU, gMicroMC achieved a speedup factor of ~540x using an NVidia TITAN Xp GPU card. Conclusions: The achieved accuracy and efficiency demonstrated that gMicroMC can facilitate research on microscopic radiation transport simulation and DNA damage calculation. gMicroMC is an open‐source package available to the research community. [ABSTRACT FROM AUTHOR]

Using the motion of accreting particles on to haloes in cosmological N -body simulations, we study the radial phase-space structures of cold dark matter (CDM) haloes. In CDM cosmology, formation of virialized haloes generically produces radial caustics, followed by multistream flows of accreted dark matter inside the haloes. In particular, the radius of the outermost caustic called the splashback radius exhibits a sharp drop in the slope of the density profile. Here, we focus on the multistream structure of CDM haloes inside the splashback radius. To analyse this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting on to the haloes, we count their number of apocentre passages, which is then used to reveal the multistream flows of the dark matter particles. The resultant multistream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that |$\sim \!30{{\ \rm per\ cent}}$| of the simulated haloes satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterize physical properties of the haloes, including the mass accretion rate and the size of the outermost caustic (i.e. the splashback radius). We discuss in detail the correlation of these fitting parameters and other measures directly extracted from the N -body simulation. [ABSTRACT FROM AUTHOR]

A framework to represent and compute two-loop $N$ -point Feynman diagrams as double-integrals is discussed. The integrands are "generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations over these two variables are to be performed numerically, whereas the ingredients involved in the integrands, in particular the "generalised one-loop type" functions, are computed analytically. The idea is illustrated on a few examples of scalar three- and four-point functions. [ABSTRACT FROM AUTHOR]