Hawking radiation in 1D quantum fluids Stefano Giovanazzi bosons fermions vs Valencia 2009
Dec 21, 2015
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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