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Singularities in hydrodynamics of degenerate 1D quantum systems

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.

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Singularities in hydrodynamics of degenerate 1D quantum systems

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

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

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

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

  10. Dispersion - asymmetry between particles and holes

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

  12. Semiclassics: single particle: quantum mechanics Burgers

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

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

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

  16. Hopf equation Wave equation- a linearized version

  17. Shock-wave solution

  18. Shock wave Witham modulation Periodic solution Modulation

  19. Distribution of solitons is sensitive to initial data

  20. Morning Glory

  21. Arena for observation: cooled alkali atomic gases

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

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