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DY: Fachverband Dynamik und Statistische Physik

DY 28: Statistical Physics far from Equilibrium

DY 28.6: Talk

Thursday, March 17, 2011, 11:30–11:45, HÜL 186

Monte-Carlo sampling of energy-constrained quantum superpositions in high-dimensional Hilbert spaces — •Frank Hantschel and Boris Fine — Institute for Theoretical Physics, Heidelberg, Germany

The quantum microcanonical (QMC) ensemble is an alternative to conventional statistical ensembles, which results in a deviation from the usual Gibbs distribution. The resulting statistics is computed by performing a Monte-Carlo simulation on high-dimensional Hilbert space.

A straightforward Monte-Carlo routine would enclose the energy constrained manifold within a larger manifold, which is easy to sample, e.g., a hypercube. We observed that the efficiency of such a sampling routine decreases exponentially with the increase of the dimension of the Hilbert space, because the volume of the enclosing manifold becomes exponentially larger than the volume of the manifold of interest. This fact imposes a problem, because it strongly limits the size of the system of interest.

The talk explores the ways to optimize the above routine by varying the shapes of the manifolds enclosing the energy-constrained manifold. The resulting improvement in the sampling efficiency is about a factor of five for a 14-dimensional Hilbert space. The advantage of the above algorithm is that it does not compromise on the rigorous statistical nature of the sampling outcome and hence can be used to test other more sophisticated Monte-Carlo routines. The present attempts to optimize the enclosing manifolds also bring insights into the geometrical properties of the energy-constrained manifold itself.