1. Quantum Shock Waves Hydrodynamic Singularities in Degenerate 1D quantum systems P. Wiegmann Together with Alexander Abanov

2. How does a wave packet propagate in degenerate Fermi gas? degenerate Bose gas?

3. Free fermions in 1D A smooth bump in density or momenta: all gradients << Fermi scale

4. A single particle: Wave packet consisting of a single particle diffuses

5. Does quantum coherence (or Fermi sea) make an impact?

6. Can this question be answered by elementary means? Free Fermions

7. Hydrodynamics of quantum coherent systems (traditionally called bosonization): String theory Methods: Integrable hierarchies /matrix models

8. Hydrodynamics: to express particles (fermions or bosons) through hydrodynamics (bosonic) modes: Bose Field

9. Initial (coherent) state Evolving state Matrix element

10. Integrability - Free Fermions Tau-function of KP-hierarchy Miwa, Jimbo, Date Virasoro currents ;

11. Currents of -algebra KP-hierarchy Benjamin-Ono hierarchy

12. bosonization - linear hydrodynamics: Linearisation of the spectrum: Shape does not change!?

13. Dispersion - asymmetry between particles and holes

15. Benjamin-Ono-equation Free Fermions =

17. Quantum degenerate (or coherent) systems obey dispersive non-dissipative hydrodynamics

18. dispersive non-dissipative hydrodynamics KdV - equation Non-periodic, non-soliton solution

19. Hopf equation Wave equation- a linearized version

20. Shock-wave solution

22. Burgers Semiclassics: single particle: quantum mechanics

23. Burgers Hopf -Riemann Benjamin-Ono Fermi-sea: quantum field theory

24. Witham Modulation

25. Witham modulation Periodic solution Modulation Shock wave

30. True, non-linearized hydrodynamics Hamiltonian Jevicki, Sakita, Polchinsky,......... Free fermions: = Non-linear bosons

31. Equations: Euler’s Hydrodynamics

32. Density Current, velocity

33. Schottky double

34. Hopf Equation:

35. Benjamin-Ono equation for matrix element Quantum Hopf equation for operators

36. Distribution of solitons is sensitive to initial data

37. Arena for observation: cooled alkali atomic gases

39. Chain of rolling cloudsMorning glory South AustraliaBelieved to be Benjamin-Ono eq

40. Morning Glory