1. Equations for free fermion correlators out of equilibrium
E. B.
P. Wiegmann
A. Abanov
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2. Shock wave physics E. g., The KdV Equation: Neglecting Dispersion:
How and why should it apply to Fermi systems?

3. Overturning in Fermi gas
Wigner function p vF pF x
Dynamics
Density E p

4. + Dispersive effects A typical Wigner function: p x pF v Nonlinearity
Dispersion +
Hopf

5. Generating functions Density too simple r p
Need more complicated correlation functions:
Appear in physical problems: Fermi Edge singularity, counting statistics r p x x

6. Math of Integrable shocks
Christie
Three fermi points may serve as moduli

7. Fermi points as moduli
Christie
Three fermi points may serve as moduli

8. Recap Free Fermions display wave overturning
Integrability may allow to place Fermionic shock waves in general mathematical context
Must obtain integrable equations for more complicated objects than density
Korepin, Izergin, Slavnov, Its, Göhnmann obtained integrable Eqs in equilibrium

9. Quantum Hopf Equation
Correct in the limit where excitations only scratch the surface
Hopf in components:
Proof:
seperate
Two Fermion
Four Fermionc

10. The equation Define: We prove mKP: Hirota Derivative:
Can be written in the form:
Semiclassically

11. Outline of the proof Dynamics: Refermionization:
add slide about whitham 11

12. Conclusion
Integrable nonlinear equation is derived for free fermionic correlators
Must find appropriate solutions relevant to different physical problems
Consistent with the notion that shocks appear which have simple Fermi point moduli