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Kondo Model
The Kondo model (sometimes referred to as the s-d model) is a model for a single localized quantum impurity coupled to a large reservoir of delocalized and noninteracting electrons. The quantum impurity is represented by a spin-1/2 particle, and is coupled to a continuous band of noninteracting electrons by an antiferromagnetic exchange coupling J. The Kondo model is used as a model for metals containing magnetic impurities, as well as quantum dot systems. Kondo Hamiltonian The Kondo Hamiltonian is given by :H = \sum_ \epsilon_ c^_c_ - J \mathbf\cdot \mathbf where \mathbf is the spin-1/2 operator representing the impurity, and :\mathbf = \sum_ c^_ \mathbf_c_ is the local spin-density of the noninteracting band at the impurity site ( \mathbf are the Pauli matrices). In the Kondo problem, J 0). The Kondo model is intimately related to the Anderson impurity model, as can be shown by Schrieffer–Wolff transformation. See also *Anderson impurity model *Kondo effect In physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Dot
Quantum dots (QDs) are semiconductor particles a few nanometres in size, having light, optical and electronics, electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconductor, semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band. The excited electron can drop back into the valence band releasing its energy as light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the conductance band and the valence band, or the transition between discrete energy states when band structure is no longer a good definition in QDs. In the language of materials science, nanoscale semiconductor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (quantum Mechanics)
Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian with two-electron nature ** Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule * Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system * Hamiltonian path, a path in a graph that visits each vertex exactly once * Hamiltonian group, a non-abelian group the subgroups of which are all normal * Hamiltonian economic program, the economic policies advocated by Alexander Hamilton, the first United States Secretary of the Treasury See also * Alexander Hamilton (1755 or 1757–1804), American statesman and one of the Founding Fathers of the US * Hamilton (other) Hamilton may refer to: People * Hamilton (name), a common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jun Kondo , a Japa ...
Jun or JUN may refer to: People and anthroponymy * Jun (given name), a common Japanese given name * Jun (singer), a member of South Korean boy band U-KISS * Tomáš Jun, Czech footballer * A spelling of common Korean family name Jeon (Korean surname) * A spelling of uncommon Korean family and given name Joon (Korean name) * Jun., Jr. or Jnr., abbreviations for Junior (other) * Jun, stage name of Chinese singer Wen Junhui Places * Jun, Granada, Spain Science * c-jun, a protein encoded by gene JUN Time * Abbreviation of June * A ten-day period in the Japanese calendar History * Commandery (China) (''jùn'' in pinyin), a division of imperial China Other * Jun (drink), a Tibetan fermented tea drink * JUN Auto JUN, or JUN Auto, is a Japanese tuning shop. JUN began as the research facility of Tanaka Industrial Co. Ltd. Originally focused on disassembling and improving engines. It now manufactures high performance car parts. Products JUN manufactures af ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter (rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m). For example, if a solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is , then the resistivity of the material is . Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter ( sigma), but (kappa) (especially in electrical engineering) and (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are intensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kondo Effect
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature. The cause of the effect was first explained by Jun Kondo, who applied third-order perturbation theory to the problem to account for scattering of s-orbital conduction electrons off d-orbital electrons localized at impurities ( Kondo model). Kondo's calculation predicted that the scattering rate and the resulting part of the resistivity should increase logarithmically as the temperature approaches 0 K. Experiments in the 1960s by Myriam Sarachik at Bell Laboratories provided the first data that confirmed the Kondo effect. Extended to a lattice of ''magnetic impurities'', the Kondo effect likely explains the formation of ''heavy fermions'' and ''Kondo insulators'' in intermetallic compounds, especially those involving rare earth elements such as cerium, praseodymium, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip W
Philip, also Phillip, is a male given name, derived from the Greek (''Philippos'', lit. "horse-loving" or "fond of horses"), from a compound of (''philos'', "dear", "loved", "loving") and (''hippos'', "horse"). Prominent Philips who popularized the name include kings of Macedonia and one of the apostles of early Christianity. ''Philip'' has many alternative spellings. One derivation often used as a surname is Phillips. It was also found during ancient Greek times with two Ps as Philippides and Philippos. It has many diminutive (or even hypocoristic) forms including Phil, Philly, Lip, Pip, Pep or Peps. There are also feminine forms such as Philippine and Philippa. Antiquity Kings of Macedon * Philip I of Macedon * Philip II of Macedon, father of Alexander the Great * Philip III of Macedon, half-brother of Alexander the Great * Philip IV of Macedon * Philip V of Macedon New Testament * Philip the Apostle * Philip the Evangelist Others * Philippus of Croton (c. 6th centur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Renormalization Group
The numerical renormalization group (NRG) is a technique devised by Kenneth Wilson to solve certain many-body problems where quantum impurity physics plays a key role. History The numerical renormalization group is an inherently non-perturbative procedure, which was originally used to solve the Kondo model. The Kondo model is a simplified theoretical model which describes a system of magnetic spin-1/2 impurities which couple to metallic conduction electrons (e.g. iron impurities in gold). This problem is notoriously difficult to tackle theoretically, since perturbative techniques break down at low-energy. However, Wilson was able to prove for the first time using the numerical renormalization group that the ground state of the Kondo model is a singlet state. But perhaps more importantly, the notions of renormalization, fixed points, and renormalization group flow were introduced to the field of condensed matter theory — it is for this that Wilson won the Nobel Prize in 1982. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 problems, such as heavy fermion systems and Kondo insulators. In its simplest form, the model contains a term describing the kinetic energy of the conduction electrons, a two-level term with an on-site Coulomb repulsion that models the impurity energy levels, and a hybridization term that couples conduction and impurity orbitals. For a single impurity, the Hamiltonian takes the form :H = \sum_\epsilon_k c^_c_ + \sum_\epsilon_ d^_d_ + Ud^_d_d^_d_ + \sum_V_k(d^_c_ + c^_d_), where the c operator is the annihilation operator of a conduction electron, and d is the annihilation operator for the impurity, k is the conduction electron wavevector, and \sigma labels the spin. The on–site Coulomb repulsion is U, and V gives the hybridization. Regimes The model yields several reg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrieffer–Wolff Transformation
In quantum mechanics, the Schrieffer–Wolff transformation is a unitary transformation used to perturbatively diagonalize the system Hamiltonian to first order in the interaction. As such, the Schrieffer–Wolff transformation is an operator version of second-order perturbation theory. The Schrieffer–Wolff transformation is often used to project out the high energy excitations of a given quantum many-body Hamiltonian in order to obtain an effective low energy model. The Schrieffer–Wolff transformation thus provides a controlled perturbative way to study the strong coupling regime of quantum-many body Hamiltonians. Although commonly attributed to the paper in which the Kondo model was obtained from the Anderson impurity model by J.R. Schrieffer and P.A. Wolff., Joaquin Mazdak Luttinger and Walter Kohn used this method in an earlier work about non-periodic k·p perturbation theory In solid-state physics, the k·p perturbation theory is an approximated semi-empirical app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
