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

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

Long time Evolution of Quantum Averages Near Stationary Points

We construct explicit expressions for quantum averages in coherent states for a Hamiltonian of degree 4 with a hyperbolic stagnation point. These expressions are valid for all times and "collapse" (i.e., become infinite) along a discrete sequence of times. We compute quantum corrections compared to classical expressions. These corrections become significant over a time period of order C log 1/\hbar.Comment: LaTeX, 8 page

Bergman kernels and local holomorphic Morse inequalities

Let X be a hermitian manifold and let L^k be a high power of a hermitian line bundle over X. Local versions of Demailly's holomorphic Morse inequalities are presented - after integration they yield the usual inequalities. The local weak inequalities hold on any hermitian manifold X, regardless of compactness and completeness. The proofs, which are elementary, are based on a new approach to pointwise Bergman kernel estimates, where the kernels are estimated by a model kernel in the standard complex space C^n.Comment: 19 pages. An extended version at http://www.math.chalmers.se/Math/Research/Preprints

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

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