Accurate prediction for the electronic structure properties of halide perovskites plays a significant role in the design of highly efficient and stable solar cells. While density functional theory (DFT) within the gen...
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We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spect...
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We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spectral components of many-body quantum states systematically with a sophisticated neural network quantum ansatz. CGSP fully exploits the linear unitary nature of the quantum dynamics and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on one-dimensional XXZ models with periodic boundary conditions are carried out to demonstrate the practicality of CGSP.
In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spheri...
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Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctu...
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Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to typical liquids, i.e., the structure factor obeys the scaling relation S(k) ∼ Bkα with B, α > 0 in the limit k → 0. Ground-state d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this work, we systematically address these questions by deriving the analytical small-k behaviors (and associatedly, α and B) of the total and spin-resolved structure factors of quasi-1D, 2D, and 3D electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our work thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple fermionic systems and paves the way for harnessing the unique hyperuniform
The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the gro...
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Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α > 0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wavenumber k ≡ |k| in t...
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Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α > 0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wavenumber k ≡ |k| in the vicinity of the origin, e.g., S(k) ∼ |k|α in cases where S(k) varies continuously with k as k → 0. In this paper, we show that the spreadability is an effective method for determining α for quasiperiodic systems where S(k) is discontinuous and consists of a dense set of Bragg peaks. It has been shown in [Torquato, Phys. Rev. E 104, 054102 (2021)] that, for media with finite α, the long-time behavior of the excess spreadability S(∞) − S(t) can be fit to a power law of the form ∼ t−(d−α)/2, where d is the space dimension, to accurately extract α for the continuous case. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density χ˜V (k) of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract α for the 1D limit-periodic period doubling chain (α = 1) and the 1D quasicrystalline Fibonacci chain (α = 3) to within 0.02% of the analytically known exact results. Moreover, we obtain a value of α = 5.97 ± 0.06 for the 2D Penrose tiling, which had not been computed previously, and present plausible theoretical arguments strongly suggesting that α is exactly equal to 6. We also show that, due to the self-similarity of the structures examined here, one can truncate the small-k region of the scattering information used to compute the spreadability and obtain an accurate value of α, with a small deviation from the untruncated case that decreases as the system size increases. This strongly suggests t
Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k|→0; and stealthy hyperuniform systems have S(k)=0 for the finite range 0<|k|≤K, called the “exclusion ...
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Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k|→0; and stealthy hyperuniform systems have S(k)=0 for the finite range 0<|k|≤K, called the “exclusion region.” Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing S(k) in the exclusion region is computationally intensive as the system size becomes large. In this paper, we present an improved methodology to generate such states using double-double precision calculations on graphical processing units (GPUs) that reduces the deviations from zero within the exclusion region by a factor of approximately 1030 for system sizes more than an order of magnitude larger. We further show that this ultrahigh accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small.
Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and...
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作者：
Haina WangSalvatore TorquatoDepartment of Chemistry
Princeton University Princeton New Jersey 08544 USA Department of Chemistry
Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA
Time-dependent interphase diffusion processes in multiphase heterogeneous media are ubiquitous phenomena in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, f...
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Time-dependent interphase diffusion processes in multiphase heterogeneous media are ubiquitous phenomena in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams, and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capacity of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from “perfect glasses,” uniformly randomized lattices (URLs), disordered stealthy hyperuniform point processes, and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate-, and long-time behaviors of S(t) sensitively capture the small-, intermediate-, and large-scale characteristics of the models. In instances in which the spectral density χ~V(k) has a power-law form B|k|α in the limit |k|→0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in χ~V(k) at small wave numbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B=χ~V(0). Interestingly, the excess spreadability S(∞)−S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time for this transition has a logarithmic divergence in th
Induction-transduction of activating-deactivating points are fundamental mechanisms of action that underlie innumerable systems and phenomena, mathematical, natural, and anthropogenic, and can exhibit complex behavior...
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