PHY 770 Spring 2014 Lecture 16 1 PHY 770 Statistical Mechanics 1200 145 P M TR Olin 107 Instructor Natalie Holzwarth Olin 300 Course Webpage httpwwwwfuedunatalies14phy770 ID: 367209
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PHY 770 Spring 2014 -- Lecture 16
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PHY 770 -- Statistical Mechanics12:00* - 1:45 PM TR Olin 107Instructor: Natalie Holzwarth (Olin 300)Course Webpage: http://www.wfu.edu/~natalie/s14phy770
Lecture 16Chap. 7 – Brownian motion and other non-equilibrium phenomenaOverviewLangevin equationCorrelation function and spectral densityFokker-Planck equation
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Partial make-up lecture -- early start time Slide2
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http://famousbiologists.org/robert-brown/Slide6
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Brownian motion:Phonomenon: Under a microscope a large particle (~1 m in diameter) immersed in a fluid with the same density as the particle, appears to be in a state of agitation, undergoing rapid and random motions.
http://upload.wikimedia.org/wikipedia/commons/c/c2/Brownian_motion_large.gifSlide7
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Brownian motion:Description based on the Langevin equation of motion
friction coefficientSlide8
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Brownian motion and Langevin equation of motion -- continuedSlide9
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Brownian motion and Langevin equation of motion – continued Note that since x(t) is a stochastic variable, so is v(t) and x(t)Slide10
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Brownian motion and Langevin equation of motion – continued Note that since x(t) is a stochastic variable, so is v(t) and x(t)Slide11
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Brownian motion and Langevin equation of motion – continued It is interesting to take the Fourier transform of the correlation functionSlide12
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Example of Brownian systemConsider a particle of mass m attached to a harmonic spring with spring constant mw02 constrained to move in one dimension:Slide13
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Example of Brownian system -- continuedSlide14
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Example of Brownian system -- continuedSlide15
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Example of Brownian system -- continuedSlide16
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Example of Brownian system -- continued
wSlide17
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Probability analysis of Brownian motion Fokker-Planck equationSlide18
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equation
xv
SSlide19
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equationSlide20
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equationSlide21
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equationSlide22
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equationSlide23
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equationSlide24
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Probability analysis of Brownian motion Fokker-Plank equationJustification of Fokker-Plank equation