2. 1. Introduction Solid state physics Model-building Use of general principles crystallographers Drude and Sommerfeld model Improved model Fermi-liquid theory Explanation of superconductivity Kepler

3. 1. Introduction Solid state physics Model-building Use of general principles Nyquist formula Onsager reciprocity relations Fluctuation-dissipation theorem Linear response theory Detailed balance Universality Fluctuation relation

4. 1. Introduction Consider a time-reversal-invariant system Prob. Consider a process made of the following three steps: 1)The initial state of the system is measured; 2)The system undergoes unitary evolution; 3)The final state is determined through measurement. There is a simple relation between the two prob.

5. 1. Introduction System N S Prob. Fluctuation relation?

6. 1. Introduction Chirality -Excitation can propagate in one direction only. Ex) The edges of certain quantum Hall liquids, Chiral transport in the quantum Hall effect(QHE) Causality principle : the past do not affected by the future. In the chiral case, the right do not affected by the past on the left. RL

7. 2. Fluctuation theorems The typical form of the fluctuation theorem The definitions of the forward and backward processes 1)Initially in both processes, the system obeys a Gibbs distribution 2)The dynamical equations in the backward process is obtained from the dynamical equations in the forward process by the time-reversal operation.

8. 2. Fluctuation theorems 0 t with

9. 2. Fluctuation theorems with Backward process Eigenstates

10. 2. Fluctuation theorems Since

11. 3. Saito-Utsumi relations 1) The electric current 2) The noise power 3) The third cumulant

12. 3. Saito-Utsumi relations 3.1 Symmetric and antisymmetric variables definition The linear conductance is an even function The equilibrium noise power does not depend on the direction of B

13. 3. Saito-Utsumi relations 3.2 Fluctuation relations for symmetric variables definition Nyquist formula

14. 3. Saito-Utsumi relations 3.3 Fluctuation relations for antisymmetric variables

15. 3. Saito-Utsumi relations 3.4 Microreversiblity

16. 3. Saito-Utsumi relations 3.5 Experiment

17. 4. Chiral systems

18. 5. Fluctuation relations in chiral systems 5.1 Qualitative argument

20. 5. Fluctuation relations in chiral systems 5.2 Toy model

21. 5. Fluctuation relations in chiral systems 5.3 General derivation

23. 5. Fluctuation relations in chiral systems 5.3 Generalizations

24. 5. Fluctuation relations in chiral systems 5.4 Applications