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Elsevier eBooks

Spin states of particles with spin ½. The density matrix of spin-½ particles

Published Jan 1, 1982• 0 citations
Publisher
DOI
10.1016/b978-0-08-026502-5.50013-6

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The density matrix of an arbitrary pure state of a system consisting of two spin‐1/2 particles is derived from the Pauli spin angular momentum operators. Mixed singlet and triplet states are then formed from linear combinations of pure states and their corresponding density matrices constructed. Singlet and triplet states are exemplified by the spin isomers parahydrogen and orthohydrogen, respectively. Partial mixing is illustrated with the example of bilinear spin–spin coupling. Various properties of the density matrices of pure and mixed states are discussed, including idempotence, factoring, and spin correlation.
The dynamics of a maximally entangled pair of spin-1/2 particles is obtained in the presence of random magnetic fields which are correlated. The two spin-1/2 particles are assumed to be maximally entangled initially and are then disturbed by the magnetic fields modeled as Gaussian vector random processes whose corresponding spatial components are correlated. The dynamics is derived in terms of the joint density matrix of the entangled pair using the ideas of stochastic calculus, from which the steady-state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix represents a state of (partial) disentanglement.