Relevant bibliographies by topics / Classical Brownian Motion

Academic literature on the topic 'Classical Brownian Motion'

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Published: 7 September 2023

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Journal articles on the topic "Classical Brownian Motion"

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Tsekov, Roumen, and Georgi N. Vayssilov. "Quantum Brownian motion and classical diffusion." Chemical Physics Letters 195, no. 4 (July 1992): 423–26. http://dx.doi.org/10.1016/0009-2614(92)85628-n.

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Ord, G. N. "Schrödinger's Equation and Classical Brownian Motion." Fortschritte der Physik 46, no. 6-8 (November 1998): 889–96. http://dx.doi.org/10.1002/(sici)1521-3978(199811)46:6/8<889::aid-prop889>3.0.co;2-z.

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Tsekov, Roumen. "Brownian Motion and Quantum Mechanics." Fluctuation and Noise Letters 19, no. 02 (November 19, 2019): 2050017. http://dx.doi.org/10.1142/s0219477520500170.

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A theoretical parallel between the classical Brownian motion and quantum mechanics is explored via two stochastic sources. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive behavior. In the case of simultaneous action of the thermal and quantum noises, the quantum Brownian motion is described as well.
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Santos, Willien O., Guilherme M. A. Almeida, and Andre M. C. Souza. "Noncommutative Brownian motion." International Journal of Modern Physics A 32, no. 23n24 (August 24, 2017): 1750146. http://dx.doi.org/10.1142/s0217751x17501469.

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We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the symplectic Weyl–Moyal formalism we find that noncommutativity induces a nonvanishing correlation between both coordinates at different times. The effect stands out as a signature of spatial noncommutativity and thus could offer a way to experimentally detect the phenomena. We further discuss some limiting scenarios and the trade-off between the scale imposed by the NC structure and the parameters of the Brownian motion itself.
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Rajput, B. S. "Quantum equations from Brownian motion." Canadian Journal of Physics 89, no. 2 (February 2011): 185–91. http://dx.doi.org/10.1139/p10-111.

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The Schrödinger free particle equation in 1+1 dimension describes second-order effects in ensembles of lattice random walks, in addition to its role in quantum mechanics, and its solutions represent the continuous limit of a property of ensembles of Brownian particles. In the present paper, the classical Schrödinger and Dirac equations have been derived from the Brownian motions of a particle, and it has been shown that the classical Schrödinger equation can be transformed into the usual Schrödinger quantum equation on applying the Heisenberg uncertainty principle between position and momentum, while the Dirac quantum equation follows from its classical counterpart on applying the Heisenberg uncertainty principle between energy and time, without applying any analytical continuation.
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Anders, J., C. R. J. Sait, and S. A. R. Horsley. "Quantum Brownian motion for magnets." New Journal of Physics 24, no. 3 (March 1, 2022): 033020. http://dx.doi.org/10.1088/1367-2630/ac4ef2.

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Abstract Spin precession in magnetic materials is commonly modelled with the classical phenomenological Landau–Lifshitz–Gilbert (LLG) equation. Based on a quantized three-dimensional spin + environment Hamiltonian, we here derive a spin operator equation of motion that describes precession and includes a general form of damping that consistently accounts for memory, coloured noise and quantum statistics. The LLG equation is recovered as its classical, Ohmic approximation. We further introduce resonant Lorentzian system–reservoir couplings that allow a systematic comparison of dynamics between Ohmic and non-Ohmic regimes. Finally, we simulate the full non-Markovian dynamics of a spin in the semi-classical limit. At low temperatures, our numerical results demonstrate a characteristic reduction and flattening of the steady state spin alignment with an external field, caused by the quantum statistics of the environment. The results provide a powerful framework to explore general three-dimensional dissipation in quantum thermodynamics.
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Ambegaokar, Vinay. "Quantum Brownian Motion and its Classical Limit." Berichte der Bunsengesellschaft für physikalische Chemie 95, no. 3 (March 1991): 400–404. http://dx.doi.org/10.1002/bbpc.19910950331.

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Khalili Golmankhaneh, Ali, Saleh Ashrafi, Dumitru Baleanu, and Arran Fernandez. "Brownian Motion on Cantor Sets." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 3-4 (May 26, 2020): 275–81. http://dx.doi.org/10.1515/ijnsns-2018-0384.

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AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.
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PARK, MOONGYU, and JOHN H. CUSHMAN. "THE COMPLEXITY OF BROWNIAN PROCESSES RUN WITH NONLINEAR CLOCKS." Modern Physics Letters B 25, no. 01 (January 10, 2011): 1–10. http://dx.doi.org/10.1142/s0217984911025481.

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Anomalous diffusion occurs in many branches of physics. Examples include diffusion in confined nanofilms, Richardson turbulence in the atmosphere, near-surface ocean currents, fracture flow in porous formations and vortex arrays in rotating flows. Classically, anomalous diffusion is characterized by a power law exponent related to the mean-square displacement of a particle or squared separation of pairs of particles: 〈|X(t)|2〉 ~tγ. The exponent γ is often thought to relate to the fractal dimension of the underlying process. If γ > 1 the flow is super-diffusive, if it equals 1 it is classical, otherwise it is sub-diffusive. In this work we illustrate how time-changed Brownian position processes can be employed to model sub-, super-, and classical diffusion, while time-changed Brownian velocity processes can be used to model super-diffusion alone. Specific examples presented include transport in turbulent fluids and renormalized transport in porous media. Intuitively, a time-changed Brownian process is a classical Brownian motion running with a nonlinear clock (Bm-nlc). The major difference between classical and Bm-nlc is that the time-changed case has nonstationary increments. An important novelty of this approach is that, unlike fractional Brownian motion, the fractal dimension of the process (space filling character) driving anomalous diffusion as modeled by Bm-nlc positions or velocities does not change with the scaling exponent, γ.
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Ulrich, Michaël. "Construction of a free Lévy process as high-dimensional limit of a Brownian motion on the unitary group." Infinite Dimensional Analysis, Quantum Probability and Related Topics 18, no. 03 (September 2015): 1550018. http://dx.doi.org/10.1142/s0219025715500186.

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It is well known that freeness appears in the high-dimensional limit of independence for matrices. Thus, for instance, the additive free Brownian motion can be seen as the limit of the Brownian motion on hermitian matrices. More generally, it is quite natural to try to build free Lévy processes as high-dimensional limits of classical matricial Lévy processes. We will focus here on one specific such construction, discussing and generalizing the work done previously by Biane in Ref.2, who has shown that the (classical) Brownian motion on the Unitary group U(d) converges to the free multiplicative Brownian motion when d goes to infinity. We shall first recall that result and give an alternative proof for it. We shall then see how this proof can be adapted in a more general context in order to get a free Lévy process on the dual group (in the sense of Voiculescu) U〈n〉. This result will actually amount to a truly noncommutative limit theorem for classical random variables, of which Biane's result constitutes the case n = 1.
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Dissertations / Theses on the topic "Classical Brownian Motion"

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Romero-Rochin, Victor Manuel. "Brownian motion and weak coupling in classical and quantum systems." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14383.

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Lange, Rutger-Jan. "Brownian motion and multidimensional decision making." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243402.

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This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, 'Potential theory, path integrals and the Laplacian of the indicator', finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, 'The problem of alternatives', considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, 'Optimal support for renewable deployment', considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.
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Santos, Joao Rafael Lucio dos. "Tópicos em defeitos deformados e o movimento Browniano." Universidade Federal da Paraí­ba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/5748.

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The non-linear science is a central topic covering several investigation areas, such as biology, chemistry, mathematics and physics. In the first part of this thesis, we studied the non-linearity in the scope of classical field theory. The discussions are based on static solutions in (1, 1) space-time dimensions, and they are focused on kinks and lumps defects. In the related procedures, we show several techniques which allowed us to determine new models with their respective analytical solutions. The main mathematical tool to obtain these results is the so called deformation method, which was also an essential piece in the construction of a new extension method. This method presents the determination of new two scalar fields models from the coupling between two one scalar field systems. The method was analyzed carefully, as well as the linear stability, the zero modes, the total energy and the superpotentials, related with the new families of potentials. Furthermore, in the second part we presented the basics concepts about the Brownian Motion, where we analised the features of the solution of the Langevin Equation, and we also introduced a path integral approach to this problem in a quantum field theory way.
A ciência não-linear é tema central de diversas linhas de investigação, cobrindo áreas como a biologia, a física, a matemática e a química. Nossa primeira vertente de trabalho nesta tese, consiste no estudo de não-linearidades via abordagem de teoria clássica de campos. As discussões estão baseadas em soluções estáticas em (1, 1) dimensões, com destaque para o chamados defeitos tipo kink e lump. Nos procedimentos relatados, discorremos a respeito de diversas técnicas para a determinação de novos modelos com suas respectivas soluções analíticas. Um ferramental fundamental para a obtenção desses resultados é o chamado método de deformação, o qual também foi parte essencial para a criação de um método de extensão de modelos, onde visamos a construção de modelos de dois campos reais a partir do acoplamento entre dois modelos de um campo. Tal método também foi exposto em detalhes, bem como as análises sobre estabilidade linear, cálculo de modos zeros, determinação da energia total e dos superpotenciais, relativos às novas famílias de potenciais. Já a segunda linha de pesquisa, refere-se aos conceitos básicos do movimento browniano, onde analisamos as propriedades da solução da equação de Langevin, e na introdução de uma abordagem via integrais de trajetória para descrevê-lo nos moldes de teoria de quântica de campos.
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Dahlqvist, Antoine. "Dualité de Schur-Weyl, mouvement brownien sur les groupes de Lie compacts classiques et étude asymptotique de la mesure de Yang-Mills." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2014. http://tel.archives-ouvertes.fr/tel-00961035.

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On s'intéresse dans cette thèse à l'étude de variables aléatoires sur les groupes de Lie compacts classiques. On donne une déformation du calcul de Weingarten tel qu'il a été introduit par B. Collins et P. Sniady. On fait une étude asymptotique du mouvement brownien sur les groupes de Lie compacts de grande dimension en obtenant des nouveaux résultats de fluctuations. Deux nouveaux objets, que l'on appelle champ maître gaussien planaire et champ maître orienté planaire, sont introduits pour décrire le comportement asymptotique des mesures de Yang-Mills pour des groupes de structure de grande dimension.
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Macháček, Adam. "Oceňování bariérových opcí." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321410.

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In the presented thesis we study three methods of pricing European currency barrier options. With help of these methods we value selected barrier options with underlying asset EUR/CZK. In the first chapter we introduce the basic definitions from the world of financial derivatives and we describe our data. In the second chapter we deal with the classical model based on geometric Brownian motion of underlying asset and we prove a theorem of valuating Up-In-barrier option in this model. In the third chapter we introduce a model with stochastic volatility, the Heston model. We calibrate this model to market data and we use it to value our barrier options. In the last chapter we describe a jump diffusion model. Again we calibrate this jump diffusion model to market data and price our barrier options. The aim of this thesis is to decribe and to compare different methods of valuating barrier options. 1
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Books on the topic "Classical Brownian Motion"

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Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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Port, Sidney. Brownian Motion and Classical Potential Theory. Elsevier Science & Technology Books, 2012.

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Milonni, Peter W. An Introduction to Quantum Optics and Quantum Fluctuations. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199215614.001.0001.

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This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.
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Harmonic Analysis. American Mathematical Society, 2018.

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Book chapters on the topic "Classical Brownian Motion"

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Lampo, Aniello, Miguel Ángel García March, and Maciej Lewenstein. "Classical Brownian Motion." In SpringerBriefs in Physics, 7–18. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16804-9_2.

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Doob, Joseph L. "Brownian Motion." In Classical Potential Theory and Its Probabilistic Counterpart, 570–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56573-1_26.

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Doob, Joseph L. "Conditional Brownian Motion." In Classical Potential Theory and Its Probabilistic Counterpart, 668–702. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56573-1_29.

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D'Aristotile, Anthony, Persi Diaconis, and Charles M. Newman. "Brownian motion and the classical groups." In Institute of Mathematical Statistics Lecture Notes - Monograph Series, 97–116. Beachwood, OH: Institute of Mathematical Statistics, 2003. http://dx.doi.org/10.1214/lnms/1215091660.

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Glover, Joseph, and Murali Rao. "Inversion and Reflecting Brownian Motion." In Classical and Modern Potential Theory and Applications, 199–215. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1138-6_18.

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Doob, Joseph L. "Brownian Motion and Martingale Theory." In Classical Potential Theory and Its Probabilistic Counterpart, 627–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56573-1_28.

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Doob, Joseph L. "Brownian Motion and the PWB Method." In Classical Potential Theory and Its Probabilistic Counterpart, 719–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56573-1_31.

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Doob, Joseph L. "Brownian Motion on the Martin Space." In Classical Potential Theory and Its Probabilistic Counterpart, 727–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56573-1_32.

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Meilijson, Isaac. "Stochastic Orders and Stopping Times in Brownian Motion." In From Classical to Modern Probability, 207–20. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8053-4_6.

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Coffey, William T., Yuri P. Kalmykov, Serguey V. Titov, and William J. Dowling. "Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach." In Advances in Chemical Physics, 111–309. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118571767.ch3.

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Conference papers on the topic "Classical Brownian Motion"

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Nualart, David. "A white noise approach to fractional Brownian motion." In Stochastic Analysis: Classical and Quantum - Perspectives of White Noise Theory. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701541_0010.

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Mansour, Nastaran, Mehdi Mohammad Kazemi, Rouhollah Karimzadeh, and Javid Zamir Anvari. "Statistical Speckle Study of Copper Nanofluids." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18406.

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We report on a statistical analysis of copper nanofluid speckle image patterns. The far-field speckle images are formed by illuminating the copper nanoparticle (CuNP) suspension using low power continuous wave laser light at 532 nm. The nanofluids is prepared by nanosecond pulsed laser ablation of the highly pure copper target in polysiloxane oil. A stochastic approach based on the fractional Brownian motion and the classical frequential method is applied on the speckle patterns. These methods enable us to extract statistical parameters such as mean speckle size, Hurst coefficient and saturation of variance. Our results show that the mean speckle size remains unchanged with respect to time while the Hurst exponent and the saturation of variance exhibit changes. It has been shown that the stochastic approach makes it possible to characterize the copper nanofluid. The statistical analysis indicates that the Brownian motion of nanoparticles play important role in thermal properties of the copper nanofluids. Including the Brownian motion, the thermal conductivity of the copper nanofluids is calculated.
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Fishman, Louis. "Symbol Analysis and the Construction of One-Way Forward and Inverse Wave Propagation Theories." In Numerical Simulation and Analysis in Guided-Wave Optics and Opto-Electronics. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/gwoe.1989.se3.

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The analysis and fast, accurate numerical computation of the wave equations of classical physics are often quite difficult for rapidly changing, multidimensional environments extending over many wavelengths. This is particularly so for ocean seismo-acoustic environments characterized by a refractive index field with a compact region of arbitrary (n-dimensional) variability superimposed upon a transversely inhomogeneous ((n-1)-dimensional) background profile. For such environments, the entire domain is in the scattering regime, with the subsequent absence of an “asymptotically free” region. While classical, macroscopic methods have resulted in direct wave field approximations, derivations of approximate wave equations, and discrete numerical approximations, mathematicians studying linear partial differential equations have developed a sophisticated, microscopic phase space analysis centered about the theory of pseudo-differential and Fourier integral operators. In conjunction with the global functional integral techniques pioneered by Wiener (Brownian motion) and Feynman (quantum mechanics), and so successfully applied today in quantum field theory and statistical physics, the n-dimensional classical physics propagators can be both represented explicitly and computed directly. The phase space, or microscopic, methods and path (functional) integral representations provide the appropriate framework to extend homogeneous Fourier methods to inhomogeneous environments, in addition to suggesting the basis for the formulation and solution of corresponding arbitrary-dimensional nonlinear inverse problems.
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Harish, S., Kei Ishikawa, Erik Einarsson, Taiki Inoue, Shohei Chiashi, Junichiro Shiomi, and Shigeo Maruyama. "Enhanced Thermal Conductivity of Water With Surfactant Encapsulated and Individualized Single-Walled Carbon Nanotube Dispersions." In ASME 2012 Third International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/mnhmt2012-75021.

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In the present work, the effective thermal conductivity of single walled carbon nanotube dispersions in water was investigated experimentally. Single-walled carbon nanotubes (SWNTs) were synthesized using the alcohol catalytic chemical vapour deposition method. The diameter distribution of the SWNTs was determined using resonance Raman spectroscopy. Sodium deoxycholate (SDC) was used as the surfactant to prepare the nanofluid dispersions. Photoluminescence excitation spectroscopy (PLE) reveals that majority of the nanotubes were highly individualized when SDC was employed as the surfactant. The nanofluid dispersions were further characterized using transmission electron microscopy, atomic force microscopy (AFM) and optical absorption spectroscopy (OAS). Thermal conductivity measurements were carried out using a transient hot wire technique. Nanotube loading of up to 0.3 vol% was used. Thermal conductivity enhancement was found to be dependent on nanotube volume fraction and temperature. At room temperature the thermal conductivity enhancement was found to be non-linear and a maximum enhancement of 13.8% was measured at 0.3 vol% loading. Effective thermal conductivity was increased to 51% at 333 K when the nanotube loading is 0.3 vol%. Classical macroscopic models fail to predict the measured thermal conductivity enhancement precisely. The possible mechanism for the enhancement observed is attributed to the percolation of nanotubes to form a three-dimensional structure. Indirect effects of Brownian motion may assist the formation of percolating networks at higher temperature thereby leading to further enhancements at higher temperature.
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Ortigueira, Manuel Duarte, and Arnaldo Guimara˜es Batista. "A New Look at the Fractional Brownian Motion Definition." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35218.

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A reinterpretation of the classic definition of fractional Brownian motion leads to a new definition involving a fractional noise obtained as a fractional derivative of white noise. To obtain this fractional noise, two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives. For these derivatives the autocorrelation functions of the corresponding fractional noises have the same representations. The obtained results are used to define and propose a new simulation procedure.
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Reports on the topic "Classical Brownian Motion"

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Соловйов, В. М., В. В. Соловйова, and Д. М. Чабаненко. Динаміка параметрів α-стійкого процесу Леві для розподілів прибутковостей фінансових часових рядів. ФО-П Ткачук О. В., 2014. http://dx.doi.org/10.31812/0564/1336.

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Modem market economy of any country cannot successfully behave without the existence of the effective financial market. In the conditions of growing financial market, it is necessary to use modern risk-management methods, which take non-gaussian distributions into consideration. It is known, that financial and economic time series return’s distributions demonstrate so-called «heavy tails», which interrupts the modeling o f these processes with classical statistical methods. One o f the models, that is able to describe processes with «heavy tails», are the а -stable Levi processes. They can slightly simulate the dynamics of the asset prices, because it consists o f two components: the Brownian motion component and jump component. In the current work the usage of model parameters estimation procedure is proposed, which is based on the characteristic functions and is applied for the moving window for the purpose of financial-economic system’ s state monitoring.
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