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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