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PHY 770 -- Statistical Mechanics 12:00 * - 1:45 P M TR Olin 107

PHY 770 -- Statistical Mechanics 12:00 * - 1:45 P M TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course Webpage: http://www.wfu.edu/~natalie/s14phy770. Lecture 18 Chap. 7 – Brownian motion and other non-equilibrium phenomena Fokker-Planck equation examples

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PHY 770 -- Statistical Mechanics 12:00 * - 1:45 P M TR Olin 107

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  1. PHY 770 -- Statistical Mechanics 12:00*- 1:45 PM TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course Webpage: http://www.wfu.edu/~natalie/s14phy770 • Lecture 18 • Chap. 7 – Brownian motion and other non-equilibrium phenomena • Fokker-Planck equation examples • Linear response theory • Fluctuation-Dissipation Theorem *Partial make-up lecture -- early start time PHY 770 Spring 2014 -- Lecture 18

  2. PHY 770 Spring 2014 -- Lecture 18

  3. PHY 770 Spring 2014 -- Lecture 18

  4. PHY 770 Spring 2014 -- Lecture 18

  5. Probability analysis of Brownian motion -- Fokker-Planck equation friction coefficient PHY 770 Spring 2014 -- Lecture 18

  6. PHY 770 Spring 2014 -- Lecture 18

  7. Example solution in the limit of large friction PHY 770 Spring 2014 -- Lecture 18

  8. Example solution in the limit of large friction -- continued PHY 770 Spring 2014 -- Lecture 18

  9. Example solution for “free” particle V(x)=0 PHY 770 Spring 2014 -- Lecture 18

  10. Example solution for “free” particle V(x)=0 PHY 770 Spring 2014 -- Lecture 18

  11. Fluctuations about equilibrium response function PHY 770 Spring 2014 -- Lecture 18

  12. Linear response function PHY 770 Spring 2014 -- Lecture 18

  13. Linear response function -- simple example PHY 770 Spring 2014 -- Lecture 18

  14. “Proof” of Kramers-Kronig relations Im(z) a Re(z) PHY 770 Spring 2014 -- Lecture 18

  15. Kramers-Kronig transform -- continued Im(z) =0 a Re(z) PHY 770 Spring 2014 -- Lecture 18

  16. Kramers-Kronig transform -- continued PHY 770 Spring 2014 -- Lecture 18

  17. Kramers-Kronig transform -- continued PHY 770 Spring 2014 -- Lecture 18

  18. Fluctuation-Dissipation Theorem • Relationship of the response and correlation functions of a system near equilibrium; allows a weak external field to probe equilibrium fluctuations PHY 770 Spring 2014 -- Lecture 18

  19. Fluctuation-Dissipation Theorem -- continued HW #17 PHY 770 Spring 2014 -- Lecture 18

  20. Fluctuation-Dissipation Theorem -- continued HW #17 PHY 770 Spring 2014 -- Lecture 18

  21. Fluctuation-Dissipation Theorem -- continued PHY 770 Spring 2014 -- Lecture 18

  22. Fluctuation-Dissipation Theorem -- continued PHY 770 Spring 2014 -- Lecture 18

  23. Fluctuation-Dissipation Theorem -- example PHY 770 Spring 2014 -- Lecture 18

  24. Fluctuation-Dissipation Theorem -- example PHY 770 Spring 2014 -- Lecture 18

  25. Microscopic linear response theory 0 PHY 770 Spring 2014 -- Lecture 18

  26. Microscopic linear response theory -- continued PHY 770 Spring 2014 -- Lecture 18

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