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Supersymmetric Theory Of Stochastic Dynamics
Supersymmetric theory of stochastic dynamics or stochastics (STS) is an exact theory of stochastic (partial) differential equations (SDEs), the class of mathematical models with the widest applicability covering, in particular, all continuous time dynamical systems, with and without noise. The main utility of the theory from the physical point of view is a rigorous theoretical explanation of the ubiquitous spontaneous long-range dynamical behavior that manifests itself across disciplines via such phenomena as 1/f, flicker, and crackling noises and the power-law statistics, or Zipf's law, of instantonic processes like earthquakes and neuroavalanches. From the mathematical point of view, STS is interesting because it bridges the two major parts of mathematical physics – the dynamical systems theory and topological field theories. Besides these and related disciplines such as algebraic topology and supersymmetric field theories, STS is also connected with the traditional theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Differential Equation
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes. Random differential equations are conjugate to stochastic differential equations. Background Stochastic differential equations originated in the theory of Brownian motion, in the work of Albert Einstein and Smoluchowski. These early examples were linear stochastic differential equations, also called 'Langevin' equations after French physicist Langevin, describing the motion of a harmonic oscillator subject to a random force. The mathematical theory of stocha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the outer product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs. Introduction In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system or allowed combination of values of the system's parameters, a point is included in the multidimensional space. The system's evolving state over time traces a path (a phase-space trajectory for the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Quantum Field Theory
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory. In condensed matter physics, topological quantum field theories are the low-energy effective theories of topologically ordered states, such as fractional quantum Hall states, string-net condensed states, and other strongly correlated quantum liquid states. Overview In a topological field theory, correlation functions do not depend on the metric of spacetime. This means that the theory is not sensitive to changes in the sha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-organization
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability. Self-organization occurs in many physical, chemical, biological, robotic, and cognitive systems. Examples of self-organization include crystallization, thermal convection of fluids, chemical oscillation, animal swarming, neural circuits, and black mark ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Onsager Reciprocal Relations
In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists. "Reciprocal relations" occur between different pairs of forces and flows in a variety of physical systems. For example, consider fluid systems described in terms of temperature, matter density, and pressure. In this class of systems, it is known that temperature differences lead to heat flows from the warmer to the colder parts of the system; similarly, pressure differences will lead to matter flow from high-pressure to low-pressure regions. What is remarkable is the observation that, when both pressure and temperature vary, temperature differences at constant pressure can cause matter flow (as in convection) and pressure differences at constant temperature can cause heat flow. Perhaps surprisingly, the heat flow per unit of pressure difference and the density (matter) flow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jarzynski Equality
The Jarzynski equality (JE) is an equation in statistical mechanics that relates free energy differences between two states and the irreversible work along an ensemble of trajectories joining the same states. It is named after the physicist Christopher Jarzynski (then at the University of Washington and Los Alamos National Laboratory, currently at the University of Maryland) who derived it in 1996. Fundamentally, the Jarzynski equality points to the fact that the fluctuations in the work satisfy certain constraints separately from the average value of the work that occurs in some process. Overview In thermodynamics, the free energy difference \Delta F = F_B - F_A between two states ''A'' and ''B'' is connected to the work ''W'' done on the system through the ''inequality'': : \Delta F \leq W , with equality holding only in the case of a quasistatic process, i.e. when one takes the system from ''A'' to ''B'' infinitely slowly (such that all intermediate states are in thermody ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluctuation-dissipation Theorem
The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior of systems that obey detailed balance. Given that a system obeys detailed balance, the theorem is a proof that thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance (to be intended in their general sense, not only in electromagnetic terms) of the same physical variable (like voltage, temperature difference, etc.), and vice versa. The fluctuation–dissipation theorem applies both to classical and quantum mechanical systems. The fluctuation–dissipation theorem was proven by Herbert Callen and Theodore Welton in 1951 and expanded by Ryogo Kubo. There are antecedents to the general theorem, including Einstein's explanation of Brownian motion during his ''annus mirabilis'' and Harry Nyquist's explanation in 1928 of Johnson noise in electrical resistors. Qualitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shang-keng Ma
Shang-keng Ma (September 24, 1940, Chongqing, Sichuan, China – November 24, 1983, La Jolla, California, ) was a Chinese theoretical physicist, known for his work on the theory of critical phenomena and random systems. He is known as the co-author with Bertrand Halperin and Pierre Hohenberg of a 1972 paper that "generalized the renormalization group theory to dynamical critical phenomena." Ma is also known as the co-author with Yoseph Imry of a 1975 paper and with Amnon Aharony and Imry of a 1976 paper that established the foundation of the random field Ising model (RFIM) Biography He transferred in 1959 from the National Taiwan University to the University of California, Berkeley. There he graduated in 1962 with a bachelor's degree in science and in 1966 with a Ph.D. His Ph.D. thesis ''Correlations of Photons from a Thermal Source'' was supervised by Kenneth M. Watson. As a postdoc in 1966, Ma went to the University of California, San Diego (UCSD) to study with Keith Brueckner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yoseph Imry
Yoseph Imry (Hebrew: יוסף אמרי; born 23 February 1939 – 29 May 2018) was an Israeli physicist. He was best known for taking part in the foundation of mesoscopic physics, a relatively new branch of condensed matter physics. It is concerned with how the behavior of systems whose size is in between micro- and macroscopic, crosses over between these two regimes. These systems can be handled and addressed by more or less usual macroscopic methods, but their behavior may still show quantum effects. Awards and honours In 1996, 2001 and 2016, Imry received the Rothschild Prize, Israel Prize and Wolf Prize in physics, respectively. Imry was the 1996 Lorentz Professor at Leiden University. He was a member of the European Academy of Sciences and Arts (Salzburg), the European Academy of Sciences, Sciences and Humanities (Paris), the National Academy of Sciences, the American Physical Society and the Israel Academy of Sciences and Humanities Israel Academy of Science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amnon Aharony
Amnon Aharony (Hebrew: אמנון אהרוני; born: 7 January 1943) is an Israeli Professor (Emeritus) of Physics in the School of Physics and Astronomy at Tel Aviv University, Israel and in the Physics Department of Ben Gurion University of the Negev, Israel. After years of research on statistical physics (critical phenomena, random systems, fractals, percolation), his current research focuses on condensed matter theory, especially in mesoscopic physics and spintronics. He is a member of the Israel Academy of Sciences and Humanities, a Foreign Honorary Member of the American Academy of Arts and Sciences and of several other academies. He also received several prizes, including the Rothschild Prize in Physical Sciences, and the Gunnar Randers Research Prize, awarded every other year by the King of Norway. Early life and education Amnon Aharony was born in Jerusalem, and grew up in Netanya, Israel. He received his B.Sc. in Physics and Mathematics in 1964 from the Hebrew unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Reduction
Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in ''D'' spacetime dimensions can be redefined in a lower number of dimensions ''d'', by taking all the fields to be independent of the location in the extra ''D'' − ''d'' dimensions. For example, consider a periodic compact dimension with period ''L''. Let ''x'' be the coordinate along this dimension. Any field \phi can be described as a sum of the following terms: :\phi_n(x) = A_n \cos \left( \frac\right) with ''A''''n'' a constant. According to quantum mechanics, such a term has momentum ''nh''/''L'' along ''x'', where ''h'' is Planck's constant. Therefore, as L goes to zero, the momentum goes to infinity, and so does the energy, unless ''n'' = 0. However ''n'' = 0 gives a field which is constant with respect to ''x''. So at this limit, and at finite energy, \phi will not depend on ''x''. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giorgio Parisi
Giorgio Parisi (born 4 August 1948) is an Italian theoretical physicist, whose research has focused on quantum field theory, statistical mechanics and complex systems. His best known contributions are the QCD evolution equations for parton densities, obtained with Guido Altarelli, known as the Altarelli–Parisi or DGLAP equations, the exact solution of the Sherrington–Kirkpatrick model of spin glasses, the Kardar–Parisi–Zhang equation describing dynamic scaling of growing interfaces, and the study of whirling flocks of birds. He was awarded the 2021 Nobel Prize in Physics jointly with Klaus Hasselmann and Syukuro Manabe for groundbreaking contributions to theory of complex systems, in particular "for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales." Career Giorgio Parisi received his degree from the University of Rome La Sapienza in 1970 under the supervision of Nicola Cabibbo. He was a researcher a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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