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Cloaking the underlying long-range order of randomly perturbed lattices

Physical Review E 2020年第3期101卷 032118-032118页

作者： Michael A. Klatt Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then “cloaked” in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ¯. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 106 particles) of disordered hyperuniform point patterns without Bragg peaks.

关键词： Classical statistical mechanics

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Raman spectrum and polarizability of liquid water from deep neural networks

arXiv

引用

arXiv 2020年

作者： Sommers, Grace M. Calegari Andrade, Marcos F. Zhang, Linfeng Wang, Han Car, Roberto Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface, the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for H2O and D2O. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes. Copyright © 2020, The Authors. All rights reserved.

关键词： Liquids

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Tuning cooperative behavior in games with nonlinear opinion dynamics

arXiv

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arXiv 2021年

作者： Park, Shinkyu Bizyaeva, Anastasia Kawakatsu, Mari Franci, Alessio Leonard, Naomi Ehrich Computer Electrical and Mathematical Science and Engineering Division Thuwal23955-6900 Saudi Arabia Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Mathematics Department National Autonomous University of Mexico Mexico City04510 Mexico

We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agent opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others (reciprocity), network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation. Copyright © 2021, The Authors. All rights reserved.

关键词： Bifurcation (mathematics)

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Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems

arXiv

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arXiv 2022年

作者： Chen, Yixiao Zhang, Linfeng Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100084 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We propose a quantum Monte Carlo approach to solve the many-body Schrödinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo, in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation. Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Isotope effects in x-ray absorption spectra of liquid water

arXiv

引用

arXiv 2020年

作者： Zhang, Chunyi Zhang, Linfeng Xu, Jianhang Tang, Fujie Santra, Biswajit Wu, Xifan Department of Physics Temple University PhiladelphiaPA19122 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The isotope effects in x-ray absorption spectra of liquid water are studied by a many-body approach within electron-hole excitation theory. The molecular structures of both light and heavy water are modeled by path-integral molecular dynamics based on the advanced deep-learning technique. The neural network is trained on ab initio data obtained with SCAN density functional theory. The experimentally observed isotope effect in x-ray absorption spectra is reproduced semi-quantitatively in theory. Compared to the spectrum in normal water, the blueshifted and less pronounced pre- and main-edge in heavy water reflect that the heavy water is more structured at short- and intermediate-range of the hydrogen-bond network. In contrast, the isotope effect on the spectrum is negligible at post-edge, which is consistent with the identical long-range ordering in both liquids as observed in the diffraction experiment. Copyright © 2020, The Authors. All rights reserved.

关键词： Heavy water

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Image Recovery from Rotational And Translational Invariants

Image Recovery from Rotational And Translational Invariants

引用

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Nicholas F. Marshall Ti-Yen Lan Tamir Bendory Amit Singer Department of Mathematics Princeton University Princeton NJ USA The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Electrical Engineering Tel Aviv University Tel Aviv Israel

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066322

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotational and translational invariants and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.

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Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids

arXiv

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arXiv 2025年

作者： Chen, Duyu Samajdar, Rhine Jiao, Yang Torquato, Salvatore Materials Research Laboratory University of California Santa BarbaraCA93106 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the Z2 QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a hidden large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally-intensive quantum numerics to confirm their status as true QSLs. © 2025, CC BY-NC-ND.

关键词： Quantum entanglement

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Liquid-liquid transition in water from first principles

arXiv

引用

arXiv 2022年

作者： Gartner, Thomas E. Piaggi, Pablo M. Car, Roberto Panagiotopoulos, Athanassios Z. Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States

A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles. Copyright © 2022, The Authors. All rights reserved.

关键词： Density functional theory

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Viscosity in water from first-principles and deep-neural-network simulations

arXiv

引用

arXiv 2022年

作者： Malosso, Cesare Zhang, Linfeng Car, Roberto Baroni, Stefano Tisi, Davide SISSA - Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States DP Technology Beijing100080 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States CNR Istituto Officina dei Materiali SISSA Unit Trieste34136 Italy

We report on an extensive study of the viscosity of liquid water at near-ambient conditions, performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics (AIMD), based on density-functional theory (DFT). In order to cope with the long simulation times necessary to achieve an acceptable statistical accuracy, our ab initio approach is enhanced with deep-neural-network potentials (NNP). This approach is first validated against AIMD results, obtained by using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and paying careful attention to crucial, yet often overlooked, aspects of the statistical data analysis. Then, we train a second NNP to a dataset generated from the Strongly Constrained and Appropriately Normed (SCAN) functional. Once the error resulting from the imperfect prediction of the melting line is offset by referring the simulated temperature to the theoretical melting one, our SCAN predictions of the shear viscosity of water are in very good agreement with experiments. Copyright © 2022, The Authors. All rights reserved.

关键词： Deep neural networks

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Manifold learning with arbitrary norms

arXiv

引用

arXiv 2020年

作者： Kileel, Joe Moscovich, Amit Zelesko, Nathan Singer, Amit Department of Mathematics Oden Institute University of Texas at Austin United States Department of Statistics and Operations Research Tel-Aviv University Israel Department of Mathematics Brown University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex with each data point and a weighted edge with each pair. Existing theory shows that the Laplacian matrix of the graph converges to the Laplace-Beltrami operator of the data manifold, under the assumption that the pairwise affinities are based on the Euclidean norm. In this paper, we determine the limiting differential operator for graph Laplacians constructed using any norm. Our proof involves an interplay between the second fundamental form of the manifold and the convex geometry of the given norm's unit ball. To demonstrate the potential benefits of non-Euclidean norms in manifold learning, we consider the task of mapping the motion of large molecules with continuous variability. In a numerical simulation we show that a modified Laplacian eigenmaps algorithm, based on the Earthmover's distance, outperforms the classic Euclidean Laplacian eigenmaps, both in terms of computational cost and the sample size needed to recover the intrinsic geometry. Copyright © 2020, The Authors. All rights reserved.

关键词： Mathematical operators

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