Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we...
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Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α)≡dΔ(α)/dα, the first derivative of the optimal gap-to-midgap ratio Δ(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a 1D quarter-wave stack, SQWS(α). Even more surprisingly, the values of S(α) for our disordered networks converge to SQWS(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic heterostructures.
作者:
Wang, HainaTorquato, SalvatoreDepartment of Chemistry
Princeton University PrincetonNJ08544 United States Department of Chemistry
Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States
Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams a...
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Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously 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 capability 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 (URL), 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 (Equation presented)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 (Equation presented)V (k) at small wavenumbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B = (Equation presented)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 f
We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator, assuming equal computational cost for the corresponding fundamental gates. The complexity of ...
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We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator, assuming equal computational cost for the corresponding fundamental gates. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a saturation determined by the UV cutoff and the number of spatial dimensions. We also study the complexity of the unitary evolution of quantum cosmological perturbations in de Sitter space, which can be written as time-dependent squeezing and rotation operators on individual Fourier mode pairs. The complexity of a single mode pair at late times grows linearly with the number of e-folds, while the complexity at early times oscillates rapidly due to the sensitivity of operator complexity to the phase of unitary time evolution. Integrating over all modes, the total complexity of cosmological perturbations scales as the square root of the (exponentially) growing volume of de Sitter space, suggesting that inflation leads to an explosive growth in complexity of the Universe.
The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundar...
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We present Classification of Cluster Galaxy Members (C2-GaMe), a classification algorithm based on a suite of machine learning models that differentiates galaxies into orbiting, infalling, and background (interloper) ...
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Proper consideration of anharmonicity is important for the calculation of thermal conductivity. However, how the anharmonicity influences the thermal conduction in amorphous materials is still an open question. In thi...
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Proper consideration of anharmonicity is important for the calculation of thermal conductivity. However, how the anharmonicity influences the thermal conduction in amorphous materials is still an open question. In this work, we uncover the role of anharmonicity on the thermal conductivity of amorphous silica (a−SiO2) by comparing the thermal conductivity predicted from the harmonic theory and the anharmonic theory. Moreover, we explore the effect of anharmonicity-induced frequency shift on the prediction of thermal conductivity. It is found that the thermal conductivity calculated by the recently developed anharmonic theory (quasi-harmonic Green-Kubo approximation) is higher than that calculated by the harmonic theory developed by Allen and Feldman. The use of anharmonic vibrational frequencies also leads to a higher thermal conductivity compared with that calculated using harmonic vibrational frequencies. The anharmonicity-induced frequency shift is a mechanism for the positive temperature dependence of the thermal conductivity of a−SiO2 at higher temperatures. Further investigation on the mode diffusivity suggests that although anharmonicity has a larger influence on locons than diffusons, the increase in thermal conductivity due to anharmonicity is mainly contributed by the anharmonicity-induced increase of the diffusivity of diffusons. Finally, it is found that the cross-correlations between diffusons and diffusons contribute most to the thermal conductivity of a−SiO2, and the locons contribute to the thermal conductivity mainly through collaboration with diffusons. These results offer new insights into the nature of the thermal conduction in a−SiO2.
A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of no...
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The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at ‘microscales’ to predict physical properties of th...
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The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at ‘microscales’ to predict physical properties of the medium at ‘macroscales’, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, ‘void’ and ‘particle’ nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears ‘hyperuniform’, as a result of primordial density fluctuations, whilst on the smallest scales, the system becomes almost ‘antihyperuniform’, as evidenced by its number variance. Additionally, via a finite scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc = 0.25 in our fiducial analysis compared to ηc = 0.34), with strong dependence on the mean density;this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension
We report precise measurement of the hyperfine splitting and calculation of the Zeeman coefficients of the 171Yb+ ground state. The absolute hyperfine splitting frequency is measured using high-resolution laser-microw...
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We study the dynamics of identical Leaky Integrate-and-Fire (LIF) neurons on a multiplex composed of two ring networks with symmetric nonlocal coupling within each ring and one-to-one connections between rings. We inv...
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