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Coherent Control
Coherent control is a quantum mechanics-based method for controlling dynamic processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of laser pulses. The basic ideas have proliferated, finding vast application in spectroscopy, mass spectra, quantum information processing, laser cooling, ultracold physics and more. Brief History The initial idea was to control the outcome of chemical reactions. Two approaches were pursued: * in the time domain, a "pump-dump" scheme where the control is the time delay between pulses * in the frequency domain, interfering pathways controlled by one and three photons. The two basic methods eventually merged with the introduction of optimal control theory. Experimental realizations soon followed in the time domain and in the frequency domain. Two interlinked developments accelerated the field of coherent control: experimentally, it was the development of pulse shaping by a spatial light m ... [...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] |
Diophantine Equation
''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: *Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated ... * Diophantine equation * Diophantine quintuple * Diophantine set {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Reactions
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur. The substance (or substances) initially involved in a chemical reaction are called reactants or reagents. Chemical reactions are usually characterized by a chemical change, and they yield one or more products, which usually have properties different from the reactants. Reactio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raman Spectroscopy
Raman spectroscopy () (named after physicist C. V. Raman) is a Spectroscopy, spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified. Raman spectroscopy relies upon inelastic scattering of photons, known as Raman scattering. A source of monochromatic light, usually from a laser in the visible spectrum, visible, near infrared, or ultraviolet, near ultraviolet range is used, although X-ray Raman scattering, X-rays can also be used. The laser light interacts with molecular vibrations, phonons or other excitations in the system, resulting in the energy of the laser photons being shifted up or down. The shift in energy gives information about the vibrational modes in the system. Time-resolved spectroscopy and infrared spectroscopy typically yields similar y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ab Initio
( ) is a Latin term meaning "from the beginning" and is derived from the Latin ("from") + , ablative singular of ("beginning"). Etymology , from Latin, literally "from the beginning", from ablative case of "entrance", "beginning", related to verb "to go into", "enter upon", "begin". Uses ''Ab initio'' (abbreviation: ''ab init.'') is used in several contexts, including the following: Law In law, ''ab initio'' refers to something being the case from the start or from the instant of the act rather than from when the court declared it so. For instance, the term "void ''ab initio''" means "to be treated as invalid from the outset." E.g., in many jurisdictions, if a person signs a contract under duress, that contract is treated as being "void ''ab initio''". Typically, documents or acts which are void ''ab initio'' cannot be fixed and if a jurisdiction, a document, or an act is so declared at law to be void ''ab initio'', the parties are returned to their respective positions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attosecond Physics
Attosecond physics, also known as attophysics, or more generally attosecond science, is a branch of physics that deals with light-matter interaction phenomena wherein attosecond (10−18 s) photon pulses are used to unravel dynamical processes in matter with unprecedented time resolution. Attosecond science mainly employs Femtochemistry#Pump–probe spectroscopy, pump–probe spectroscopic methods to investigate the physical process of interest. Due to the complexity of this field of study, it generally requires a synergistic interplay between state-of-the-art experimental setup and advanced theoretical tools to interpret the data collected from attosecond experiments. The main interests of attosecond physics are: # Atomic physics: investigation of Electronic correlation, electron correlation effects, photo-emission delay and Tunnel ionization, ionization tunneling. # Molecular physics and molecular chemistry: role of electronic motion in molecular excited states (e.g. Charge-tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crysta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retinal
Retinal (also known as retinaldehyde) is a polyene chromophore. Retinal, bound to proteins called opsins, is the chemical basis of visual phototransduction, the light-detection stage of visual perception (vision). Some microorganisms use retinal to convert light into metabolic energy. One study suggests that approximately three billion years ago, most living organisms on Earth used retinal, rather than chlorophyll, to convert sunlight into energy. Because retinal absorbs mostly green light and transmits purple light, this gave rise to the Purple Earth hypothesis. Retinal itself is considered to be a form of vitamin A when eaten by an animal. There are many forms of vitamin A, all of which are converted to retinal, which cannot be made without them. The number of different molecules that can be converted to retinal varies from species to species. Retinal was originally called retinene, and was renamed after it was discovered to be vitamin A aldehyde. Vertebrate animals inge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function (mathematics), function subject to constraint (mathematics), equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variable (mathematics), variables). It is named after the mathematician Joseph-Louis Lagrange. Summary and rationale The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function or Lagrangian. In the general case, the Lagrangian is defined as \mathcal(x, \lambda) \equiv f(x) + \langle \lambda, g(x)\rangle for functions f, g; the notation \langle \cdot, \cdot \rangle denotes an inner prod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of functionals: Map (mathematics), mappings from a set of Function (mathematics), functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
