Related papers: Non-linear and non-empirical double hybrid density…
Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of…
Remarkable achievements have been attained by deep neural networks in various applications. However, the increasing depth and width of such models also lead to explosive growth in both storage and computation, which has restricted the…
This study presents a systematic machine learning approach for creating efficient hybrid models and discovering sorption uptake models in non-linear advection-diffusion-sorption systems. It demonstrates an effective method to train these…
Multi-Layer Perceptrons (MLPs) rely on pre-defined, fixed activation functions, imposing a static inductive bias that forces the network to approximate complex topologies solely through increased depth and width. Kolmogorov-Arnold Networks…
In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we compared two Kohn-Sham density functionals based on physical modelling and theory with the best density-functional power-series fits in the…
The adiabatic connection curve of density functional theory (DFT) is accurately calculated beyond the physical interaction strength for Hooke's atom, two interacting electrons in a harmonic well potential. Extrapolation of the accurate…
Deep convolutional neural networks (DCNN) have enjoyed great successes in many signal processing applications because they can learn complex, non-linear causal relationships from input to output. In this light, DCNNs are well suited for the…
In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…
We systematically characterize the dynamical evolution of time-parity (PT )-symmetric two-level systems with spin-dependent dissipations. If the control parameters of the gap are linearly tuned with time, the dynamical evolution can be…
Electronic structure calculations based on Density Functional Theory have successfully predicted numerous ground state properties of a variety of molecules and materials. However, exchange and correlation functionals currently used in the…
Non-Hermitian skin effect (NHSE) is a novel phenomenon appearing in non-Hermitian systems. Here, we report the experimental observation of NHSE. Different from the previous non-reciprocal circuit implementation scheme using logic…
Non-abelian lattice spin models with symmetry group SU(N) or U(N) can be formulated in terms of link variables which are subject to the Bianchi constraints. Using this representation we derive exact and local dual formulation for the…
Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\"odinger equations. To relate N^2…
The bulk properties and impurity effect in the one-dimensional S=1/2 Heisenberg model with dimerization and next-nearest-neighbor exchange are studied by the density matrix renormalization group (DMRG) and exact diagonalization methods.…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density-functional theory of so-called strictly correlated electrons (SCE). We map out the…
Recent advancements in exchange-correlation functionals within density functional theory highlight the need for rigorous validation across diverse types of materials properties. In this study, we assess the performance of the newly…
We present an approach for evaluating Wannier functions, offering an alternative perspective on their role in many-body systems. Unlike traditional methods, such as the maximally localized Wannier functions approach, which focuses on…
The known and usable truly nonlocal functionals for exchange-correlation energy of the inhomogeneous electron gas are the ADA (average density approximation) and the WDA (weighted density approximation). ADA, by design, yields the correct…