Singularities in hydrodynamics of degenerate 1 D quantum

Singularities in hydrodynamics of degenerate 1 D quantum systems P. Wiegmann Together with Abanov

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

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

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

Does quantum coherence (or Fermi sea) make an impact

Can this question be answered by elementary means?

• Hydrodynamics of quantum coherent systems (traditionally called bosonization): • String theory (tachion dynamics); • Methods: Integrable hierarchies /matrix models

Hydrodynamics: to express particles (fermions or bosons) through hydrodynamics (bosonic) modes:

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

Dispersion asymmetry between particles and holes

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

Semiclassics: single particle: quantum mechanics Burgers

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

Initial coherent state Evolving coherent state tau-function ( a decay rate) momentum Benjamin-Ono equation and hierarchy

True, non-linearized hydrodynamics Hamiltonian Free fermions: Jevicki, Sakita, Polchinsky, . .

Hopf equation Wave equation- a linearized version

Shock-wave solution

Shock wave Witham modulation Periodic solution Modulation

Distribution of solitons is sensitive to initial data

Morning Glory

Arena for observation: cooled alkali atomic gases

Morning glory South Australia Chain of rolling clouds Believed to be Benjamin-Ono eq