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

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Presentation transcript:

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

Dispersive hydrodynamics Morning Glory Collective Field Theory (Non-Linear Bosonization) Hopf Equation, Benjamin-Ono equation Dispersive shock waves Witham modulations

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

Equations: Euler’s Hydrodynamics

Density Current, velocity

Schottky double

Hopf Equation:

Hopf equation Wave equation- a linearized version

Shock-wave solution

Classical limit of the quantum Hoph equation Benjamin-Ono equation

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 AustraliaBelieved to be Benjamin-Ono eq