singularities in hydrodynamics of degenerate 1d quantum systems p. wiegmann together with abanov
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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