|
Lieb–Liniger Model
The Lieb–Liniger model describes a gas of particles moving in one dimension and satisfying Bose–Einstein statistics. Introduction A model of a gas of particles moving in one dimension and satisfying Bose–Einstein statistics was introduced in 1963 Elliott H. Lieb and Werner Liniger, ''Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State'', Physical Review 130: 1605–1616, 1963Elliott H. Lieb, ''Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum'', Physical Review 130:1616–1624,1963 in order to study whether the available approximate theories of such gases, specifically Bogoliubov's theory, would conform to the actual properties of the model gas. The model is based on a well defined Schrödinger Hamiltonian for particles interacting with each other via a two-body potential, and all the eigenfunctions and eigenvalues of this Hamiltonian can, in principle, be calculated exactly. Sometimes it is called one dimensional Bose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bose–Einstein Statistics
In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles can be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose. The Bose–Einstein statistics applies only to the particles not limited to single occupancy of the same state – that is, particles that do not obey the Pauli exclusion principle restrictions. Such particles have integer values of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bose Gas
An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin, and abide by Bose–Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for a photon gas, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas. This condensate is known as a Bose–Einstein condensate. Introduction and examples Bosons are quantum mechanical particles that follow Bose–Einstein statistics, or equivalently, that possess integer spin. These particles can be classified as elementary: these are the Higgs boson, the photon, the gluon, the W/Z and the hypothetical graviton; or composite like the atom of hydrogen, the atom of 16 O, the nucleus of deuterium, mesons etc. Additionally, some quasiparticles in more complex systems can also be c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear Schrödinger Equation
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta Function
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., f(x)) to its value at zero of its domain (f(0)), or as the weak limit of a sequence of bump functions (e.g., \delta(x) = \lim_ \frace^), which are zero over most of the real line, with a tall spike at the origin. Bump functions are thus sometimes called "approximate" or "nascent" delta distributions. The delta function was introduced by physicist Paul Dirac as a tool for the normalization of state vectors. It also has uses in probability theory and signal processing. Its validity was disputed until Laurent Schwartz developed the theory of distributions where it is defined as a linear form actin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonks–Girardeau Gas
In physics, a Tonks–Girardeau gas is a Bose gas in which the repulsive interactions between bosonic particles confined to one dimension dominate the system's physics. It is named after physicists Marvin D. Girardeau and Lewi Tonks. It is not a Bose–Einstein condensate as it does not demonstrate any of the necessary characteristics, such as off-diagonal long-range order or a unitary two-body correlation function, even in a thermodynamic limit and as such cannot be described by a macroscopically occupied orbital (order parameter) in the Gross–Pitaevskii formulation. Definition A row of bosons all confined to a one-dimensional line cannot pass each other and therefore cannot exchange places. The resulting motion has been compared to a traffic jam: the motion of each boson is strongly correlated with that of its two neighbors. This can be thought of as the large-''c'' limit of the delta Bose gas. Because the particles cannot exchange places, their behavior might be expected t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Teunis C
Teunis is a Dutch masculine given name. Like Theunis, it is a derivative of Antonius (Anthony). It is also considered a diminutive form of Antonius, Anton, Antoon, Anthonis, Anthoon, Antonie, and Antonis used in Belgium, Netherlands, Suriname, South Africa, Namibia, and Indonesia. Its popularity as a birth name has dropped since the middle of the last century, taken over partially by its short form Teun. at the database of given names in the Netherlands. People with the name include: * Teunis G. Bergen (1806–1881), United States Representative from New York. * (1927–2014), Dutch Old Catholic bishop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journal Citation Reports'' impact factor and the journal ''h''-index proposed by Google Scholar, many physicists and other scientists consider ''Physical Review Letters'' to be one of the most prestigious journals in the field of physics. ''According to Google Scholar, PRL is the journal with the 9th journal h-index among all scientific journals'' ''PRL'' is published as a print journal, and is in electronic format, online and CD-ROM. Its focus is rapid dissemination of significant, or notable, results of fundamental research on all topics related to all fields of physics. This is accomplished by rapid publication of short reports, called "Letters". Papers are published and available electronically one article at a time. When published in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
