A time-dependent variational principle for dissipative dynamics

We extend the time-dependent variational principle to the setting of dissipative dynamics. This provides a locally optimal (in time) approximation to the dynamics of any Lindblad equation within a given variational manifold of mixed states. In contrast to the pure-state setting there is no canonical information geometry for mixed states and this leads to a family of possible trajectories --- one for each information metric. We focus on the case of the operationally motivated family of monotone riemannian metrics and show further, that in the particular case where the variational manifold is given by the set of fermionic gaussian states all of these possible trajectories coincide. We illustrate our results in the case of the Hubbard model subject to spin decoherence.Comment: Published versio

A mechanism for pair formation in strongly correlated systems

We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.Comment: 13 pages, corrected some notations and made some clarification

"Australopithecus afarensis" and A. Africanus: Critique and an alternative hypothesis

Main articleDuring the seventies, a succession of East African discoveries has been claimed to represent the "true" ancestral line of modern man, thus relegating A. africanus, and especially its Transvaal subspecies, to a subordinate role in hominid phylogeny. The latest such attempt has been the claim of Johanson and his co-workers that the 3, 7-2,6 My-old hominids of Laetoli in Tanzania and of Hadar in Ethiopia represent a new species, "A. afarensis", which led to H. habilis, whilst A. africanus represents early stages in a specialized side-branch leading to A. robustus and A. boisei. A critique of the diagnostic criteria of "A. afarensis" reveals that on the available evidence, the Laetoli and Hadar fossils cannot be distinguished at specific level from A. africanus transvaalensis. Furthermore, it is by no means clear that the pooling for statistical and comparative purposes of the Hadar and Laetoli fossils is justified. Hominids from the two sites are separated by about 800 000 years and about 1 600 km as well as by morphometric differences. As an alternative hypothesis, it is proposed that the Laetoli and Hadar hominids belong to the same lineage as that represented by the hominids of Makapansgat Members 3 and 4 and of Sterkfontein Member 4. Moreover, it is hypothesized that the Laetoli and Hadar hominids cannot be separated morphologically from A. africanus and that they represent two new subspecies of that species. Since "A. afarensis" is tied to a Laetoli specimen as holotype, only the Laetoli specimens should be designated A. africanus afarensis (though A. africanus tanzaniensis suggested by the author in 1978 would have been a more appropriate nomen) and the Hadar fossils A. africanus aethiopicus. These newest East African discoveries afford strong confirmation of the hypothesis that A. africanus is the common ancestor of the two later hominid lineages, A. robustuslboisei and Homo, leading from H. habilis through H. erectus to H. sapiens.The Council for Scientific and Industrial research, the University of the Witwatersrand Council Research Committee, and the Bernard Price Institution for Palaeontological researc

Alun Rhun Hughes: a tribute after forty four years of companionship in Anatomy and Anthropology

A tribute to Alun R Hughe