we have applied the method of integration of the heisenberg equation of motion proposed by bender and dunne, and m. kamella and m. razavy to the potential v(q) = v q - µ q with linear and nonlinear dissipation. we concentrate our calculations on the evolution of basis set of weyl ordered operators and calculate the mean position , velocity , the commutation relation [q, p], and the energy of pa...

Under certain conditions it is possible to describe time evolution using different times for different particles. Use of multiple times is optional in the independent particle approximation, where interparticle interactions are removed, and the N-particle evolution operator factors into N single-particle evolution operators. In this limit one may use either a single time, with a single energy-t...

We summarize recent calculations concerning the evolution kernels of the two-particle B-meson distribution amplitudes φ + and φ − taking into account three-particle contributions, as well as the evolution kernel of the combination of three-particle distribution amplitudes Ψ A − Ψ V. We exploit these results to confirm constraints on φ + and φ − derived from the light-quark equation of motion.

We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias α with respect to the other type (called cooperator). However, a cooperator helps a neighbor (either defector or cooperator) to reproduce at rate γ. We prove that the one-dimensional ne...

We present a new fast method for simulating pencil-beam type light-cones, using the MLAPM-code (Multi Level Adaptive Particle Mesh) with light-cone additions. We show that by a careful choice of the light-cone orientation, it is possible to avoid extra periodicities in the light-cone. As an example, we apply the method to simulate a 6 Gpc deep light-cone, create the dark matter halo catalogue f...

A survey is given of recent developments on the resummed small-x evolution, in a framework based on the renormalization group equation, of non–singlet and singlet structure functions in both unpolarized and polarized deep–inelastic scattering. The available resummed anomalous dimensions are discussed for all these cases, and the most important analytic and numerical results are compiled. The qu...