Related papers: Why neural functionals suit statistical mechanics

Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In…

Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…

We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density…

The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by means of a reformulation of the original equilibrium theory in…

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…

Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…

The multi-terminal generalization of the steady-state density functional theory for the description of electronic and thermal transport (iq-DFT) is presented. The linear response regime of the framework is developed leading to exact…

Bifurcation theory is a powerful tool for studying how the dynamics of a neural network model depends on its underlying neurophysiological parameters. However, bifurcation theory has been developed mostly for smooth dynamical systems and…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [Tschopp et al., Phys. Rev. E 106, 014115 (2022)]. We compare inhomogeneous density profiles for hard sphere fluids to…

The density-functional (DF) theory provides a simple method for calculating the properties of an interacting system under an external potential by associating it with a corresponding non-interacting system. Here, we find some relations in…

Based on our earlier works [Phys. Rev. B 75, 195127 (2007) & J. Chem. Phys. 128, 234703 (2008)], we propose a formally exact and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The…

We introduce machine learning (ML) models that predict the electronic structure of materials across a wide temperature range. Our models employ neural networks and are trained on density functional theory (DFT) data. Unlike most other ML…

We present a general multi-component density functional theory in which electrons and nuclei are treated completely quantum mechanically, without the use of a Born-Oppenheimer approximation. The two fundamental quantities in terms of which…

Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…

By introducing the self-energy density functionals for the dissipative interactions between the reduced system and its environment, we develop a time-dependent density-functional theory formalism based on an equation of motion for the…

Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…

At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented…

Improvements in technique in conjunction with an evolution of the theoretical and conceptual approach to neuronal networks provide a new perspective on living neurons in culture. Organization and connectivity are being measured…

Drawing on the theory of quantum mechanical stress, we introduce the stress density in density functional theory. In analogy with the Chetty-Martin energy density, the stress density provides a spatial resolution of the contributions to the…