Wave function collapses in a single spin magnetic resonance force microscopy

We study the effects of wave function collapses in the oscillating cantilever driven adiabatic reversals (OSCAR) magnetic resonance force microscopy (MRFM) technique. The quantum dynamics of the cantilever tip (CT) and the spin is analyzed and simulated taking into account the magnetic noise on the spin. The deviation of the spin from the direction of the effective magnetic field causes a measurable shift of the frequency of the CT oscillations. We show that the experimental study of this shift can reveal the information about the average time interval between the consecutive collapses of the wave functionComment: 5 pages 2 figure

A General Relativistic Rotating Evolutionary Universe

We show that when we work with coordinate cosmic time, which is not proper time, Robertson-Walker's metric, includes a possible rotational state of the Universe. An exact formula for the angular speed and the temporal metric coefficient, is found.Comment: 5 pages including front cover. Publishe

Bergman kernels and equilibrium measures for ample line bundles

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power of L. In this paper various convergence results are obtained for the corresponding Bergman kernels. The convergence is studied in the large k limit and is expressed in terms of the equilibrium metric associated to the fixed metric, as well as in terms of the Monge-Ampere measure of the fixed metric itself on a certain support set. It is also shown that the equilibrium metric has Lipschitz continuous first derivatives. These results can be seen as generalizations of well-known results concerning the case when the curvature of the fixed metric is positive (the corresponding equilibrium metric is then simply the fixed metric itself).Comment: 22 page

Resource rents, universal basic income, and poverty among Alaska’s Indigenous peoples

The Alaska Permanent Fund Dividend (PFD) program provides universal basic income (UBI) to all residents from investment earnings of a state sovereign wealth fund created from oil rents. This paper evaluates the effect of the PFD to mitigate poverty among the state’s rural Indigenous (Alaska Native) peoples: a population with historically high poverty rates living in a region with limited economic opportunities. Errors in recording PFD income in data used to calculate official poverty statistics cause them to misrepresent poverty in Alaska and understate the effect of the PFD. Estimating poverty rates with and without PFD income therefore requires reconstruction of family incomes from household-level data. Estimated poverty rates from reconstructed income show that the PFD has had a substantial, although diminishing mitigating effect on poverty for rural Indigenous families. The PFD has had a larger effect on poverty among children and elders than for the rural Alaska Native population as a whole. Alaska Native seniors, who receive additional sources of UBI derived primarily from resource rents besides the PFD, have seen a decline in poverty rates, while poverty rates for children have increased. Evidence has not appeared for commonly hypothesized potential adverse social and economic consequences of UBI.Ye

Holomorphic Morse inequalities on manifolds with boundary

Let X be a compact manifold with boundary and let L^k be a high power of a hermitian holomorphic line bundle over X. When X has no boundary, Demailly's holomorphic Morse inequalities give asymptotic bounds on the dimensions on the Dolbeault cohomology groups with values in L^k. We extend Demailly's inequalities to the case when X has a boundary by adding a boundary term expressed as a certain average of the curvature of the line bundle and the Levi curvature of the boundary. Examples are given that show that the inequalities are sharp and it is shown that they are compatible with hole filling. The most interesting case is when X is a pseudoconcave manifold with a positive line bundle L. If the curvature of L is conformally equivalent to the Levi curvature of the boundary, the Morse inequalities are shown to be equalities, so that the space of global sections of L have maximal asymptotic growth, i.e. L is big. The sharp examples show that the corresponding cohomology group of (0,1)-forms may have maximal asymptotic growth, as well, unless the conformal equivalence holds.Comment: 42 pages. Typos fixed. Section on Strong Morse inequalites added. Treatment of model case simplified by use of new metric, conformally equivalent to the old on

Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n

Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is differentiable and all of its first partial derivatives are locally Lipshitz continuous. The convergence is studied in the large k limit and is expressed in terms of the global equilibrium potential associated to the weight function, as well as in terms of the Monge-Ampere measure of the weight function itself on a certain set. A setting of polynomials associated to a given Newton polytope, scaled by k, is also considered. These results apply directly to the study of the distribution of zeroes of random polynomials and of the eigenvalues of random normal matrices.Comment: v1: 11 pages v2: 19 pages. Substantial revision: regularity assumption on the weight weakened to C^1,1, setting of polynomials with a given Newton polytope considered, examples and a figure adde

Suicide Among Young Alaska Native Men: Community Risk Factors and Alcohol Control

Indigenous residents of Alaska (Alaska Natives) die by suicide at a rate nearly 4 times the US average and the average for all American Indians and Alaska Natives (AI/ANs).1---3 An astonishing 7% of Alaska respondents to a 2003 international household survey of Arctic Indigenous people indicated that they had seriously contemplated suicide within the past year.4 Studies have shown that alcohol is directly or indirectly involved in most of these deaths.5---9 Although Alaska Natives have encountered alcohol for well over a century, the high suicide risk is an entrenched but comparatively recent phenomenon affecting only the past 2 generations.9,10 Figure 1 shows that crude suicide rates for this group rose rapidly in the decade after Alaska achieved statehood in 1959. The 3-year moving average rate peaked at more than 50 per 100 000 in the early 1980s, before declining to a level of about 40 per 100 000 during the past decade. The dip in suicide rates in the late 1970s likely represents faulty data rather than a real departure from the secular trend.11 An emerging new pattern of risk drove the increase in suicide rates in the 1960s. Higher suicide rates among young men led the rise in suicide as a whole.9,12,13 More recently, another important pattern of differential risk emerged as more Alaska Natives moved to the state’s growing urban areas in search of jobs. Suicide rates among Alaska Native residents remaining in small rural communities are more than twice as high as those among Native residents of urban areas and vary greatly among communities even in the same region (Alaska Bureau of Vital Statistics, unpublished data).13 In fact, suicide rates may have declined since the peak in the 1980s (Figure 1) only because the lower risk population of urbandwelling Alaska Natives has grown relative to the more vulnerable rural population. The large disparities among populations with similar ethnicity and histories suggest that the elevated suicide risk is not simply an unfortunate side effect of rapid social change but may be influenced directly by contemporary living conditions. The associationYe

T-duality and non-geometric solutions from double geometry

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles in extended geometry. A proposal for solving this problem is given in the framework of double field theory. It is based on a clearly defined extension of the definition of gauge symmetry by isometries of an underlying pseudo-Riemannian manifold. The ensuing relation between transformations of coordinates and fields, which is now derived from first principles, differs from earlier proposals.Comment: 13 pp., plain te

On the Machian Origin of Inertia

We examine Sciama's inertia theory: we generalise it, by combining rotation and expansion in one unique model, we find the angular speed of the Universe, and we stress that the theory is zero-total-energy valued. We compare with other theories of the same null energy background. We determine the numerical value of a constant which appears in the Machian inertial force expression devised by Graneau and Graneau[2], by introducing the above angular speed. We point out that this last theory is not restricted to Newtonian physics as those authors stated but is, in fact, compatible with other cosmological and gravitational theories. An argument by Berry[7] is shown in order to "derive" Brans-Dicke relation in the present context.Comment: 10 pages including front one. New version was accepted to publication by Astrophysics and Space Scienc