The Runge-Gross theorem is a fundamental result in the field of many-body quantum mechanics, specifically in the context of time-dependent density functional theory (TDDFT). It establishes a mathematical connection between the time-dependent electron density of a system and the external potential acting on it.
Pulay stress is a phenomenon that arises in electronic structure calculations, particularly in the context of density functional theory (DFT) and other wavefunction-based methods. It occurs due to the finite basis set used to represent the electronic wavefunctions in these calculations. When performing electronic structure calculations, especially for periodic systems (such as crystals), one typically uses a finite basis set (like plane waves or localized atomic orbitals) to approximate the electronic wavefunctions.
Minnesota functionals refer to a specific type of statistical tool or model used primarily in economic contexts, particularly in the analysis of consumption and production behaviors. They are often associated with the work of economists from the University of Minnesota, especially in relation to economic growth and business cycles. One well-known application of Minnesota functionals is in the estimation of economic relationships using econometric models, where they are employed in conjunction with Bayesian methods.
The Local-Density Approximation (LDA) is an approach used in the field of density functional theory (DFT) to approximate the exchange-correlation energy of a many-electron system. In LDA, it is assumed that the exchange-correlation energy at a point in space is a function of the electron density at that same point. This means that the approximation relies on the idea that the behavior of the system can be described by the properties of an electron gas with uniform density.
A hybrid functional is a type of exchange-correlation functional used in density functional theory (DFT) calculations to describe the electronic structure of many-body systems, particularly atoms, molecules, and solids. In DFT, the total energy of a system is expressed as a functional of the electron density, and the exchange-correlation functional is a key component that accounts for the complex interactions between electrons.
The Harris functional, often referred to in the context of mathematical analysis and calculus of variations, is associated with a certain type of energy integral. It was introduced by the mathematician C. A. Harris in the context of studying minimal surfaces and surface area functionals. In simple terms, the Harris functional represents a mathematical tool used for characterizing energy configurations, particularly for problems involving surfaces or interfaces in variational calculus.
Density Functional Theory (DFT) software refers to computational tools and programs used to perform quantum mechanical calculations based on DFT principles. DFT is a widely used method in physics, chemistry, and materials science for studying the electronic structure of many-body systems, particularly atoms, molecules, and the condensed phases of matter.
The Demidov Prize is a prestigious award in the field of science, primarily recognizing outstanding achievements in the fields of natural sciences and engineering. Established in 1884, the prize is named after the Demidov family, notable patrons of science and industry in Russia. The award is presented by the Russian Academy of Sciences and is typically given to researchers and scientists for their significant contributions to advancing knowledge and innovation.
Sydney Chapman (1888–1970) was a notable British mathematician and geophysicist, renowned for his work in the fields of mathematics, astrophysics, and atmospheric science. He made significant contributions to the understanding of atmospheric physics, especially in areas related to the Earth's ionosphere, gas dynamics, and the behavior of gases in the atmosphere.
Joseph Larmor (1857-1942) was an Irish physicist and mathematician known for his contributions to the field of theoretical physics. He is best known for his work on the Larmor formula, which describes the radiation emitted by a charged particle accelerating in a magnetic field. This formula has implications in various areas of physics, including electromagnetism and quantum mechanics.
E. W. Hobson refers to Edward William Hobson, a prominent British mathematician known for his contributions to various fields within mathematics, particularly in the areas of analysis and mathematical physics. He is often associated with the study of series, potential theory, and the theory of functions. Hobson's work includes important texts and research papers that have influenced both theoretical mathematics and its applications. If you're referring to a different context for "E.W. Hobson," please provide more details for clarification!
Alfred George Greenhill (1862–1944) was an English painter, known for his contributions to the genre of landscape painting. He was associated with the late Victorian and early 20th-century art movements in Britain. Greenhill's work often focused on the countryside and rural scenes, characterized by attention to light and atmosphere. He also painted various subjects including still lifes and portraits.
David Abrahams is a mathematician known for his contributions to various areas of mathematics, including topology and category theory. He is also notable for his work in the field of computer science, particularly in programming language design and the development of libraries and tools for software development. Abrahams has a background in both mathematics and computer science, and he is recognized for his research and publications in these fields.
The X17 particle is a proposed hypothetical particle that has garnered interest within the physics community, particularly in the context of dark matter and new physics beyond the Standard Model. The name "X17" comes from a potential particle that is theorized to have a mass of approximately 17 MeV/c² (mega-electronvolts per speed of light squared) and is suggested to interact weakly with ordinary matter, making it a candidate for dark matter.
A Weakly Interacting Massive Particle (WIMP) is a hypothetical elementary particle that is a candidate for dark matter, which makes up a significant fraction of the universe's mass-energy content. WIMPs are predicted to have mass and interact primarily through the weak nuclear force and gravity, but not through electromagnetic interactions, which means they do not emit, absorb, or reflect light, making them difficult to detect directly.
Warm dark matter (WDM) is a theoretical form of dark matter that falls in energy and mass characteristics between cold dark matter (CDM) and hot dark matter (HDM). The primary distinctions among these categories relate to the speed of the particles and their thermal properties during the early universe.