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