project title: Universality of the Hawking Effect - Superfluid Helium Analogues
project leader: Dr. Ralf Schuetzhold and Mrs Sarah Mostame
access given (in days): 92
access used (in days): 30
local host: Prof. Grigory Volovik
home institution: Institut fuer Theoretische Physik, Technische Universitaet Dresden
country of institution: Germany
starting date (yyyy-mm-dd): 2004-04-15
The objective was to investigate the potential impact of short-scale (e.g., trans-Planckian) degrees of freedom on large-scale phenomena such as Hawking radiation by means of the analogy between quantum fields in curved space-times on the one hand and quantised quasiparticle excitations in condensed matter systems such as superfluid Helium on the other hand.
In this project we concluded during the first reporting period that the Hawking effect is basically unaffected in black hole analogues within Bose-Einstein condensates -whereas black hole analogues within superfluid Helium may generate deviations from the usual thermal spectrum in view of the non-monotonic dispersion relation ('roton' dip) as well as a possible coupling with respect to the rest frame (container walls) instead of the freely falling frame (fluid frame). During the reporting period the above results were developed and applied to the scenario of cosmic inflation, where similar questions are of interest (see Michael Uhlmann, Yan Xu and Ralf Schützhold, "Aspects of Cosmic Inflation in Expanding Bose-Einstein Condensates", New J. Phys. 7, 248 (2005)). Detectability of quantum radiation using atomic Bose-Einstein condensates has been susggested by Ralf Schützhold in his resent reprint arXiv:quant-ph/0602180. In these 2 papers the financial support of ULTI project has been acknowledged. During the fourth reporting period the similarity between adiabatic quantum algorithms and quantum phase transitions has been exploited in the paper by Gernot Schaller and Ralf Schuetzhold "The role of symmetries in adiabatic quantum algorithms" arXiv:0708.1882. In this paper the financial support of ULTI project has been acknowledged. The authors argued that second-order transitions - typically associated with broken or restored symmetries - should be advantageous for adiabatic quantum computation. A symmetry-restoring adiabatic quantum algorithm has been constructed. It only contains contributions linear and quadratic in the Pauli matrices and can easily be generalized to other problem Hamiltonians which are decomposed of terms involving one and two qubits.