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

Shear and Vorticity in a Combined Einstein-Cartan-Brans-Dicke Inflationary Lambda-Universe

A combined BCDE (Brans-Dicke and Einstein-Cartan) theory with lambda-term is developed through Raychaudhuri's equation, for inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density, cosmic pressure, shear, vorticity, and Hubble's parameter, while the scale factor, total spin and scalar field increase exponentially. The post-inflationary fluid resembles a perfect one, though total spin grows, but the angular speed does not (Berman, 2007d). Keywords: Cosmology; Einstein; Brans-Dicke; Cosmological term; Shear; Spin; Vorticity; Inflation; Einstein-Cartan; Torsion. PACS: 04.20.-q ; 98.80.-k ; 98.80.Bp ; 98.80.JkComment: 8 pages including front one. Published versio

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

A Quantum Full Adder for a Scalable Nuclear Spin Quantum Computer

We demonstrate a strategy for implementation a quantum full adder in a spin chain quantum computer. As an example, we simulate a quantum full adder in a chain containing 201 spins. Our simulations also demonstrate how one can minimize errors generated by non-resonant effects.Comment: 15 pages RevTex including 2 figure

General Relativistic Singularity-Free Cosmological Model

We "explain", using a Classical approach, how the Universe was created out of "nothing", i.e., with no input of initial energy nor mass. The inflationary phase, with exponential expansion, is accounted for, automatically, by our equation of state for the very early Universe. This is a Universe with no-initial infinite singularity of energy density.Comment: Astrophysics and Space Science, 321,157 (2009

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

Entropy of the Universe

After a discussion on several limiting cases where General Relativity turns into less sophisticated theories, we find that in the correct thermodynamical and cosmological weak field limit of Einstein's field equations the entropy of the Universe is R^(3/2) -- dependent, where R stands for the radius of the causally related Universe. Thus, entropy grows in the Universe, contrary to Standard Cosmology prediction.Comment: To be published by International Journal of Theoretical Physic

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

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