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Relevant bibliographies by topics / Classical Brownian Motion

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Journal articles

Academic literature on the topic 'Classical Brownian Motion'

Author: Grafiati

Published: 7 September 2023

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Journal articles on the topic "Classical Brownian Motion"

1

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

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2

Ord, G. N. "Schrödinger's Equation and Classical Brownian Motion." Fortschritte der Physik 46, no. 6-8 (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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3

Tsekov, Roumen. "Brownian Motion and Quantum Mechanics." Fluctuation and Noise Letters 19, no. 02 (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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4

Santos, Willien O., Guilherme M. A. Almeida, and Andre M. C. Souza. "Noncommutative Brownian motion." International Journal of Modern Physics A 32, no. 23n24 (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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5

Rajput, B. S. "Quantum equations from Brownian motion." Canadian Journal of Physics 89, no. 2 (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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6

Anders, J., C. R. J. Sait, and S. A. R. Horsley. "Quantum Brownian motion for magnets." New Journal of Physics 24, no. 3 (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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7

Ambegaokar, Vinay. "Quantum Brownian Motion and its Classical Limit." Berichte der Bunsengesellschaft für physikalische Chemie 95, no. 3 (1991): 400–404. http://dx.doi.org/10.1002/bbpc.19910950331.

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8

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 (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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9

PARK, MOONGYU, and JOHN H. CUSHMAN. "THE COMPLEXITY OF BROWNIAN PROCESSES RUN WITH NONLINEAR CLOCKS." Modern Physics Letters B 25, no. 01 (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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10

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 (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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