Wave relations

The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian evolution are not problematic from the viewpoint of relations. In the two-dimensional Minkowski case, these relations are shown to be Lagrangian. This result is then extended to a wide class of metrics and is conjectured to be true also in higher dimensions for nice enough metrics. A counterexample where the relation is not Lagrangian is provided by the Misner space.Comment: 27 pages; minor clarifying changes added; to appear in CM

A New Keynesian Workbook

A large literature has recently developed to place the New Keynesian framework for analyzing business cycle fluctuations and the conduct of monetary policy into undergraduate economics curricula. New Keynesian models offer several attractive modeling aspects: straightforward linear specifications of structural relations, intuitive and clear dynamic properties, derivation from microfoundations. This paper provides a description of an Excel-based application that presents several versions of the New Keynesian model: static, with adaptive expectations, and with rational expectations. The latter two versions also provide dynamic descriptions of variables' evolution in terms of impulse response functions.

The rotationally stabilized VPOS and predicted proper motions of the Milky Way satellite galaxies

The satellite galaxies of the Milky Way (MW) define a vast polar structure (VPOS), a thin plane perpendicular to the MW disc. Proper motion (PM) measurements are now available for all of the 11 brightest, `classical' satellites and allow an updated analysis of the alignment of their orbital poles with this spatial structure. The coherent orbital alignment of 7 to 9 out of 11 satellites demonstrates that the VPOS is a rotationally stabilized structure and not only a pressure-supported, flattened ellipsoid. This allows us to empirically and model independently predict the PMs of almost all satellite galaxies by assuming that the MW satellite galaxies orbit within the VPOS. As a test of our method, the predictions are best met by satellites whose PMs are already well constrained, as expected because more uncertain measurements tend to deviate more from the true values. Improved and new PM measurements will further test these predictions. A strong alignment of the satellite galaxy orbital poles is not expected in dark matter based simulations of galaxy formation. Coherent orbital directions of satellite galaxies are, however, a natural consequence of tidal dwarf galaxies formed together in the debris of a galaxy collision. The orbital poles of the MW satellite galaxies therefore lend further support to tidal scenarios for the origin of the VPOS and are a very significant challenge for the standard LCDM model of cosmology. We also note that the dependence of the MW satellite speeds on Galactocentric distance appear to map an effective potential with a constant velocity of approximately 240 km/s to about 250 kpc. The individual satellite velocities are only mildly radial.Comment: 17 pages, 8 figures, 4 tables, accepted for publication in MNRA

Separated spin-up and spin-down evolution of degenerated electrons in two dimensional systems: Dispersion of longitudinal collective excitations in plane and nanotube geometry

Applying the separated spin evolution quantum hydrodynamics to two-dimensional electron gas in plane samples and nanotubes located in external magnetic fields we find new kind of wave in electron gas, which is called the spin-electron acoustic wave. Separate spin-up electrons and spin-down electrons evolution reveals in replacement of the Langmuir wave by the couple of hybrid waves. One of two hybrid waves is the modified Langmuir wave. Another hybrid wave is the spin-electron acoustic wave. We study dispersion of these waves in two dimensional structures of electrons. We also consider dependence of dispersion properties on spin polarisation of electrons in external magnetic field.Comment: 5 pages, 5 figure