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Luttinger
Joaquin (Quin) Mazdak Luttinger (December 2, 1923 – April 6, 1997) was an American physicist well known for his contributions to the theory of interacting electrons in one-dimensional metals (the electrons in these metals are said to be in a Luttinger-liquid state) and the Fermi-liquid theory. He received his BS and PhD in physics from MIT in 1947. His brother was the physical chemist Lionel Luttinger (1920–2009) and his nephew is the mathematician Karl Murad Luttinger (born 1961). See also * Negative mass * Schrieffer–Wolff transformation * Wiener sausage * Fermi liquid * Many-body problem * Anomalous magnetic moment * Effective mass theory * k·p perturbation theory Notes Some publications (Note: For a complete list, seJ. Stat. Phys. 103, 641 (2001)) * W. Kohn, and J. M. Luttinger, ''Quantum Theory of Electrical Transport Phenomena'', Physical Review, Vol. 108, pp. 590–611 (1957)APS* W. Kohn, and J. M. Luttinger, ''Quantum Theory of Electrical Transport ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger Liquid
A Luttinger liquid, or Tomonaga–Luttinger liquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor (e.g. quantum wires such as carbon nanotubes). Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension. The Tomonaga–Luttinger liquid was first proposed by Tomonaga in 1950. The model showed that under certain constraints, second-order interactions between electrons could be modelled as bosonic interactions. In 1963, J.M. Luttinger reformulated the theory in terms of Bloch sound waves and showed that the constraints proposed by Tomonaga were unnecessary in order to treat the second-order perturbations as bosons. But his solution of the model was incorrect; the correct solution was given by and Elliot H. Lieb 1965. Theory Luttinger liquid theory describes low energy excitations in a 1D electron gas as bosons. Starting with the free electron Hamiltonian: H = \sum_ \epsilon_k c_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger–Ward Functional
In solid state physics, the Luttinger–Ward functional, proposed by Joaquin Mazdak Luttinger and John Clive Ward in 1960, is a scalar functional of the bare electron-electron interaction and the renormalized one-particle propagator. In terms of Feynman diagrams, the Luttinger–Ward functional is the sum of all closed, bold, two-particle irreducible diagrams, i.e., all diagrams without particles going in or out that do not fall apart if one removes two propagator lines. It is usually written as \Phi /math> or \Phi ,U/math>, where G is the one-particle Green's function and U is the bare interaction. The Luttinger–Ward functional has no direct physical meaning, but it is useful in proving conservation laws. The functional is closely related to the Baym–Kadanoff functional constructed independently by Gordon Baym and Leo Kadanoff in 1961. Some authors use the terms interchangeably; if a distinction is made, then the Baym–Kadanoff functional is identical to the two-particle i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger's Theorem
In condensed matter physics, Luttinger's theorem is a result derived by J. M. Luttinger and J. C. Ward in 1960 that has broad implications in the field of electron transport. It arises frequently in theoretical models of correlated electrons, such as the high-temperature superconductors, and in photoemission, where a metal's Fermi surface can be directly observed. Definition Luttinger's theorem states that the volume enclosed by a material's Fermi surface is directly proportional to the particle density. While the theorem is an immediate result of the Pauli exclusion principle in the case of noninteracting particles, it remains true even as interactions between particles are taken into consideration provided that the appropriate definitions of Fermi surface and particle density are adopted. Specifically, in the interacting case the Fermi surface must be defined according to the criteria that :G(\omega=0,\,p) \to 0 or \infty, where G is the single-particle Green function in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger Parameter
In semiconductors, valence bands are well characterized by 3 Luttinger parameters. At the ''Г''-point in the band structure, p_ and p_ orbitals form valence bands. But spin–orbit coupling splits sixfold degeneracy into high energy 4-fold and lower energy 2-fold bands. Again 4-fold degeneracy is lifted into heavy- and light hole bands by phenomenological Hamiltonian by J. M. Luttinger. Three valence band state In the presence of spin–orbit interaction, total angular momentum should take part in. From the three valence band, ''l''=1 and ''s''=1/2 state generate six state of \left, j, m_j \right\rangle as \left, \frac, \pm \frac \right\rangle, \left, \frac, \pm \frac \right\rangle, \left, \frac, \pm \frac \right\rangle The spin–orbit interaction from the relativistic quantum mechanics, lowers the energy of j = \frac states down. Phenomenological Hamiltonian for the ''j''=3/2 states Phenomenological Hamiltonian in spherical approximation is written as H= \ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Liquid
Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interactions among the particles of the many-body system do not need to be small. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas (i.e. non-interacting fermions), and why other properties differ. Important examples of where Fermi liquid theory has been successfully applied are most notably electrons in most metals and liquid helium-3. Liquid helium-3 is a Fermi liquid at low temperatures (but not low enough to be in its superfluid phase). Helium-3 is an isotope of helium, with 2 protons, 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter Kohn
Walter Kohn (; March 9, 1923 – April 19, 2016) was an Austrian-American theoretical physicist and theoretical chemist. He was awarded, with John Pople, the Nobel Prize in Chemistry in 1998. The award recognized their contributions to the understandings of the electronic properties of materials. In particular, Kohn played the leading role in the development of density functional theory, which made it possible to calculate quantum mechanical electronic structure by equations involving the electronic density (rather than the many-body wavefunction). This computational simplification led to more accurate calculations on complex systems as well as many new insights, and it has become an essential tool for materials science, condensed-phase physics, and the chemical physics of atoms and molecules. Early years in Canada Kohn arrived in England as part of the Kindertransport rescue operation immediately after the annexation of Austria by Hitler. He was from a Jewish family, and has wr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Clive Ward
John Clive Ward, (1 August 1924 – 6 May 2000) was a British-Australian physicist. He introduced the Ward–Takahashi identity, also known as "Ward Identity" (or "Ward's Identities"). Andrei Sakharov said Ward was one of the titans of quantum electrodynamics. He made significant contributions to quantum solid-state physics, statistical mechanics and the Ising model. Ward was one of the authors of the Standard Model of gauge particle interactions: his contributions were published in a series of papers he co-authored with Abdus Salam. He is also credited with being an early advocate of the use of Feynman diagrams. It has been said that physicists have made use of his principles and developments "often without knowing it, and generally without quoting him." In 1955, Ward was recruited to work at the Atomic Weapons Research Establishment at Aldermaston. There, he independently derived a version of the Teller-Ulam design, for which he has been called the "father of the Brit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K·p Perturbation Theory
In solid-state physics, the k·p perturbation theory is an approximated semi-empirical approach for calculating the band structure (particularly effective mass) and optical properties of crystalline solids. It is pronounced "k dot p", and is also called the "k·p method". This theory has been applied specifically in the framework of the Luttinger–Kohn model (after Joaquin Mazdak Luttinger and Walter Kohn), and of the Kane model (after Evan O. Kane). Background and derivation Bloch's theorem and wavevectors According to quantum mechanics (in the single-electron approximation), the quasi-free electrons in any solid are characterized by wavefunctions which are eigenstates of the following stationary Schrödinger equation: :\left(\frac+V\right)\psi = E\psi where p is the quantum-mechanical momentum operator, ''V'' is the potential, and ''m'' is the vacuum mass of the electron. (This equation neglects the spin–orbit effect; see below.) In a crystalline solid, ''V'' is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger–Kohn Model
A flavor of the k·p perturbation theory used for calculating the structure of multiple, degenerate electronic bands in bulk and quantum well semiconductors. The method is a generalization of the single band k ·p theory. In this model the influence of all other bands is taken into account by using Löwdin's perturbation method. Background All bands can be subdivided into two classes: * Class A: six valence bands (heavy hole, light hole, split off band and their spin counterparts) and two conduction bands. * Class B: all other bands. The method concentrates on the bands in ''Class A'', and takes into account ''Class B'' bands perturbatively. We can write the perturbed solution \phi^_ as a linear combination of the unperturbed eigenstates \phi^_: :\phi = \sum^_ a_ \phi^_ Assuming the unperturbed eigenstates are orthonormalized, the eigenequation are: :(E-H_)a_m = \sum^_H_a_ + \sum^_H_a_, where :H_ = \int \phi^_ H \phi^_d^3 \mathbf = E^_\delta_+H^_. From this expressi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Sausage
In the mathematical field of probability, the Wiener sausage is a neighborhood of the trace of a Brownian motion up to a time ''t'', given by taking all points within a fixed distance of Brownian motion. It can be visualized as a sausage of fixed radius whose centerline is Brownian motion. The Wiener sausage was named after Norbert Wiener by because of its relation to the Wiener process; the name is also a pun on Vienna sausage, as "Wiener" is German for "Viennese". The Wiener sausage is one of the simplest non-Markovian functionals of Brownian motion. Its applications include stochastic phenomena including heat conduction. It was first described by , and it was used by to explain results of a Bose–Einstein condensate, with proofs published by . Definitions The Wiener sausage ''W''δ(''t'') of radius δ and length ''t'' is the set-valued random variable on Brownian paths b (in some Euclidean space) defined by :W_\delta(t)() is the set of points within a distance δ of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Mass
In theoretical physics, negative mass is a type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg. Such matter would violate one or more energy conditions and show some strange properties such as the oppositely oriented acceleration for negative mass. It is used in certain speculative hypothetical technologies, such as time travel to the past and future, construction of traversable artificial wormholes, which may also allow for time travel, Krasnikov tubes, the Alcubierre drive, and potentially other types of faster-than-light warp drives. Currently, the closest known real representative of such exotic matter is a region of negative pressure density produced by the Casimir effect. In cosmology In December 2018, astrophysicist Jamie Farnes from the University of Oxford proposed a "dark fluid" theory, related, in part, to notions of gravitationally repulsive negative masses, presented earlier by Albert Einstein, that may help better un ... [...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] |
