|
Open Quantum System
In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the ''environment'' or a ''bath''. In general, these interactions significantly change the dynamics of the system and result in quantum dissipation, such that the information contained in the system is lost to its environment. Because no quantum system is completely isolated from its surroundings, it is important to develop a theoretical framework for treating these interactions in order to obtain an accurate understanding of quantum systems. Techniques developed in the context of open quantum systems have proven powerful in fields such as quantum optics, quantum measurement theory, quantum statistical mechanics, quantum information science, quantum thermodynamics, quantum cosmology, quantum biology, and semi-classical approximations. Quantum system and environment A complete description of a quantum system requires the inclusion of the environment. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Bloch
Felix Bloch (; ; 23 October 1905 – 10 September 1983) was a Swiss-American physicist who shared the 1952 Nobel Prize in Physics with Edward Mills Purcell "for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith".Sohlman, M (Ed.) ''Nobel Foundation directory 2003.'' Vastervik, Sweden: AB CO Ekblad; 2003. Bloch made fundamental theoretical contributions to the understanding of ferromagnetism and electron behavior in Bravais lattice, crystal lattices. He is also considered one of the developers of nuclear magnetic resonance. Biography Early life, education, and family Bloch was born in Zürich, Switzerland to Jewish parents Gustav and Agnes Bloch. Gustav Bloch, his father, was financially unable to attend university and worked as a wholesale grain dealer in Zürich. Gustav moved to Zürich from Moravia in 1890 to become a Swiss citizen. Their first child was a girl born in 1902 while Felix was born three years lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completely Positive Map
In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one that satisfies a stronger, more robust condition. Definition Let A and B be C*-algebras. A linear map \phi: A\to B is called a positive map if \phi maps positive elements to positive elements: a\geq 0 \implies \phi(a)\geq 0. Any linear map \phi:A\to B induces another map :\textrm \otimes \phi : \mathbb^ \otimes A \to \mathbb^ \otimes B in a natural way. If \mathbb^\otimes A is identified with the C*-algebra A^ of k\times k-matrices with entries in A, then \textrm\otimes\phi acts as : \begin a_ & \cdots & a_ \\ \vdots & \ddots & \vdots \\ a_ & \cdots & a_ \end \mapsto \begin \phi(a_) & \cdots & \phi(a_) \\ \vdots & \ddots & \vdots \\ \phi(a_) & \cdots & \phi(a_) \end. We then say \phi is k-positive if \textrm_ \otimes \phi is a positive map and completely positive if \phi is k-positive for all k. Properties * Positive maps are mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Element
In mathematics, an element of a *-algebra is called positive if it is the sum of elements of the form Definition Let \mathcal be a *-algebra. An element a \in \mathcal is called positive if there are finitely many elements a_k \in \mathcal \; (k = 1,2,\ldots,n), so that a = \sum_^n a_k^*a_k This is also denoted by The set of positive elements is denoted by A special case from particular importance is the case where \mathcal is a complete normed *-algebra, that satisfies the C*-identity (\left\, a^*a \right\, = \left\, a \right\, ^2 \ \forall a \in \mathcal), which is called a C*-algebra. Examples * The unit element e of an unital *-algebra is positive. * For each element a \in \mathcal, the elements a^* a and aa^* are positive by In case \mathcal is a C*-algebra, the following holds: * Let a \in \mathcal_N be a normal element, then for every positive function f \geq 0 which is continuous on the spectrum of a the continuous functional calculus defines a positiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redfield Equation
Redfield may refer to: People * Redfield (surname) Places ;United Kingdom *Redfield, Bristol, an area within the City of Bristol ;United States * Mount Redfield, a mountain in Essex County, New York *Redfield, Arkansas, a city in northwestern Jefferson County *Redfield, Iowa, a city in Dallas County * Redfield, Kansas, a city in Bourbon County * Redfield, New York, a town in Oswego County *Redfield, South Dakota Redfield is a city in and the county seat of Spink County, South Dakota, United States. The population was 2,214 at the 2020 United States Census, 2020 census. The city was named for J. B. Redfield, a railroad official. Geography According to th ..., a city in and the county seat of Spink County * Redfield, Texas, a census-designated place in Nacogdoches County * Redfield School Historic District, a former school and historic district in Redfield, Arkansas * Redfield Township, Spink County, South Dakota, a township in Spink County, South Dakota * Redfield & West Str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markovian Property
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
