Non-Relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in earth's gravitational field may form a gravitationally bound quantized state, which had already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are discussed in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.Comment: 12 pages, no figur

Precursor problem and holographic mutual information

The recent proposal of Almheiri et al.http://arxiv.org/abs/1411.7041, together with the Ryu-Takayanagi formula, implies the entanglement wedge hypothesis for certain choices of boundary subregions. This fact is derived in the pure AdS space. A similar conclusion holds in the presence of quantum corrections, but in a more restricted domain of applicability. We also comment on http://arxiv.org/abs/1601.05416 and some similarities and differences with this workComment: 13 pages, 1 figur

Work Distributions in 1-D Fermions and Bosons with Dual Contact Interactions

We extend the well-known static duality \cite{girardeau1960relationship, cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version. By utilizing this dynamical duality we find the duality of non-equilibrium work distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau (TG) gas is identical to that of 1-D free fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1-D noninteracting distinguishable particles, although their elemetary excitations (quasi-particles) obey different statistics, e.g. the Bose-Einstein, the Fermi-Dirac and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.Comment: 8 pages, 2 figure, 2 table

r-Process Nucleosynthesis in Shocked Surface Layers of O-Ne-Mg Cores

We demonstrate that rapid expansion of the shocked surface layers of an O-Ne-Mg core following its collapse can result in r-process nucleosynthesis. As the supernova shock accelerates through these layers, it makes them expand so rapidly that free nucleons remain in disequilibrium with alpha-particles throughout most of the expansion. This allows heavy r-process isotopes including the actinides to form in spite of the very low initial neutron excess of the matter. We estimate that yields of heavy r-process nuclei from this site may be sufficient to explain the Galactic inventory of these isotopes.Comment: 11 pages, 1 figure, to appear in the Astrophysical Journal Letter

The effects of decision flexibility in the hierarchical investment decision process

Large institutional investors allocate their funds over a number of classes (e.g. equity, fixed income and real estate), various geographical regions and different industries. In practice, these allocation decisions are usually made in a hierarchical (top-down), consecutive way. At the higher decision level, the allocation is made on basis of benchmark portfolios (indexes). Such indexes are then set as targets for the lower levels. For example, at the top level the allocation decision is made on the basis of asset class benchmark indexes, on the second level the decisions are made on the basis of sector benchmark indexes, etc. Obviously, the lower levels have considerable flexibility to deviate from these targets. That is the reason why targets often come with limits on the maximally allowed deviation (or "tracking error") from these targets. The potential consequences of deviations from the benchmark portfolios have received very little attention in the literature. In this paper, we discuss and illustrate this influence. The lower level tracking errors with respect to the benchmark indexes propagate to the top level. As a result the risk-return characteristics of the actual aggregate portfolio will be different from those of the initial benchmark-based portfolio. We illustrate this effect for a two level process to allocate funds over individual US stocks and sectors. We show that the benchmark allocation approaches used in practice yield inferior solutions when compared to a non-hierarchical approach where full information about individual lower level investment opportunities is available. Our results reveal that even small deviations from the benchmark portfolios can cause large shifts in the top-level risk-return space. This implies that the incorporation of lower level information in the initial top-level decision process will lead to a different (possibly better) allocation.decision flexibility;multi-level decision process;porfolio management;tracking error analysis

Superconductivity Near a Quantum Critical Point in Ba(Fe,Co)2As2

We will examine the possible link between spin fluctuations and the superconducting mechanism in the iron-based high temperature superconductor Ba(Fe,Co)2As2 based on NMR and high pressure transport measurements.Comment: Invited paper to m2s-IX (2009