Hawking radiation in 1D quantum fluids
Stefano Giovanazzi
bosons fermionsvs
Valencia 2009
From Cennini et al.Tuebingen
How to make subsonic to supersonic transitions ?
The Atom laser is a beautiful example of a sonic black hole.
… before starting with 1D stuff …
•Why 1D?
•Why fermions?
•Introducing the non-ideal flow of non-interacting fermions
•Superfluidity in 1D? Bosons vs fermions
•Presenting an exact microscopic model for Hawking radiation
•Hawking temperature: Bosons vs fermions
Description of the flow of non-interacting fermions
The many-particles wave-function can be easily written as a Slater determinant (scattering description)
reservoirreservoir1D channel
µL µR
T=0 T=0
Hydrodynamic description …. ->
From the semiclassical to the hydrodynamic description
Thermal distribution of right-coming fermions
reservoirreservoir1D channel
µL µR
T=0 T≠0
What happens if the reservoir on the right is replaced by a sonic event horizon with a non-negligible Hawking temperature?
Reflection coefficient from the very smooth barrier
What are the quantum effects?
where is related to the curvature of the potential barrier
V (x) ≈V(0) +12mω x
2x2
ω x
Reflection coefficient from the very smooth barrier
What are the quantum effects?
Expressing Hawking temperature in terms of the external potential parameters
Using hydrodynamics of a general 1D quantum fluid is possible to prove that
where for a 1D Bose gas in the mean field regime
and for a 1D Bose gas in the Tonks-Girardeau regime or for 1D non-interacting Fermi gas
η =3
4
η =1
Aspects of Hawking radiations:
• Statistic of fluid’s particles plays no role in Hawking temperature formula
• Correlations on opposite side of the event horizon
• Incoherence of the radiation when probed only on one side of the horizon
• Thermal distribution
Which are the aspects that survives kTH ≈ mc2 ?
Thank you for listening !Thank you for listening !
bosonsfermions
vs
SG, C. Farrell, T. Kiss, and U. Leonhardt, PRA 70, 063602 (2004);SG, PRL 94, 061302 (2005); SG, JPB 39, S109 (2006).
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