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Studies in fuzziness and soft computing

Quantum Dynamics of Non Commutative Algebras: The SU(2) Case

Claudia M. Sarris, Araceli N. Proto

Published Jan 1, 2010• 0 citations
Publisher
DOI
10.1007/978-3-642-15976-3_20

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In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schrödinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian) commutators. These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.