Mathematik
Refine
Year of publication
- 2003 (2) (remove)
Document Type
- Conference Proceeding (2) (remove)
Language
- English (2)
Has Fulltext
- yes (2)
Is part of the Bibliography
- no (2)
Keywords
- Quantum Zeno dynamics (1)
- W*-dynamical system (1)
- X-Y model (1)
- quantum spin systems (1)
- return to equilibrium (1)
Institute
- Mathematik (2)
- Informatik (1)
Presentation at the Università di Pisa, Pisa, Itlay 3 July 2002, the conference on Irreversible Quantum Dynamics', the Abdus Salam ICTP, Trieste, Italy, 29 July - 2 August 2002, and the University of Natal, Pietermaritzburg, South Africa, 14 May 2003. Version of 24 April 2003: examples added; 16 December 2002: revised; 12 Sptember 2002. See the corresponding papers "Zeno Dynamics of von Neumann Algebras", "Zeno Dynamics in Quantum Statistical Mechanics" and "Mathematics of the Quantum Zeno Effect"
We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n exp 2 *(k/6) exp (k/4)) average time a shorter vector than b1 provided that b1 is (k/6) exp (n/(2k)) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method. n2