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...
详细信息
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 ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different Ansätze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs=37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.
The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family o...
详细信息
Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memb...
详细信息
Multilevel Monte Carlo (MLMC) has become an important methodology in appliedmathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of...
详细信息
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...
详细信息
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.
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 ...
详细信息
We solve Poisson’s equation by combining a spectral-element method with a mapped infinite-element method. We focus on problems in geostatics and geodynamics, where Earth’s gravitational field is determined by Poisso...
详细信息
Composite materials are ideally suited to achieve multifunctionality since the best features of different materials can be combined to form a new material that has a broad spectrum of desired properties. Nature’s ult...
详细信息
Composite materials are ideally suited to achieve multifunctionality since the best features of different materials can be combined to form a new material that has a broad spectrum of desired properties. Nature’s ultimate multifunctional composites are biological materials. There are presently no simple examples that rigorously demonstrate the effect of competing property demands on composite microstructures. To illustrate the fascinating types of microstructures that can arise in multifunctional optimization, we maximize the simultaneous transport of heat and electricity in three-dimensional, two-phase composites using rigorous optimization techniques. Interestingly, we discover that the optimal three-dimensional structures are bicontinuous triply periodic minimal surfaces.
In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph sign...
详细信息
暂无评论