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Landau–Lifshitz Model
In solid-state physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a partial differential equation describing time evolution of magnetism in solids, depending on 1 time variable and 1, 2, or 3 space variables. Landau–Lifshitz equation The LLE describes an anisotropic magnet. The equation is described in as follows: it is an equation for a vector field S, in other words a function on R1+''n'' taking values in R3. The equation depends on a fixed symmetric 3-by-3 matrix ''J'', usually assumed to be diagonal; that is, J=\operatorname(J_, J_, J_). The LLE is then given by Hamilton's equation of motion for the Hamiltonian :H=\frac\int \left sum_i\left(\frac\right)^-J(\mathbf)\right, dx\qquad (1) (where ''J''(S) is the quadratic form of ''J'' applied to the vector S) which is : \frac = \mathbf\wedge \sum_i\frac + \mathbf\wedge J\mathbf.\qquad (2) In 1+1 dimensions, this equation is : \frac = \mathbf\wedge \frac + \mathbf\wedge J\mathbf.\qq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid-state Physics
Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. Along with solid-state chemistry, it also has direct applications in the technology of transistors and semiconductors. Background Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and Elasticity (physics), elasticity), Heat conduction, thermal, Electrical conduction, electrical, Magnetism, magnetic and Crystal optics, optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric patt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Schrödinger Equation
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers, planar waveguides and hot rubidium vapors and to Bose–Einstein condensates confined to highly anisotropic, cigar-shaped traps, in the mean-field regime. Additionally, the equation appears in the studies of small-amplitude gravity waves on the surface of deep inviscid (zero-viscosity) water; the Langmuir waves in hot plasmas; the propagation of plane-diffracted wave beams in the focusing regions of the ionosphere; the propagation of Davydov's alpha-helix solitons, which are responsible for energy transport along molecular chains; and many others. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Ordering
Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Demagnetizing a magnet is also possible. Only a few substances are ferromagnetic; the most common ones are iron, cobalt, nickel, and their alloys. All substances exhibit some type of magnetism. Magnetic materials are classified according to their bulk susceptibility. Ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, but there are actually several types of magnetism. Paramagnetic substances, such as aluminium and oxygen, are weakly attracted to an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naukova Dumka
Naukova Dumka ( — literally "scientific thought") is a publishing house in Kyiv, Ukraine. It was established by the National Academy of Sciences of Ukraine in 1922, largely owing to the efforts of Ahatanhel Krymsky, a prominent Ukrainian linguist and orientalist. It is one of the oldest scientific and academic publishing houses in the former Soviet Union and became known as ''Naukova Dumka'' in 1964, before which it simply functioned as the official publisher of the National Academy of Sciences of Ukraine. It continues its operations in Ukraine, publishing primarily scientific and historical works as well as dictionaries A dictionary is a listing of lexemes from the lexicon of one or more specific languages, often arranged Alphabetical order, alphabetically (or by Semitic root, consonantal root for Semitic languages or radical-and-stroke sorting, radical an .... Products “Naukova Dumka” has published dictionaries of synonyms of the Ukrainian language, foreign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Kosevich
Arnold Markovych Kosevich (; July 7, 1928 – October 3, 2006) was a Soviet and Ukrainian physicist, known for contributions to the theoretical understanding of metals and crystals. Biography Arnold Kosevich was born in Tulchyn, Ukraine. He graduated from Kharkiv University in 1951, and received his PhD in 1954 under the supervision of Ilya Lifshitz. In 1954–1957 he worked at Chernivtsi University, in 1957–1974 at the Kharkiv Institute of Physics and Technology. In the years 1974–2003 he headed the department of theoretical physics at the Verkin Institute for Low Temperature Physics and Engineering. In 1990, he was elected corresponding member of the National Academy of Sciences of Ukraine. He was twice awarded with the State Prizes of Ukraine (1978, 2001). In 1999 he received the Sinelnikov Prize of the National Academy of Sciences of Ukraine. In 2004. he was awarded the title of Doctor (honoris causa) of Kharkiv National University. He was on the committee of the S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone). In physics, multiple types of material magnetism have been distinguished. Ferromagnetism (along with the similar effec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets. A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic). These include the elements iron, nickel and cobalt and their alloys, some alloys of rare-earth metals, and some naturally occurring minerals such as lodestone. Although ferromagnetic (and ferrimagnetic) materials are the only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ishimori Equation
The Ishimori equation is a partial differential equation proposed by the Japanese mathematician . Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable . Equation The Ishimori equation has the form Lax representation The Lax representation of the equation is given by Here the \sigma_i are the Pauli matrices and I is the identity matrix. Reductions The Ishimori equation admits an important reduction: in 1+1 dimensions it reduces to the continuous classical Heisenberg ferromagnet equation (CCHFE). The CCHFE is integrable. Equivalent counterpart The equivalent counterpart of the Ishimori equation is the Davey-Stewartson equation. See also * Nonlinear Schrödinger equation * Heisenberg model (classical) * Spin wave * Landau–Lifshitz model * Soliton * Vortex * Nonlinear systems In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Micromagnetism
Micromagnetics is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored (the continuum approximation), yet small enough to resolve magnetic structures such as domain walls or vortices. Micromagnetics can deal with static equilibria, by minimizing the magnetic energy, and with dynamic behavior, by solving the time-dependent dynamical equation. History Micromagnetics originated from a 1935 paper by Lev Landau and Evgeny Lifshitz on antidomain walls. Micromagnetics was then expanded upon by William Fuller Brown Jr. in several works in 1940-1941 using energy expressions taken from a 1938 paper by William Cronk Elmore. According to D. Wei, Brown introduced the name "micromagnetics" in 1958. The field prior to 1960 was summarised in Brown's book ''Micromagnetics''. In the 1970s computational methods were developed for the analysis of recor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Wave
In condensed matter physics, a spin wave is a propagating disturbance in the ordering of a magnetic material. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are bosonic modes of the spin lattice that correspond roughly to the phonon excitations of the nuclear lattice. As temperature is increased, the thermal excitation of spin waves reduces a ferromagnet's spontaneous magnetization. The energies of spin waves are typically only in keeping with typical Curie points at room temperature and below. Theory The simplest way of understanding spin waves is to consider the Hamiltonian \mathcal for the Heisenberg ferromagnet: :\mathcal = -\frac J \sum_ \mathbf_i \cdot \mathbf_j - g \mu_ \sum_i \mathbf \cdot \mathbf_i where is the exchange energy, the operators represent the spins at Bravais lattice points, is the Landé -factor, is the Bohr m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisenberg Model (classical)
In statistical physics, the classical Heisenberg model, developed by Werner Heisenberg, is the n = 3 case of the n-vector model, ''n''-vector model, one of the models used to model ferromagnetism and other phenomena. Definition The classical Heisenberg model can be formulated as follows: take a d-dimensional lattice (group), lattice, and place a set of spins of unit length, :\vec_i \in \mathbb^3, , \vec_i, =1\quad (1), on each lattice node. The model is defined through the following Hamiltonian mechanics, Hamiltonian: : \mathcal = -\sum_ \mathcal_ \vec_i \cdot \vec_j\quad (2) where : \mathcal_ = \begin J & \mboxi, j\mbox \\ 0 & \mbox\end is a coupling between spins. Properties * The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model. * In the continuum limit the Heisenberg model (2) gives the following equation of motion :: \vec_=\vec\wedge \vec_. :This equation is called th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Landau
Lev Davidovich Landau (; 22 January 1908 – 1 April 1968) was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. He was considered as one of the last scientists who were universally well-versed and made seminal contributions to all branches of physics. He is credited with laying the foundations of twentieth century condensed matter physics, and is also considered arguably the greatest Soviet theoretical physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, invention of order parameter technique, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
