Singularities in hydrodynamics of degenerate 1D quantum systems

P. Wiegmann

Together with Abanov

How does a wave packet propagate in degenerate Fermi gas?

degenerate Bose gas?

Free fermions in 1D

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

Burgers

Semiclassics:

single particle: quantum mechanics

Burgers

Hopf -Riemann

Benjamin-Ono

Fermi-sea: quantum field theory

Initial coherent state

Evolving coherent state

tau-function ( a decay rate)

momentum

Benjamin-Ono equation and hierarchy

QuickTime™ and aGIF decompressor

are needed to see this picture.

True, non-linearized hydrodynamics Hamiltonian

Jevicki, Sakita, Polchinsky, .........

Free fermions:

Hopf equation

Wave equation- a linearized version

Shock-wave solution

Witham modulation

Periodic solution

Modulation

Shock wave

Distribution of solitons is sensitive to initial data

Morning Glory

Arena for observation:

cooled alkali atomic gases

Chain of rolling cloudsMorning glory

South Australia Believed to be Benjamin-Ono eq