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Anderson Orthogonality Theorem
The Anderson orthogonality theorem is a theorem in physics by the physicist P. W. Anderson. It relates to the introduction of a magnetic impurity in a metal. When a magnetic impurity is introduced into a metal, the conduction electrons will tend to screen the potential V(r) that the impurity creates. The N-electron ground state for the system when V(r) = 0, which corresponds to the absence of the impurity and V(r) \neq 0, which corresponds to the introduction of the impurity are orthogonal In mathematics, orthogonality is the generalization of the geometric notion of '' perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ... in the thermodynamic limit N \to \infty . References * * Condensed matter physics {{CMP-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Impurity
A magnetic impurity is an impurity in a host metal that has a magnetic moment. The magnetic impurity can then interact with the conduction electrons of the metal, leading to interesting physics such as the Kondo effect, and heavy fermion behaviour. Some examples of magnetic impurities that metals can be doped with are iron and nickel. Such an impurity will contribute a Curie-Weiss term to the magnetic susceptibility, :\chi_ = \frac. Early theoretical work concentrated on explaining the trend observed as the impurity was varied across the transition metal group. Based on the idea of a virtual bound state, Anderson proposed a model that was successful in explaining the formation of a localized magnetic moment from a magnetic impurity. See also * Anderson impurity model The Anderson impurity model, named after Philip Warren Anderson, is a Hamiltonian that is used to describe magnetic impurities embedded in metals. It is often applied to the description of Kondo effect-type pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conduction Electron
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it. The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands. Band gap In semiconductors and insulators the two bands are separated by a band gap, while in semimetals the bands overlap. A band gap is an energy range in a solid where no electron states can exist due to the quantizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Field Screening
In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases (classical plasmas), electrolytes, and charge carriers in electronic conductors (semiconductors, metals). In a fluid, with a given permittivity , composed of electrically charged constituent particles, each pair of particles (with charges and ) interact through the Coulomb force as \mathbf = \frac\hat, where the vector is the relative position between the charges. This interaction complicates the theoretical treatment of the fluid. For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable. The difficulty lies in the fact that even though the Coulomb force diminishes with distance as , the average number of particles at each distance is proportional to , assuming the fluid is fairly isotropic. As a result, a charge f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ground State
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of '' perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry. Etymology The word comes from the Ancient Greek ('), meaning "upright", and ('), meaning "angle". The Ancient Greek (') and Classical Latin ' originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word ''orthogonalis'' came to mean a right angle or something related to a right angle. Mathematics Physics * In optics, polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization. * In special relativity, a time axis determined by a rapidity of motion is hyperbolic-orthogonal to a space axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
