Hawking Corrections from Universal Planck Scale Physics and the Formation of Sonic Black Hole Horizons in Freely Expanding BECs

Date(s)
Monday 9th September 2024 (13:00-14:00)
Contact
Event Convenor Contact: Patrik.Svancara@nottingham.ac.uk

Description
Speaker's Name: Liam Farrell
Speaker's Affiliation: McMaster University
Speaker's Research Theme(s): NCoG,Mathematical Physics
Abstract:
In this talk I will discuss two separate projects that I have been working on: 1) Caustics are regions of high intensity created generically by the natural focusing of waves, and are universally described by catastrophe theory. Each distinct class of catastrophe is uniquely described by its own diffraction pattern, the simplest two being the Airy and Pearcey functions. A more exotic form of logarithmic wave singularity occurs near event horizons, which have acoustic analogues in quantum fluids such as Bose-Einstein condensates where Hawking radiation can be simulated. In such systems logarithmic singularities are regulated by taking into account non-linear dispersive effects, and are properly described by an Airy-type wave function supplemented by a logarithmic phase term. We find the presence of additional sub-dominant waves not yet predicted near the horizon. Our catastrophe theory motivated approach allows us to comment on the stability/universality of the Hawking effect and its inter-atomic length scale corrections to the Hawking spectrum (analogous to Planck scale corrections for gravitational Hawking radiation). 2) The second topic pivots from catastrophe theory and studies the free evolution of dilute BEC gases which have been initially trapped and released from box-like confining potentials. By numerically solving the Gross-Pitaevskii equation and analytically solving the hydrodynamic Thomas-Fermi theory, we find the presence of acoustic horizons within rarefaction waves which form in the outer edges of the BECs. We comment on the horizon dynamics, the formation of oscillations near the horizon, and connections to acoustic Hawking radiation.

Venue: B17 Physics and Teams
Online Conference Link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_Yjc3MmNhMGEtMzk1NC00ZTQ0LWE1NzgtY2IzNzA5NWJhMjQ4%40thread.v2/0?context=%7b%22Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%22cf0a8c52-3e98-48ff-9457-2bd97783fb39%22%7d

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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