Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein–Maxwell field equations for this gas becomes a dynamical system in a 4D phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3D sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H ₀ is negative. If H ₀ is positive the trajectories end up in a curvature singularity that can be, depending on initial conditions, isotropic or anisotropic. In particular, if the initial magnetic field intensity is sufficiently large the collapsing singularity will always be anisotropic and pointing in the same direction of the field.     

Inner Coulomb corrections to pion-nucleus scattering

A semiclassical model for inner Coulomb corrections to pion-nucleus scattering in the Δ-resonance region is suggested. Its main consequence is a change of the nuclear radius R, giving $\text{R(π}{}^{\mathrm{?}}\text{)}\text{R(π}{}^{\mathrm{+}}\text{)}\text{= 1+2Z}\text{αE}\text{k}{}^2\text{R}$. The Glauber model can be extended to include these effects.     

Equivalence of a Bit Pixel Image to a Quantum Pixel Image

We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight. All qubits are linear superposition, changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit. Classically, these states are just bytes represented in a binary matrix, having code combinations of 1 or 0 at all pixel locations. This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods.     

Equivalence of a Bit Pixel Image to a Quantum Pixel Image

We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight.All qubits are linear superposition,changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit.Classically,these states are just bytes represented in a binary matrix,having code combinations of 1 or 0 at all pixel locations.This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods.     

Quantum spreading of a self-gravitating wave-packet in singularity free gravity

In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein’s general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential – such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future.     

Coulomb scattering of an electron by a monopole

The Coulomb scattering of an electron by a magnetic monopole is analyzed using a lowest-order quantum perturbation approximation suggested by a two-potential Lagrangian form for classical electromagnetism, generalized through the use of spacetime algebra to include magnetic monopoles. Good agreement with existing conventional analyses of this problem is demonstrated.1. Work supported by Department of Energy contract DE-AC03-76SF00515.2. The idea to employ spacetime algebra (sometimes called Dirac algebra) to incorporate magnetic monopoles into classical electromagnetic theory was proposed by de Faria-Rosaet al. [3].3. This is a factori difference between the definition of 5 by Eq. (3) and that by Bjorken and Drell [6]. Since a cross section (without interference terms) is being calculated, we can ignore this distinction.     

Quantum mechanical stability approach to the Coulomb quasipotential

The critical coupling constant characterizing the stability behaviour of the Coulomb quasipotential has been evaluated as α ? α_c = 2. The present stability approach is based on the quantum-mechanical controllability requirement of the dispersion shifts due to the interactions. The dispersions characterizing the Coulomb quasipotential have been established suitably within the high-energy euclidian region.     

Coulomb scattering of dirac particles

The continuum Coulomb wave function in the Johnson and Deck form—a matrix operator acting on a plane wave spinor—is discussed. General relations for the elastic differential cross section, the asymmetry parameters, and the precession and nutation of polarization are developed. An expansion of the asymptotic wave function correct to third order in λ = αZ for all Born parameters $\text{ν =}\text{αZ}\text{β}$ is obtained. This expansion involves a two parameter function T(θ, ν) which in turn may be expanded for small ν to give results previously obtained by Johnson, Weber, and Mullin. On the other hand, a large ν asymptotic expansion of T(θ, ν) valid for |2πν| > 1 permits a discussion of the non-relativistic limit. Both the small and large approximations substantially agree for $\text{|ν| ⋍}\text{1}\text{2}$. Consequently, these two approximations may be used to span the whole range of Born parameters.The asymptotic Born parameter approximation predicts markedly different scattering behavior for electrons and positrons. A striking feature is that functions pertaining to electron scattering are oscillatory in the scattering angle θ while the positron functions are not. In particular, the oscillations in the asymmetry parameter for electron scattering obtained numerically by Sherman are contained in the analytical approximate form. Also, the approach to the Rutherford cross section is different than that quoted by Mott and Massey.     

Classical and quantum scattering by a Coulomb potential

For relativistic energies the small-angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in other terms can be avoided if the sum of all corrections to the first Born approximation for large enough Coulomb charge contains the classical terms which are independent of that charge. The difference in classical and quantum cross sections may be partly attributed to the fact that the relativistic quantum particle can rush through the field without interaction. We expect that smaller impact parameters and spin facilitate this effect. The text was submitted by the authors in English.     

Equivalence of inelastic impurity scattering to the Kondo problem

The partition function for inelastic conduction electron scattering from a non-magnetic two-level impurity is shown to be equivalent to that of the Kondo problem.     

量子态的等价类与量子逻辑门

在量子力学中,态的演化是一个幺正演化过程,态的演化过程可以用演化算子对态的作用来表示,幺正演化过程是时间可逆的.基于这一基本事实,Gerard't Hoofl引进了量子态的等价类概念,并用两组等价类之间的变换来描述量子态的幺正演化.本文利用等价类的概念及其变换来探究构建量子信息论中常用的通用量子门,给出通用量子门的推广形式.最后说明这些通用量子门可以基于双qubit体系内在的相互作用Hamilton量得以实现.