The geodesic flow on nilmanifolds

In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an example we develop the Heisenberg Lie group equipped with its canonical metric. We prove that a family of first integrals giving the complete integrability can be read off at the Lie algebra of the isometry group. We also explain the complete integrability on compact quotients and for any invariant metric.Comment: 24 page

Can quantum regression theorem be reconciled with quantum fluctuation dissipation theorem ?

In the attempt to derive the regression theorem from the fluctuation dissipation theorem several authors claim the violation of the former theorem in the quantum case. Here we pose the question: does it exists a quantum fluctuation dissipation theorem (QFDT) in its conventional interpretation? It is shown that the relation usually called as the QFDT is the condition of detailed macroscopic energetic balance. Following this interpretation the existing conflict between the two theorems in the quantum case is removed.Comment: 13 pages, 3rd Int. Conf. on Unsolved Problems on Noise (will be published in Proceedings

Large mixing angle solution to the solar neutrino problem and random matter density perturbations

There are reasons to believe that mechanisms exist in the solar interior which lead to random density perturbations in the resonant region of the Large Mixing Angle solution to the solar neutrino problem. We find that, in the presence of these density perturbations, the best fit point in the (sin^2(2\theta), Delta_m^2) parameter space moves to smaller values, compared with the values obtained for the standard LMA solution. Combining solar data with KamLAND results, we find a new compatibility region, which we call VERY-LOW LMA, where sin^2(2\theta) ~ 0.6 and Delta_m^2~2e-5 eV^2, for random density fluctuations of order 5% < \xi< 8%. We argue that such values of density fluctuations are still allowed by helioseismological observations at small scales of order 10 - 1000 km deep inside the solar core.Comment: References and discussion added, with some small numerical corrections implemente

Networks, commuting and spatial structures: An introduction

JTLU vol. 2, no. 3, (2010) pp 1-4This article introduces vol. 2, no. 3 issue of Journal of Transport and Land Use