Equations for free fermion correlators out of equilibrium E. B. P. Wiegmann A. Abanov TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA

Shock wave physics E. g., The KdV Equation: Neglecting Dispersion: How and why should it apply to Fermi systems?

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

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

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

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

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

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

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

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

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

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