A dynamic systems approach to fermions and their relation to spins
Institute for Scientific Interchange Foundation, Via Alassio 11/c, Torino, 10126, Italy
2 Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, Bilbao, E-48080, Spain
3 Department of Computer Science, University College London, Gower St, London, WC1E 6BT, UK
4 Department Chemie, Technische Universität München, Lichtenbergstrasse 4, Garching, 85747, Germany
5 Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, Garching, 85748, Germany
* e-mail: email@example.com
Accepted: 21 July 2014
Published online: 11 September 2014
The key dynamic properties of fermionic systems, like controllability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. It just requires knowing drift and control Hamiltonians of an experimental set-up. Then one can easily determine all the states that can be reached from any given initial state. Likewise all the quantum operations that can be simulated with a given set-up can be identified. Observing the parity superselection rule, we treat the fully controllable and quasifree cases of fermions, as well as various translation-invariant and particle-number conserving cases. We determine the respective dynamic system Lie algebras to express reachable sets of pure (and mixed) states by explicit orbit manifolds.
PACS Codes: 03.67.Ac, 02.30.Yy, 75.10.Pq.
Key words: quantum simulation / control theory / fermionic systems / spin chains
© The Author(s), 2014