Finite-Size Effects in Integrable Systems - Lecture 3

Finite-Size Effects in Integrable Systems - Lecture 3

International Centre for Theoretical Sciences via YouTube Direct link

Q&A

25 of 25

25 of 25

Q&A

Class Central Classrooms beta

YouTube videos curated by Class Central.

Classroom Contents

Finite-Size Effects in Integrable Systems - Lecture 3

Automatically move to the next video in the Classroom when playback concludes

  1. 1 Start
  2. 2 Relaxation of time averages & the "Diagonal Ensemble"
  3. 3 It is believed that for local observables
  4. 4 diagonal ensemble
  5. 5 Finite-size effects: traversals & revivals
  6. 6 This "traversal" is a generic effect and is very different from a revival:
  7. 7 Revivals are related to regularities in the spectrum of H:
  8. 8 Example:
  9. 9 Revivals in split ID Bose gases
  10. 10 Exercise: [Requires Mathematica to plot]
  11. 11 VI. Macro states & conservation laws in free theories
  12. 12 Mode occ. #s are conserved & related to extensive cons. laws with local densities
  13. 13 Macro states in the thermodynamic limit
  14. 14 Expectation values of local operators in macro states
  15. 15 Generalized Micro-Canonical Ensemble
  16. 16 Counting the number of micro states in a large, finite L thhat correspond to the same macro state nk
  17. 17 Thermodynamic entropy
  18. 18 A. Energy eigenstates
  19. 19 Solve the Schrodinger eqn
  20. 20 B. Analog of Occupation numbers: "String Hypothesis"
  21. 21 Composition principle:
  22. 22 C. Analogs of particle/hole densities
  23. 23 Each set of positive functions
  24. 24 VIII. Conservation laws in interacting integrable models Example:
  25. 25 Q&A

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.