caa a22 4500 445865725 CHVBK 20180317145457.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1140/epjd/e2011-10673-7 doi (NATIONALLICENCE)springer-10.1140/epjd/e2011-10673-7 MonteCarlo sampling of energy-constrained quantum superpositions in high-dimensional Hilbert spaces [Elektronische Daten] [F. Hantschel, B. Fine] Recent studies into the properties of quantum statistical ensembles in high-dimensional Hilbert spaces have encountered difficulties associated with the MonteCarlo sampling of quantum superpositions constrained by the energy expectation value. A straightforward MonteCarlo routine would enclose the energy constrained manifold within a larger manifold, which is easy to sample, for example, a hypercube. 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. The present paper explores the ways to optimise 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 MonteCarlo routines. The present attempts to optimise the enclosing manifolds also bring insights into the geometrical properties of the energy-constrained manifold itself. EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2011 Hantschel F. Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120, Heidelberg, Germany aut Fine B. Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120, Heidelberg, Germany aut The European Physical Journal D Springer-Verlag 63/1(2011-06-01), 73-80 1434-6060 63:1<73 2011 63 10053 https://doi.org/10.1140/epjd/e2011-10673-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1140/epjd/e2011-10673-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hantschel F. Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120, Heidelberg, Germany aut NATIONALLICENCE 700 1- Fine B. Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120, Heidelberg, Germany aut NATIONALLICENCE 773 0- The European Physical Journal D Springer-Verlag 63/1(2011-06-01), 73-80 1434-6060 63:1<73 2011 63 10053 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer