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E.H. Lieb
Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis. Lieb is a prolific author, with over 400 publications both in physics and mathematics. In particular, his scientific 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 He 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. He has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boston
Boston (), officially the City of Boston, is the state capital and most populous city of the Commonwealth of Massachusetts, as well as the cultural and financial center of the New England region of the United States. It is the 24th- most populous city in the country. The city boundaries encompass an area of about and a population of 675,647 as of 2020. It is the seat of Suffolk County (although the county government was disbanded on July 1, 1999). The city is the economic and cultural anchor of a substantially larger metropolitan area known as Greater Boston, a metropolitan statistical area (MSA) home to a census-estimated 4.8 million people in 2016 and ranking as the tenth-largest MSA in the country. A broader combined statistical area (CSA), generally corresponding to the commuting area and including Providence, Rhode Island, is home to approximately 8.2 million people, making it the sixth most populous in the United States. Boston is one of the oldest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brascamp–Lieb Inequality
In mathematics, the Brascamp–Lieb inequality is either of two inequalities. The first is a result in geometry concerning integrable functions on ''n''-dimensional Euclidean space \mathbb^. It generalizes the Loomis–Whitney inequality and Hölder's inequality. The second is a result of probability theory which gives a concentration inequality for log-concave probability distributions. Both are named after Herm Jan Brascamp and Elliott H. Lieb. The geometric inequality Fix natural numbers ''m'' and ''n''. For 1 ≤ ''i'' ≤ ''m'', let ''n''''i'' ∈ N and let ''c''''i'' > 0 so that :\sum_^m c_i n_i = n. Choose non-negative, integrable functions :f_i \in L^1 \left( \mathbb^ ; , + \infty\right) and surjective linear maps :B_i : \mathbb^n \to \mathbb^. Then the following inequality holds: :\int_ \prod_^m f_i \left( B_i x \right)^ \, \mathrm x \leq D^ \prod_^m \left( \int_ f_i (y) \, \mathrm y \right)^, where ''D'' is given by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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''. Winners 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). *2022 Deepak Dhar (IISER Pune) and John J. Hopfield (Princeton University) * 2019 Herbert Spohn (Technical University Munich) * 2016 Daan Frenkel (University of Cambridge) and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 honour 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 established in 1967 and currently (2020) amounts to US$5,000. Recipients See also * List of mathematics awards * Prizes named after people A prize is an award to be given to a person or a group of people (such as sporting teams and organizations) to recognize and reward their actions and achievements. Notes {{DEFAULTSOR ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 *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 Viatcheslav Mukhanov *2014 David Ruelle *2013 Werne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 *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, , Raymond Stora and Igor Tyutin *2008 Mitchell Feigenbaum *2007 Juan Maldacena and Joseph Polchinski *2006 Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. 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. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. 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 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Lattice
Artificial lattice is a term encompassing every atomic-scale structures designed and controlled to confine electrons onto a chosen lattice. Research has been done on multiple geometries and one of the most notable being what is called molecular graphene (in order to mimic graphene structure). Molecular graphene is a part of two-dimensional artificial lattices. Artificial lattices can be studied to test theoretical topology predictions or for their engineered electronic proprieties. Those materials should still be considered at a research stage. Synthesis Synthesis of such materials is often achieved using Atomic manipulation by scanning tunneling microscope or atomic force microscope. More and more efforts are being made to achieve a similar atomic precision with focused electron beams. Those methods aren't adapted for a mass production of nanostructures as each molecule has to be moved one by one. To solve this issue, new methods of synthesize those compounds are being resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1D Chain Of Hydrogen Atoms
1D, 1-D, or 1d can refer to: * Alpha-1D adrenergic receptor * Astra 1D, a satellite * Canon EOS-1D, Canon's first professional digital camera * Long March 1D, a satellite * One-dimensional space in physics and mathematics * One Direction, an English-Irish boy band * Penny (British pre-decimal coin), routinely abbreviated ''1d.'' * 1D, the hexadecimal code for the Group Separator The C0 and C1 control code or control character sets define control codes for use in text by computer systems that use ASCII and derivatives of ASCII. The codes represent additional information about the text, such as the position of a cursor, ... control character See also * ID (other) * LD (other) {{Letter-NumberCombDisambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wehrl Entropy
In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi-entropy defined for the Husimi Q representation of the phase-space quasiprobability distribution. See for a comprehensive review of basic properties of classical, quantum and Wehrl entropies, and their implications in statistical mechanics. Definitions The Husimi function is a " classical phase-space" function of position and momentum , and in one dimension is defined for any quantum-mechanical density matrix by :Q_\rho(x,p)=\int \phi(x,p , y)^* \rho (y, y')\phi (x,p, y')dy dy', where is a " (Glauber) coherent state", given by :\phi(x,p, y)=\pi^\exp(-, y-x, ^2/2)+i\, px). (It can be understood as the Weierstrass transform of the Wigner quasi-probability distribution.) The Wehrl entropy is then defined as : S_W(\rho) = -\int Q_\rho(x,p) \log Q_\rho(x,p) \, dx \, dp ~. The definition can be easily generalized to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger–Newton Equation
The Schrödinger–Newton equation, sometimes referred to as the Newton–Schrödinger or Schrödinger–Poisson equation, is a nonlinear modification of the Schrödinger equation with a Newtonian gravitational potential, where the gravitational potential emerges from the treatment of the wave function as a mass density, including a term that represents interaction of a particle with its own gravitational field. The inclusion of a self-interaction term represents a fundamental alteration of quantum mechanics. It can be written either as a single integro-differential equation or as a coupled system of a Schrödinger and a Poisson equation. In the latter case it is also referred to in the plural form. The Schrödinger–Newton equation was first considered by Ruffini and Bonazzola in connection with self-gravitating boson stars. In this context of classical general relativity it appears as the non-relativistic limit of either the Klein–Gordon equation or the Dirac equation in a cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adiabatic Accessibility
Adiabatic accessibility denotes a certain relation between two equilibrium states of a thermodynamic system (or of different such systems). The concept was coined by Constantin Carathéodory in 1909 ("adiabatische Erreichbarkeit") and taken up 90 years later by Elliott Lieb and J. Yngvason in their axiomatic approach to the foundations of thermodynamics. It was also used by R. Giles in his 1964 monograph.Robin Giles: "Mathematical Foundations of Thermodynamics", Pergamon, Oxford 1964 Description A system in a state ''Y'' is said to be adiabatically accessible from a state ''X'' if ''X'' can be transformed into ''Y'' without the system suffering transfer of energy as heat or transfer of matter. ''X'' may, however, be transformed to ''Y'' by doing work on ''X''. For example, a system consisting of one kilogram of warm water is adiabatically accessible from a system consisting of one kilogram of cool water, since the cool water may be mechanically stirred to warm it. However, the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
