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 
status:  COMPLETED 
local host:  Prof. Grigory Volovik 
home institution:  Institut fuer Theoretische Physik, Technische Universitaet Dresden 
country of institution:  Germany 
starting date (yyyymmdd):  20040415 
objectives:  The objective was to investigate the potential impact of shortscale
(e.g., transPlanckian) degrees of freedom on largescale phenomena
such as Hawking radiation by means of the analogy between quantum
fields in curved spacetimes on the one hand and quantised
quasiparticle excitations in condensed matter systems such as
superfluid Helium on the other hand.

achievements:  In this project we concluded during the first reporting period that the Hawking effect is basically unaffected in black hole analogues within BoseEinstein condensates whereas black hole analogues within superfluid Helium may generate deviations from the usual thermal spectrum in view of the nonmonotonic 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 BoseEinstein Condensates", New J. Phys. 7, 248 (2005)). Detectability of quantum radiation using atomic BoseEinstein condensates has been susggested by Ralf Schützhold in his resent reprint arXiv:quantph/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 secondorder transitions  typically associated with broken or restored symmetries  should be advantageous for adiabatic quantum computation. A symmetryrestoring 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.
