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Dynamical Theories of Brownian Motion
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Edward Nelson
Language:
English
Published/Copyright:
2020
About this book
These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.
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Frontmatter
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CONTENTS
iii -
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§1. Apology
1 -
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§2. Robert Brown
5 -
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§3. The period before Einstein
11 -
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§4. Albert Einstein
17 -
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§5. Derivation of the Wiener process
23 -
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§6. Gaussian processes
33 -
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§7. The Wiener integral
37 -
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§8. A class of stochastic differential equations
43 -
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§9. The Ornstein-Uhlenbeck theory of Brownian motion
53 -
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§10. Brownian motion in a force field
63 -
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§11. Kinematics of stochastic motion
79 -
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§12. Dynamics of stochastic motion
101 -
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§13. Kinematics of Markoffian motion
103 -
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§14. Remarks on quantum mechanics
107 -
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§15. Brownian motion in the aether
129 -
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§16. Comparison with quantum mechanics
137
Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 24, 2021
eBook ISBN:
9780691219615
Pages and Images/Illustrations in book
eBook ISBN:
9780691219615
Keywords for this book
Brownian motion; Quantum mechanics; Theory; Wiener process; Probability; Schrödinger equation; Wave function; Stochastic process; Quantum superposition; Wave–particle duality; Quantum field theory; Langevin equation; Heisenberg picture; Special relativity; Newton's laws of motion; Statistical mechanics; Quantum statistical mechanics; Random variable; Theory of relativity; Probability space; Kinetic theory of gases; Newton's law of universal gravitation; Boltzmann constant; Uncertainty principle; Colloid; Mechanics; Theoretical physics; Equipartition theorem; Measurement; Hilbert space; Infinitesimal generator (stochastic processes); Atomic theory; Wave packet; Fokker–Planck equation; Gaussian process; Classical mechanics; Markov chain; Measurement in quantum mechanics; Stochastic differential equation; Quantum state; Electron diffraction; Commutative property; Fermion; Martingale (probability theory); Stochastic; Molecule; Scalar potential; Gaussian measure; Probability theory; Unitary representation; Lebesgue measure; Vibration; Eigenfunction; Physicist; Photon; Richard Feynman; Configuration space; Kinematics; Oscillation; Power series; Free particle; Covariance matrix; Phase space; Hypothesis; Fourier analysis; Variable (mathematics); Equation; Number density; Linear motion; Joint probability distribution
Audience(s) for this book
For an expert adult audience, including professional development and academic research
