177,158 research outputs found
The RSB order parameter in finite-dimensional spin glasses: numerical computation at zero temperature
No full textThis thesis is focused on the computation of the overlap distribution which characterizes spin glasses with finite connectivity upon an RSB transition at zero temperature.
Two models are considered: the J± Bethe lattice spin glass and the Edwards-Anderson spin glass in three dimensions with random regular bond dilution (random dilution with the constraint of fixed connectivity z = 3). The approach is based on the study of the effects of a bulk perturbation on the energy landscape. In ultrametric spin glasses, the distribution of the excited states is known to be related to the order parameter through a universal formula. This formula is used for deriving the order parameter from the experimental distributions. In addition, the finite-size corrections to the ground state energy are computed for the two models
Quantum dynamics of coupled bosonic wells within the Bose-Hubbard picture
No full textWe relate the quantum dynamics of the Bose-Hubbard model (BHM) to the semiclassical nonlinear equations that describe an array of interacting Bose condensates by implementing a standard variational procedure based on the coherent state method. We investigate the dynamics of the two-site BHM from the purely quantum viewpoint by recasting first the model within a spin picture and using then the related dynamical algebra. The latter allows us to study thoroughly the energy spectrum structure and to interpret quantally the classical symmetries of the two-site dynamics. The energy spectrum is also evaluated through various approximations relying on the coherent state approach
Weight Space Structure and Internal Representations: aDirect Approach to Learning and Generalization in Multilayer Neural Network
No full text
Coloring random graphs
No full textWe study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase cis an element of[c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms
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