Hawking radiation in 1D quantum fluids Stefano Giovanazzi bosons fermionsvs Valencia 2009.

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Presentation transcript:

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) reservoir 1D channel µLµL µRµR T=0 Hydrodynamic description …. ->

From the semiclassical to the hydrodynamic description

Thermal distribution of right-coming fermions reservoir 1D channel µLµL µRµR 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

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

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 kT H ≈ mc 2 ?

Thank you for listening ! bosons fermions vs SG, C. Farrell, T. Kiss, and U. Leonhardt, PRA 70, (2004); SG, PRL 94, (2005); SG, JPB 39, S109 (2006). ?