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Elliott H. Lieb
Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physicist. He is a professor of mathematics and physics at Princeton University. Lieb's works pertain to quantum and classical many-body problem, atomic structure, the stability of matter, functional inequalities, the theory of magnetism, and the Hubbard model. Biography Lieb was born in Boston in 1932, the family moved to New York when he was five. His father came from Lithuania and was an accountant, his mother came from Bessarabia and worked as a secretary. Lieb received his B.S. in physics from the Massachusetts Institute of Technology in 1953 and his PhD in mathematical physics from the University of Birmingham in England in 1956. Lieb was a Fulbright Fellow at Kyoto University, Japan (1956–1957), and worked as the Staff Theoretical Physicist for IBM from 1960 to 1963. In 1961–1962, Lieb was on leave as professor of applied mathematics at Fourah Bay College, the University of Sierra Leone. In 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Boston
Boston is the capital and most populous city in the Commonwealth (U.S. state), Commonwealth of Massachusetts in the United States. The city serves as the cultural and Financial centre, financial center of New England, a region of the Northeastern United States. It has an area of and a population of 675,647 as of the 2020 United States census, 2020 census, making it the third-largest city in the Northeastern United States after New York City and Philadelphia. The larger Greater Boston metropolitan statistical area has a population of 4.9 million as of 2023, making it the largest metropolitan area in New England and the Metropolitan statistical area, eleventh-largest in the United States. Boston was founded on Shawmut Peninsula in 1630 by English Puritans, Puritan settlers, who named the city after the market town of Boston, Lincolnshire in England. During the American Revolution and American Revolutionary War, Revolutionary War, Boston was home to several seminal events, incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
AKLT Model
In condensed matter physics, the Affleck–Kennedy–Lieb–Tasaki (AKLT) model is an extension of the one-dimensional quantum Heisenberg spin model. The proposal and exact solution of this model by Ian Affleck, Elliott H. Lieb, Tom Kennedy and provided crucial insight into the physics of the spin-1 Heisenberg chain. It has also served as a useful example for such concepts as valence bond solid order, symmetry-protected topological order and matrix product state wavefunctions. Background A major motivation for the AKLT model was the Majumdar–Ghosh chain. Because two out of every set of three neighboring spins in a Majumdar–Ghosh ground state are paired into a singlet, or valence bond, the three spins together can never be found to be in a spin 3/2 state. In fact, the Majumdar–Ghosh Hamiltonian is nothing but the sum of all projectors of three neighboring spins onto a 3/2 state. The main insight of the AKLT paper was that this construction could be generalized to obt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Boltzmann Medal
The Boltzmann Medal (or Boltzmann Award) is a prize awarded to physicists that obtain new results concerning statistical mechanics; it is named after the celebrated physicist Ludwig Boltzmann. The Boltzmann Medal is awarded once every three years by the Commission on Statistical Physics of the International Union of Pure and Applied Physics, during the STATPHYS conference. The award consists of a gilded medal; its front carries the inscription ''Ludwig Boltzmann, 1844–1906''. Recipients All the winners are influential physicists or mathematicians whose contribution to statistical physics have been relevant in the past decades. Institution with multiple recipients are Sapienza University of Rome (3) and École Normale Supérieure, Cornell University, University of Cambridge and Princeton University (2). The Medal cannot be awarded to a scientist who already has been a laureate of a Nobel Prize. Three recipients of the Boltzmann Medal have gone on to win the Nobel Prize in Physi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Birkhoff Prize
The George David Birkhoff Prize in applied mathematics is awarded jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) in honor of George David Birkhoff (1884–1944). It is currently awarded every three years for an outstanding contribution to "applied mathematics in the highest and broadest sense." The recipient of the prize has to be a member of one of the awarding societies, as well as a resident of the United States of America, Canada, or Mexico. The prize was endowed in 1967, first issued in 1968, and currently (2020) amounts to US$5,000. Recipients See also * List of mathematics awards * Prizes named after people This is a list of awards that are named after people. A B C D E F G H I J K L M N O P R S T U–V W Y Z See also * Lists of awards * List of eponyms * List of awards named after governo ... Notes {{DEFAULTSORT:Birkhoff Prize Awards est ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Max Planck Medal
The Max Planck Medal is the highest award of the German Physical Society , the world's largest organization of physicists, for extraordinary achievements in theoretical physics. The prize has been awarded annually since 1929, with few exceptions, and usually to a single person. The winner is awarded with a gold medal and hand-written parchment. In 1943 it was not possible to manufacture the gold medal because the Berlin foundry was hit by a bomb. The board of directors of the German Physical Society decided to manufacture the medals in a substitute metal and to deliver the gold medals later. The highest award of the German Physical Society for outstanding results in experimental physics is the Stern–Gerlach Medal. List of recipients *2025 Reinhard F. Werner *2024 Erwin Frey *2023 Rashid A. Sunyaev *2022 Annette Zippelius *2021 Alexander Markovich Polyakov *2020 Andrzej Buras *2019 Detlef Lohse *2018 Juan Ignacio Cirac *2017 Herbert Spohn *2016 Herbert Wagner *2015 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dannie Heineman Prize For Mathematical Physics
Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman. As of 2010, the prize consists of US$10,000 and a certificate citing the contributions made by the recipient plus travel expenses to attend the meeting at which the prize is bestowed. Past Recipients Source: American Physical Society *2025 Samson Shatashvili *2024 David C. Brydges *2023 Nikita Nekrasov *2022 Antti Kupiainen and Krzysztof Gawędzki *2021 Joel Lebowitz *2020 Svetlana Jitomirskaya *2019 T. Bill Sutherland, Francesco Calogero and Michel Gaudin *2018 Barry Simon *2017 Carl M. Bender *2016 Andrew Strominger and Cumrun Vafa *2015 Pierre Ramond *2014 Gregory W. Moore *2013 Michio Jimbo and Tetsuji Miwa *2012 Giovanni Jona-Lasinio *2011 Herbert Spohn *2010 Michael Aizenman *2009 Carlo Becchi, Alain Rouet, Raymond Sto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark, New Jersey, Newark in 1747 and then to its Mercer County, New Jersey, Mercer County campus in Princeton nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate instruction in the hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Strong Subadditivity Of Quantum Entropy
In quantum information theory, strong subadditivity of quantum entropy (SSA) is the relation among the von Neumann entropies of various quantum subsystems of a larger quantum system consisting of three subsystems (or of one quantum system with three degrees of freedom). It is a basic theorem in modern quantum information theory. It was conjectured by D. W. Robinson and D. Ruelle in 1966 and O. E. Lanford III and D. W. Robinson in 1968 and proved in 1973 by E.H. Lieb and M.B. Ruskai, building on results obtained by Lieb in his proof of the Wigner-Yanase-Dyson conjecture. The classical version of SSA was long known and appreciated in classical probability theory and information theory. The proof of this relation in the classical case is quite easy, but the quantum case is difficult because of the non-commutativity of the reduced density matrices describing the quantum subsystems. Some useful references here include: *"Quantum Computation and Quantum Information" *"Quantum Entr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Stability Of Matter
In physics, the stability of matter refers to the ability of a large number of charged particles, such as electrons and protons, to form macroscopic objects without collapsing or blowing apart due to electromagnetic interactions. Classical physics predicts that such systems should be inherently unstable due to attractive and repulsive electrostatic forces between charges, and thus the stability of matter was a theoretical problem that required a quantum mechanical explanation. The first solution to this problem was provided by Freeman Dyson and Andrew Lenard in 1967–1968, but a shorter and more conceptual proof was found later by Elliott Lieb and Walter Thirring in 1975 using the Lieb–Thirring inequality. The stability of matter is partly due to the uncertainty principle and the Pauli exclusion principle. Description of the problem In statistical mechanics, the existence of macroscopic objects is usually explained in terms of the behavior of the energy or the free ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dicke Model
The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the ''light'' component is described as a single quantum mode, while the ''matter'' is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes. Description The Dicke model is a quantum mechanical model that describes the coupling between a single-mode cavity and N two-level systems, or equivalently N spin-1/2 degrees of freedom. The model was first introduced in 1973 by K. Hepp and E. H. Lieb. Their study was inspired by the pioneering work of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Temperley–Lieb Algebra
In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrix, transfer matrices, invented by Harold Neville Vazeille Temperley, Neville Temperley and Elliott H. Lieb, Elliott Lieb. It is also related to integrable models, knot theory and the braid group, braid groups, quantum groups and subfactors of von Neumann algebras. Structure Generators and relations Let R be a commutative ring and fix \delta \in R. The Temperley–Lieb algebra TL_n(\delta) is the algebra (ring theory), R-algebra generated by the elements e_1, e_2, \ldots, e_, subject to the Jones relations: *e_i^2 = \delta e_i for all 1 \leq i \leq n-1 *e_i e_ e_i = e_i for all 1 \leq i \leq n-2 *e_i e_ e_i = e_i for all 2 \leq i \leq n-1 *e_i e_j = e_j e_i for all 1 \leq i,j \leq n-1 such that , i-j, \neq 1 Using these relations, any product of generators e_i can be brought to Jones' normal form: : E= \big(e_e_\cdots e_\big)\big(e_e_\cdots e_\big)\cdots\big(e_e_\cdots e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Strong Subadditivity Of Quantum Entropy
In quantum information theory, strong subadditivity of quantum entropy (SSA) is the relation among the von Neumann entropies of various quantum subsystems of a larger quantum system consisting of three subsystems (or of one quantum system with three degrees of freedom). It is a basic theorem in modern quantum information theory. It was conjectured by D. W. Robinson and D. Ruelle in 1966 and O. E. Lanford III and D. W. Robinson in 1968 and proved in 1973 by E.H. Lieb and M.B. Ruskai, building on results obtained by Lieb in his proof of the Wigner-Yanase-Dyson conjecture. The classical version of SSA was long known and appreciated in classical probability theory and information theory. The proof of this relation in the classical case is quite easy, but the quantum case is difficult because of the non-commutativity of the reduced density matrices describing the quantum subsystems. Some useful references here include: *"Quantum Computation and Quantum Information" *"Quantum Entr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
