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Short time density fluctuations
Miroslaw Brewczyk, Uniwersytet w
Bialymstoku Mariusz Gajda, IF PAN,
Warsaw Kazimierz Rzazewski, CFT, Warsaw
Torun 18-19.05.2007
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Considered problems

• excitation spectrum of a uniform weakly
  interacting Bose gas
• photoassociation of molecules
• dissipative dynamics of a vortex
• decay of multiply charged vortex
• phase coherence of a condensate at finite
  temperatures
• determination of the critical velocity for
  superfluidity
• dynamics of spinor condensates at finite
  temperatures

M. Brewczyk, M. Gajda, K. Rzazewski, J. Phys. B
40, R1 (2007)
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Condensate in a periodic box
Initial condition we choose randomly the complex
amplitudes and evolve the system
The system reaches the equilibrium
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Our strategy

• choose the suitable spatial grid (the spatial
  step must be of the
• order of thermal wavelength)
• calculate the ground state of GP equation (using
  the imaginary
• time propagation technique)
• scramble the ground state wave function by
  randomly disturbing
• the amplitude and/or the phase to inject the
  desired amount of
• energy to the system
• evolve the solution to reach the equilibrium
• diagonalize the coarse-grained one-particle
  density matrix

J. Phys. B 40, R1 (2007)
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One-particle density
instantaneous distribution after
the coarse graining
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Condensate and the thermal cloud
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Spatial versus momentum distribution
spatial density
momentum density
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Is it real?