Black Hole phenomena in Quantum Hall Systems 2: The Hawking-Unruh effect

In this talk, we present a parallel between dynamics in quantum Hall systems and the Hawking-Unruh effect associated with black holes. Hawking-Unruh radiation can be looked upon as a thermal distribution that arises from a Bogoliubov transformation generated by the Rindler Hamiltonian, corresponding to accelerated observers. We show that the Rindler Hamiltonian is functionally identical to that of Hamiltonian governing electrons in the lowest Landau level in the presence of a saddle potential. We show that this arises from a deeper connection between the symmetries of the two disparate systems – the isomorphism between the lie algebras of the 2+1D Lorentz group and that of SL(2,R) group of area- preserving transformations. This connection further allows us to see quantum Hall phenomena in the light of Lorentz kinematics.