|
Quantum Boltzmann Equation
The quantum Boltzmann equation, also known as the Uehling–Uhlenbeck equation, is the quantum mechanical modification of the Boltzmann equation, which gives the nonequilibrium time evolution of a gas of quantum-mechanically interacting particles. Typically, the quantum Boltzmann equation is given as only the “collision term” of the full Boltzmann equation, giving the change of the momentum distribution of a locally homogeneous gas, but not the drift and diffusion in space. It was originally formulated by L.W. Nordheim (1928), and by and E. A. Uehling and George Uhlenbeck (1933). In full generality (including the p-space and x-space drift terms, which are often neglected) the equation is represented analogously to the Boltzmann equation. \left frac + \mathbf \cdot \nabla_x + \mathbf \cdot \nabla_p \rightf(\mathbf,\mathbf,t) = \mathcal \mathbf,\mathbf) where \mathbf represents an externally applied potential acting on the gas' p-space distribution and \mathcal is the collisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M2An
M, or m, is the thirteenth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of several western European languages and others worldwide. Its name in English is ''em'' (pronounced ), plural ''ems''. History The letter M is derived from the Phoenician Mem via the Greek Mu (Μ, μ). Semitic Mem is most likely derived from a " Proto-Sinaitic" (Bronze Age) adoption of the "water" ideogram in Egyptian writing. The Egyptian sign had the acrophonic value , from the Egyptian word for "water", ''nt''; the adoption as the Semitic letter for was presumably also on acrophonic grounds, from the Semitic word for "water", '' *mā(y)-''. Use in writing systems English In English, represents the voiced bilabial nasal . The Oxford English Dictionary (first edition) says that is sometimes a vowel, such as in words like ''spasm'' and in the suffix ''-ism''. In modern terminology, this is described as a syllabic consonant (IPA: ). M is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Equation
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerner, G. L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid. In the modern literature the term Boltzmann equation is often used in a more general sense, referring to any kinetic equation that describes the change of a macroscopic quantity in a thermodynamic system, such as energy, charge or particle number. The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lothar Wolfgang Nordheim
LotharHis name is sometimes misspelled as ''Lother''. Wolfgang Nordheim (November 7, 1899, Munich – October 5, 1985, La Jolla, California) was a German-born American theoretical physicist. He was a pioneer in the applications of quantum mechanics to solid-state problems, such as thermionic emission, work function of metals, field electron emission, rectification in metal-semiconductor contacts and electrical resistance in metals and alloys. He also worked in the mathematical foundations of quantum mechanics, cosmic rays and in nuclear physics. Life He obtained his PhD in 1923, under the supervision of Max Born in the University of Göttingen. He also worked with Edward Teller on the muon, sparkling his interest in cosmic rays. As a "physical assistant" to David Hilbert (like his teacher Born before him), he worked with him John von Neumann and Eugene Wigner on the mathematical formulation of quantum mechanics in 1928. He wrote extensive articles for the ''Lehrbuch der P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edwin Albrecht Uehling
Edwin Albrecht Uehling (January 27, 1901 – May 18, 1985) was an American theoretical physicist known for the formulation of the Uehling potential to describe vacuum polarization in quantum electrodynamics. He also worked in condensed matter physics, particularly in the field of ferroelectricity. Life After his bachelor's degree from the University of Wisconsin–Madison in 1925, he worked at Bell Telephone Laboratories in radio frequency communication, where he wrote several patents. He received his PhD from the University of Michigan in 1932 on the quantum theory of transport processes, advised by George Uhlenbeck. His research lead to his famous paper on vacuum polarization and the formulation of the now-called Uehling potential. As described by Uehling theory, the effects of vacuum polarization were later confirmed with the discovery of the Lamb shift in 1947. After his PhD he left for a ten-month collaboration with Werner Heisenberg in the Institute of Theoretical Physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Uhlenbeck
George Eugene Uhlenbeck (December 6, 1900 – October 31, 1988) was a Dutch-American theoretical physicist, known for his significant contributions to quantum mechanics and statistical mechanics. He co-developed the concept of electron spin, alongside Samuel Goudsmit, in 1925. The formalization of Langevin equation for the Brownian motion as a stochastic process, is known as the Ornstein–Uhlenbeck process, derived in 1930 from his work with Leonard Ornstein. I. I. Rabi said that Uhlenbeck and Goudsmit's omission for the Nobel Prize in Physics "will always be a mystery to me". Background and education George Uhlenbeck was the son of Eugenius and Anne Beeger Uhlenbeck. He attended the Hogere Burgerschool (High School) in The Hague, from which he graduated in 1918. He subsequently entered Delft University of Technology as a student in chemical engineering. During the next year, he transferred to Leiden University, to study physics and mathematics, and he earned his bachelor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy (arrow Of Time)
Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, Irreversible process, but not decrease. Thus, entropy measurement is a way of distinguishing the past from the future. In thermodynamic systems that are not isolated, local entropy can decrease over time, accompanied by a compensating entropy increase in the Environment (systems), surroundings; examples include objects undergoing cooling, entropy and life, living systems, and Crystallization, the formation of typical crystals. Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy. For example, it is often very easy to tell the difference between a video being played forwards or backwards. A video may depict a wood fire that melts a nearby ice block; played in reve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Physics
''Annals of Physics'' is a monthly peer-reviewed scientific journal covering all aspects of physics. It was established in 1957 and is published by Elsevier. The editor-in-chief is Neil Turok ( University of Edinburgh School of Physics and Astronomy). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 2.73. References External links * Physics journals Monthly journals Academic journals established in 1957 English-language journals Elsevier academic journals {{physics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poincaré Recurrence Theorem
In mathematics and physics, the Poincaré recurrence theorem states that certain dynamical systems will, after a sufficiently long but finite time, return to a state arbitrarily close to (for continuous state systems), or exactly the same as (for discrete state systems), their initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence. This time may vary greatly depending on the exact initial state and required degree of closeness. The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. Systems to which the Poincaré recurrence theorem applies are called conservative systems. The theorem is named after Henri Poincaré, who discussed it in 1890. A proof was presented by Constantin Carathéodory using measure theory in 1919. Precise formulation Any dynam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Age Of The Universe
In physical cosmology, the age of the universe is the cosmological time, time elapsed since the Big Bang: 13.79 billion years. Astronomers have two different approaches to determine the age of the universe. One is based on a particle physics model of the early universe called Lambda-CDM model, Lambda-CDM, matched to measurements of the distant, and thus old features, like the cosmic microwave background. The other is based on the distance and relative velocity of a series or "ladder" of different kinds of stars, making it depend on local measurements late in the history of the universe. These two methods give slightly different values for the Hubble constant, which is then used in a formula to calculate the age. The range of the estimate is also within the range of the estimate for the List of oldest stars, oldest observed star in the universe. History In the 18th century, the concept that the age of Earth was millions, if not billions, of years began to appear. Nonetheless ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annalen Der Physik
''Annalen der Physik'' (English: ''Annals of Physics'') is one of the oldest scientific journals on physics; it has been published since 1799. The journal publishes original, peer-reviewed papers on experimental, theoretical, applied, and mathematical physics and related areas. The editor-in-chief is Stefan Hildebrandt. Prior to 2008, its ISO 4 abbreviation was ''Ann. Phys. (Leipzig)'', after 2008 it became ''Ann. Phys. (Berl.)''. The journal is the successor to , published from 1790 until 1794, and ', published from 1795 until 1797. The journal has been published under a variety of names (', ', ', ''Wiedemann's Annalen der Physik und Chemie'') during its history. History Originally, was published in German, then a leading scientific language. From the 1950s to the 1980s, the journal published in both German and English. Initially, only foreign authors contributed articles in English but from the 1970s German-speaking authors increasingly wrote in English in order to reach a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exciton
An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb's law, Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as an elementary excitation primarily in condensed matter, such as Electrical insulation, insulators, semiconductors, some metals, and in some liquids. It transports energy without transporting net electric charge. An exciton can form when an electron from the valence band of a crystal is promoted in energy to the conduction band e.g., when a material absorbs a photon. Promoting the electron to the conduction band leaves a positively charged hole in the valence band. Here 'hole' represents the unoccupied quantum mechanical electron state with a positive charge, an analogue in crystal of a positron. Because of the attractive coulomb force between the electron and the hole, a bound state is formed, akin to that of the electron and proton in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
