Efficient Simulation of Quantum State Reduction

The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the phenomenon of quantum state reduction. Here we construct a general closed form solution to this equation, for any given initial condition, in terms of a random variable representing the terminal value of the energy and an independent Brownian motion. The solution is essentially algebraic in character, involving no integration, and is thus suitable as a basis for efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur

Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and $\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right]$.Comment: 10 pages REVTex3.0, 3 PS figure

Strategies for distributing goals in a team of cooperative agents

This paper addresses the problem of distributing goals to individual agents inside a team of cooperative agents. It shows that several parameters determine the goals of particular agents. The first parameter is the set of goals allocated to the team; the second parameter is the description of the real actual world; the third parameter is the description of the agents' ability and commitments. The last parameter is the strategy the team agrees on: for each precise goal, the team may define several strategies which are orders between agents representing, for instance, their relative competence or their relative cost. This paper also shows how to combine strategies. The method used here assumes an order of priority between strategie

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.Comment: 5 pages, 9 figure

Matrix models without scaling limit

In the context of hermitean one--matrix models we show that the emergence of the NLS hierarchy and of its reduction, the KdV hierarchy, is an exact result of the lattice characterizing the matrix model. Said otherwise, we are not obliged to take a continuum limit to find these hierarchies. We interpret this result as an indication of the topological nature of them. We discuss the topological field theories associated with both and discuss the connection with topological field theories coupled to topological gravity already studied in the literature.Comment: Latex, SISSA-ISAS 161/92/E

The effects of magnetic fields in cold clouds in cooling flows

Large masses of absorbing material are inferred to exist in cooling flows in clusters of galaxies from the excess X-ray absorption in the spectra of some X-ray clusters. The absorbing material is probably in the form of cold clouds pressure-confined by the surrounding, hot, X-ray emitting gas. The cold clouds could remain relatively static until they are destroyed by evaporation or ablation, or give rise to star formation. If the final fate of the clouds is stars, the IMF of the stars formed over the whole cooling flow region ($r \sim 100$ kpc) should be biased to low masses, to avoid a very luminous, blue halo for the central galaxy of the cooling flow. However, there is evidence for bright star formation in the innermost (r < 10 kpc) regions of some cooling flows, and, therefore, the biasing of the IMF towards low masses should not occur or be less important at smaller radii. The consideration of magnetic fields may shed light on these two points. If magnetic fields are present, the magnetic critical mass should be considered, besides the Jeans mass, in establishing a natural mass scale for star formation. When this new mass scale is taken into account, we obtain the right variation of the biasing of the IMF with the radius in addition to inhibition of high-mass star formation at large radii. We also demonstrate that magnetic reconnection is a efficient than ambipolar diffusion in removing magnetic fields in cold clouds.Comment: 9 pages, 1 figure, accepted for publication in MNRA