Singularities in hydrodynamics of degenerate 1D quantum systems

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Singularities in hydrodynamics of degenerate 1D
quantum systems
P. Wiegmann
Together with Abanov
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How does a wave packet propagate in degenerate
Fermi gas?
degenerate Bose gas?
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Free fermions in 1D
A smooth bump in density or momenta all
gradients ltlt Fermi scale
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A single particle
Wave packet consisting of a single particle
diffuses
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Does quantum coherence (or Fermi sea) make an
impact?
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Can this question be answered by elementary
means?
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• Hydrodynamics of quantum coherent systems
  (traditionally called bosonization)
• String theory (tachion dynamics)
• Methods Integrable hierarchies /matrix models

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Hydrodynamics to express particles (fermions
or bosons)
through hydrodynamics (bosonic) modes
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bosonization - linear hydrodynamics
Linearisation of the spectrum
Shape does not change!?
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Dispersion - asymmetry between particles and
holes
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Quantum degenerate (or coherent) systems obey
dispersive non-dissipative hydrodynamics
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Semiclassics
single particle quantum mechanics
Burgers
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Burgers
Fermi-sea quantum field theory
Benjamin-Ono
Hopf -Riemann
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Initial coherent state
Evolving coherent state
tau-function ( a decay rate)
momentum
Benjamin-Ono equation and hierarchy
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• Dispersive hydrodynamics
• Morning Glory
• Collective Field Theory (Non-Linear Bosonization)
• Hopf Equation, Benjamin-Ono equation
• Dispersive shock waves
• Witham modulations

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True, non-linearized hydrodynamics Hamiltonian
Free fermions
Jevicki, Sakita, Polchinsky, .........
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Equations Eulers Hydrodynamics
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Density
Current, velocity
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Schottky double
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Hopf Equation
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Hopf equation
Wave equation- a linearized version
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Shock-wave solution
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Classical limit of the quantum Hoph equation
Benjamin-Ono equation
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Shock wave
Witham modulation
Periodic solution
Modulation
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Distribution of solitons is sensitive to
initial data
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Morning Glory
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Arena for observation cooled alkali
atomic gases
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Chain of rolling clouds
Morning glory
South Australia
Believed to be Benjamin-Ono eq