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Heisenberg–Langevin Equations
The Heisenberg–Langevin equations (named after Werner Heisenberg and Paul Langevin) are equations for open quantum systems. They are a specific case of quantum Langevin equations. In the Heisenberg picture the time evolution of a quantum system is the operators themselves. The solution to the Heisenberg equation of motion determines the subsequent time evolution of the operators. The Heisenberg–Langevin equation is the generalization of this to 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 an ...s. References Quantum mechanics {{Quantum-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Werner Heisenberg
Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle, which he published in 1927. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Heisenberg also made contributions to the theories of the hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles. He was a principal scientist in the German nuclear weapons program during World War II. He was also instrumental in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor in Munich, in 1957. Following World War II, he was appointed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Langevin
Paul Langevin (; ; 23 January 1872 – 19 December 1946) was a French physicist who developed Langevin dynamics and the Langevin equation. He was one of the founders of the ''Comité de vigilance des intellectuels antifascistes'', an anti-fascist organization created after the 6 February 1934 far right riots. Being a public opponent of fascism in the 1930s resulted in his arrest and being held under house arrest by the Vichy government for most of World War II. Langevin was also president of the Human Rights League (LDH) from 1944 to 1946, having recently joined the French Communist Party. He was a doctoral student of Pierre Curie and later a lover of widowed Marie Curie. He is also known for his two US patents with Constantin Chilowsky in 1916 and 1917 involving ultrasonic submarine detection. He is entombed at the Panthéon. Life Langevin was born in Paris, and studied at the '' École de Physique et Chimie'' and the ''École Normale Supérieure''. He then went to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum System
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Stochastic Calculus
Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum trajectories. Just as the Lindblad master equation provides a quantum generalization to the Fokker–Planck equation, quantum stochastic calculus allows for the derivation of quantum stochastic differential equations (QSDE) that are analogous to classical Langevin equations. For the remainder of this article ''stochastic calculus'' will be referred to as ''classical stochastic calculus'', in order to clearly distinguish it from quantum stochastic calculus. Heat baths An important physical scenario in which a quantum stochastic calculus is needed is the case of a system interacting with a heat bath. It is appropriate in many circumstances to model the heat bath as an assembly of harmonic oscillators. One type of interaction between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langevin Equations
In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Langevin equation typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast (microscopic) variables are responsible for the stochastic nature of the Langevin equation. One application is to Brownian motion, which models the fluctuating motion of a small particle in a fluid. Brownian motion as a prototype The original Langevin equation describes Brownian motion, the apparently random movement of a particle in a fluid due to collisions with the molecules of the fluid, m\frac=-\lambda \mathbf+\boldsymbol\left( t\right). Here, \mathbf is the velocity of the particle, and m is its mass. The force acting on the particle is written as a sum of a viscous fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisenberg Picture
In physics, the Heisenberg picture (also called the Heisenberg representation) is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory. It stands in contrast to the Schrödinger picture in which the operators are constant, instead, and the states evolve in time. The two pictures only differ by a basis change with respect to time-dependency, which corresponds to the difference between active and passive transformations. The Heisenberg picture is the formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal. It further serves to define a third, hybrid, picture, the interaction picture. Mathematical details In the Heisenberg picture of quantum mechanics the state vectors , ''ψ''⟩ do not change with time, while observables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
