Modified TAP equations for the SK spin glass

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed.Comment: 7 pages, 2 figures, final revised version to appear in Europhys. Let

Semiclassical Evolution of Dissipative Markovian Systems

A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra "open" term is added to the double Hamiltonian by the non-hermitian part of the Lindblad operators in the general case of dissipative markovian evolution. The particular case of generic hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighborhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further "small-chord" approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.

Significance of Ghost Orbit Bifurcations in Semiclassical Spectra

Gutzwiller's trace formula for the semiclassical density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation ("ghost orbits") can produce pronounced signatures in the semiclassical spectra in the vicinity of the bifurcation. It is the purpose of this paper to demonstrate that these ghost orbits themselves can undergo bifurcations, resulting in complex, nongeneric bifurcation scenarios. We do so by studying an example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling of the balloon orbit. By application of normal form theory we construct an analytic description of the complete bifurcation scenario, which is then used to calculate the pertinent uniform approximation. The ghost orbit bifurcation turns out to produce signatures in the semiclassical spectrum in much the same way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.

Quantum Effects in Neural Networks

We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter decomposition reduces the problem to that of a random Ising model. It turns out that the effects of quantum fluctuations on macroscopic variables play the same roles as those of thermal fluctuations. For an extensive number of embedded patterns, we apply the replica method to the Trotter-decomposed system. The result is summarized as a ground-state phase diagram drawn in terms of the number of patterns per site, $\alpha$, and the strength of the transverse field, $\Delta$. The phase diagram coincides very accurately with that of the conventional classical Hopfield model if we replace the temperature T in the latter model by $\Delta$. Quantum fluctuations are thus concluded to be quite similar to thermal fluctuations in determination of the macroscopic behavior of the present model.Comment: 34 pages, LaTeX, 9 PS figures, uses jpsj.st

Replica field theory and renormalization group for the Ising spin glass in an external magnetic field

We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero magnetic field fixed-point, from the application of the renormalization group. In the spin glass limit, n going to 0, this fixed-point governs the critical behaviour of a class of systems characterised by a single cubic interaction parameter. For this universality class, the spin glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, the so-called anomalous one, however, behaves unusually, having a jump at criticality. The physical consequences of this unusual behaviour are discussed, and a comparison with the conventional de Almeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev. Let

Importância do mel na composição da renda familiar em assentamentos rurais de Corumbá, MS.

Desde março de 2009 a Embrapa Pantanal e parceiros (AAPAN, AGRAER, Fundação Terra do Pantanal, assentados) vêm executando um projeto de pesquisa participativa em dois assentamentos rurais de Corumbá, MS, com o objetivo de avaliar as tecnologias apícolas adotadas e propor ajustes e inclusões ao sistema produtivo. A avaliação inclui um componente econômico que busca identificar a importância da apicultura na renda familiar total dos assentados. Para tanto, o produtor utiliza uma planilha onde anota diariamente as tarefas realizadas, produtos e insumos comprados e vendidos, entre outros. Os resultados do acompanhamento econômico dependem muito do adequado preenchimento desta planilha, sendo uma dificuldade inerente ao processo participativo. Observou-se que a apicultura é uma atividade complementar à renda familiar, mas pode vir a tornar-se a principal fonte de renda para alguns assentados, dependendo de certos requisitos e condicionantes do produtor, do lote e da própria cadeia produtiva.Disponível também em: Cadernos de Agroecologia, V. 5, n.1, 2010