1 / 26

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

micah-vance
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related