|
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 natural science that studies matter, its 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." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "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 physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time and was said to have been "the last representative of the great mathematicians who were equally at home in both pure and applied mathematics". He integrated pure and applied sciences. Von Neumann made major contributions to many fields, including mathematics (foundations of mathematics, measure theory, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, matrix theory, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics, ballistics, nuclear physics and quantum statistical mechanics), economics ( game theory and general equilibrium theory), computing ( Von Neumann architecture, linear programming, numerical meteo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redfield Equation
In quantum mechanics, the Redfield equation is a Markovian master equation that describes the time evolution of the reduced density matrix of a strongly coupled quantum system that is weakly coupled to an environment. The equation is named in honor of Alfred G. Redfield, who first applied it, doing so for nuclear magnetic resonance spectroscopy. There is a close connection to the Lindblad master equation. If a so-called secular approximation is performed, where only certain resonant interactions with the environment are retained, every Redfield equation transforms into a master equation of Lindblad type. Redfield equations are trace-preserving and correctly produce a thermalized state for asymptotic propagation. However, in contrast to Lindblad equations, Redfield equations do not guarantee a positive time evolution of the density matrix. That is, it is possible to get negative populations during the time evolution. The Redfield equation approaches the correct dynamics for suf ... [...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 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, usually by 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markovian Property
A Markov chain or Markov process is a stochastic model 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). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CC-BY Icon
A Creative Commons (CC) license is one of several public copyright licenses that enable the free distribution of an otherwise copyrighted "work".A "work" is any creative material made by a person. A painting, a graphic, a book, a song/lyrics to a song, or a photograph of almost anything are all examples of "works". A CC license is used when an author wants to give other people the right to share, use, and build upon a work that the author has created. CC provides an author flexibility (for example, they might choose to allow only non-commercial uses of a given work) and protects the people who use or redistribute an author's work from concerns of copyright infringement as long as they abide by the conditions that are specified in the license by which the author distributes the work. There are several types of Creative Commons licenses. Each license differs by several combinations that condition the terms of distribution. They were initially released on December 16, 2002, by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (quantum Mechanics)
Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian with two-electron nature ** Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule * Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system * Hamiltonian path, a path in a graph that visits each vertex exactly once * Hamiltonian group, a non-abelian group the subgroups of which are all normal * Hamiltonian economic program The Hamiltonian economic program was the set of measures that were proposed by American Founding Father and first Secretary of the Treasury Alexander Hamilton in four notable reports and implemented by the US Congress during George Washington's ..., the economic policies advocated by Alexander Hamilton ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitary Transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation. Formal definition More precisely, a unitary transformation is an isomorphism between two inner product spaces (such as Hilbert spaces). In other words, a ''unitary transformation'' is a bijective function U : H \to H_2\, between two inner product spaces, H and H_2, such that \langle Ux, Uy \rangle_ = \langle x, y \rangle_ \quad \text x, y \in H. Properties A unitary transformation is an isometry In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' ..., as one can see by setting x=y in this formula. Unitary operator In the case when H_1 and H_2 are the same space, a unitary tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Decoherence
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics. If a quantum system were perfectly isolated, it would maintain coherence indefinitely, but it would be impossible to manipulate or investigate it. If it is not perfectly isolated, for example during a measurement, coherence is shared with the environment and appears to be lost with time; a process called quantum decoherence. As a result of this process, quantum behavior is apparently lost, just as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Coherence
In physics, two wave sources are coherent if their frequency and waveform are identical. Coherence is an ideal property of waves that enables stationary (i.e., temporally or spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets. Interference is the addition, in the mathematical sense, of wave functions. A single wave can interfere with itself, but this is still an addition of two waves (see Young's slits experiment). Constructive or destructive interference are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable. When interfering, two waves can add together to create a wave of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Master Equation
In physics, chemistry and related fields, master equations are used to describe the time evolution of a system that can be modelled as being in a probabilistic combination of states at any given time and the switching between states is determined by a transition rate matrix. The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states. Introduction A master equation is a phenomenological set of first-order differential equations describing the time evolution of (usually) the probability of a system to occupy each one of a discrete set of states with regard to a continuous time variable ''t''. The most familiar form of a master equation is a matrix form: : \frac=\mathbf\vec, where \vec is a column vector (where element ''i'' represents state ''i''), and \mathbf is the matrix of connections. The way connections among states are made determines the dimension of the problem; it is either *a d-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
