Resonating valence bond wave function for the two dimensional fractional spin liquid

The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on ${\rm Cs_2 Cu Cl_4}$, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/2 systems, and remains similarly accurate in the two-dimensional model corresponding to ${\rm Cs_2 Cu Cl_4}$, thus representing a good ansatz for describing spin fractionalization in two dimensions.Comment: 5 pages, 4 figures. To appear in Phys. Rev. Let

Vertex routing models

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.Comment: 12 pages, 6 figure

Intrinsic adaptation in autonomous recurrent neural networks

A massively recurrent neural network responds on one side to input stimuli and is autonomously active, on the other side, in the absence of sensory inputs. Stimuli and information processing depends crucially on the qualia of the autonomous-state dynamics of the ongoing neural activity. This default neural activity may be dynamically structured in time and space, showing regular, synchronized, bursting or chaotic activity patterns. We study the influence of non-synaptic plasticity on the default dynamical state of recurrent neural networks. The non-synaptic adaption considered acts on intrinsic neural parameters, such as the threshold and the gain, and is driven by the optimization of the information entropy. We observe, in the presence of the intrinsic adaptation processes, three distinct and globally attracting dynamical regimes, a regular synchronized, an overall chaotic and an intermittent bursting regime. The intermittent bursting regime is characterized by intervals of regular flows, which are quite insensitive to external stimuli, interseeded by chaotic bursts which respond sensitively to input signals. We discuss these finding in the context of self-organized information processing and critical brain dynamics.Comment: 24 pages, 8 figure

Real time localization of Gamma Ray Bursts with INTEGRAL

The INTEGRAL satellite has been successfully launched in October 2002 and has recently started its operational phase. The INTEGRAL Burst Alert System (IBAS) will distribute in real time the coordinates of the GRBs detected with INTEGRAL. After a brief introduction on the INTEGRAL instruments, we describe the main IBAS characteristics and report on the initial results. During the initial performance and verification phase of the INTEGRAL mission, which lasted about two months, two GRBs have been localized with accuracy of about 2-4 arcmin. These observations have allowed us to validate the IBAS software, which is now expected to provide quick (few seconds delay) and precise (few arcmin) localization for about 10-15 GRBs per year.Comment: 6 pages, latex, 3 figures, submitted to Adv. Sp. Res., Proceedings of the 34th COSPAR Scientific Assembly, Houston, 10-19 October 200

Breakdown of the Luttinger sum-rule at the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model

We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating spin-gapped state in their respective ground-state momentum distribution functions

The de Rham-Witt and Z_p-cohomologies of an algebraic variety

We show how the Z_p(r)-cohomologies of a smooth projective algebraic variety can be obtained via its de Rham-Witt complex.Comment: 6 page

Quantum antiferromagnetism and high TCT_C superconductivity: a close connection between the t-J model and the projected BCS Hamiltonian

A connection between quantum antiferromagnetism and high $T_C$ superconductivity is theoretically investigated by analyzing the t-J model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the t-J model at half filling (i.e., the 2D antiferromagnetic Heisenberg model) is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wavefunction overlap between the ground states of the t-J model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the t-J model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.Comment: 18 pages, 9 figures, the final version published in Phys. Rev.