Dynamical Collapse of White Dwarfs in Hartree- and Hartree-Fock Theory

We study finite-time blow-up for pseudo-relativistic Hartree- and Hartree-Fock equations, which are model equations for the dynamical evolution of white dwarfs. In particular, we prove that radially symmetric initial configurations with negative energy lead to finite-time blow-up of solutions. Furthermore, we derive a mass concentration estimate for radial blow-up solutions. Both results are mathematically rigorous and are in accordance with Chandrasekhar’s physical theory of white dwarfs, stating that stellar configurations beyond a certain limiting mass lead to “gravitational collapse” of these objects. Apart from studying blow-up, we also prove local well-posedness of the initial-value problem for the Hartree- and Hartree-Fock equations underlying our analysis, as well as global-in-time existence of solutions with sufficiently small initial data, corresponding to white dwarfs whose stellar mass is below the Chandrasekhar limit.     

Stability and structure of Newtonian gravitars

The solution r² for a scalar field (gravitational constant), which is asymptotically exact for supercompact configurations and which Saakyan and Mnatsakanyan obtained from the numerical solution of the hydrostatics equations in the Newtonian approximation of the Jordan-Brans-Dicke theory, is used to study the gravitational stability of such configurations. We have found the stability condition 2/3 for polytropic configurations ( is the polytropic exponent) instead of 4/3, which is known for configurations of low compactness. Analytic solutions of the equations of internal structure are found for configurations which are intermediate with respect to stability (=2/3) and for some other important series of configurations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 98–102, July, 1982.In conclusion, the present author expresses his indebtedness and gratitude to V. N. Ponomarev, for assistance in executing the work.     

Photoionization of the hydrogen atom in strong magnetic fields of White Dwarfs

The photoionization cross-sections of the hydrogen atom in strong magnetic fields of magnetic White Dwarf stars were calculated with a direct numerical integration method using the Landau basis as a high field approach. The validity regime of these solutions overlap with those of the spherical symmetry and complement other recently developed methods. An important result is the relation between the density of states and the normalization for the more than one open channel regime leading to additional coupling terms not taken into account by multi channel quantum defect methods. Received: 16 March 1998 / Revised and Accepted: 14 July 1998     

Structure of Rotating Neutron Stars in Uniform Strong Magnetic Field

Properties and deformations of the rotating neutron stars in uniform strong magnetic field are calculated. The magnetic field will soften the equation of state of the neutron star matters and make an obvious effect on the structure of the rotating neutron star. If the magnetic field is superstrong （B=10^17 T）, the mass, radius, and the deformation will become smaller effectively.     

两种计算旋转中子星性质方法的比较(英文)

对两种基于广义相对论的计算旋转中子星性质的数值方法:Hartle法和Butterworth 和Ipser法(简记为BI法)进行了较详细的介绍、讨论和比较。对基于不同物态方程给出的旋转中子星的性质进行对比,结果表明两种方法给出的相关结果例如旋转中子星的质量、半径和形变等基本一致,特别是在观测值范围内的计算等均能较好地解释观测结果.     

The Stability of Some Viable Stars and Electromagnetic Field

We examine the impact of electromagnetic field on the stability of compact stars corresponding' to embedded class one metric using the concept of cracking.For this purpose,we develop the generalized hydrostatic equilibrium equation for charged perfect fluid distribution of compact stars and perturb it by means of local density perturbation scheme to check the stability of inner matter configuration.We investigate the cracking of Her X-1,PSR 1937+21,PSR J 1614-2230,PSR J 0348+0432 and RX J 1856-37.We conclude that PSR J 0348+0432 and RX J 1856-37 exhibit cracking when charge is introduced on these astrophysical objects.     

Differential System＇s Nonlinear Behaviour of Real Nonlinear Dynamical Systems

Chaos attractor behaviour is usually preserved if the four basic arithmetic operations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dimensional real discrete dynamical systems and nonautonomous real continuous-time dynamical systems are also dynamical systems and their Lyapunov exponents are kept, if they are twice differentiable. These two conclusions are shown here by the definitions of dynamical system and Lyapunov exponent. Numerical simulations support our analytical results. The conclusions can apply to higher order differential systems if their corresponding order differentials exist.     

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger picture of a given field theory. While, for simplicity, we study the example of a \(\mathcal{U}(1)\) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, similar to recently studied Schrödinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. A probabilistic interpretation (Born’s rule) holds, provided the underlying model is scale free.     

Frame Dragging Effect on Properties of Rotating Neutron Stars with Strong Magnetic Field

The general relativistic frame dragging effect on the properties, such as the moments of inertia and the radii of gyration of fast rotating neutron stars with a uniform strong magnetic field, is calculated accurate to the first order in the uniform angular velocity. The results show that compared with the corresponding non-rotating static spherical symmetric neutron star with a weaker magnetic field, a fast rotating neutron star （millisecond pulsar） with a stronger magnetic field has a relative smaller moment of inertia and radius of gyration.     

Properties of Neutron Stars Rotating at Kepler Frequency with Uniform Strong Magnetic Field

A uniform strong magnetic field is considered in calculating the properties of neutron star rotating at the Kepler frequency. The results show that the effect of the magnetic field on the properties of neutron star is evident, and the properties of the neutron stars rotating at the Kepler frequency can be used as a criterion to the equations of states of the neutron star matters.     

Frame Dragging Effect on Properties of Rotating Neutron Stars with Strong Magnetic Field

The general relativistic frame dragging effect on the properties, such as the moments of inertia and the radii of gyration of fast rotating neutron stars with a uniform strong magnetic field, is calculated accurate to the first order in the uniform angular velocity. The results show that compared with the corresponding non-rotating static spherical symmetric neutron star with a weaker magnetic field, a fast rotating neutron star (millisecond pulsar) with a stronger magnetic field has a relative smaller moment of inertia and radius of gyration.     

Nonlinear Dynamical Symmetries of Some Two-Dimensional Quantum Systems

In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as theKepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalizedpseudo-oscillators in the two-dimensional flat space. Their nonlinear spectrum generating algebras are shown to berelevant to polynomial angular momentum algebras.     

Time Periodicity and Dynamical Stability in Two-Boson Systems

We calculate the period of recurrence of dynamical systems comprising two interacting bosons. A number of theoretical issues related to this problem are discussed, in particular, the conditions for small periodicity. The knowledge gathered in this way is then used to propose a notion of dynamical stability based on the stability of the period. Dynamical simulations show good agreement with the proposed scheme. We also apply the results to the phenomenon known as coherent population trapping and find stability conditions for this specific case.     

Nonlinear Dynamical Symmetries of Some Two-Dimensional Quantum Systems

In this paper nonlinear dynamical symmetries of three quantum systems are studied in detail, such as the Kepler-Coulomb system and the isotropic harmonic oscillator in a two-dimensional curved space, and the generalized pseudo-oscillators in the two-dimensional fiat space. Their nonlinear spectrum generating algebras are shown to be relevant to polynomial angular momentum algebras.     

Dynamical Evolution and Entanglement in a Nonlinear Interacting System

We investigate a few features of entanglement of two types of particles coupled through a nonlinear interaction. It is shown that the entanglement created by the nonlinear interaction can reflect nonlinearity of the system. Possible observation of our prediction in a double-well trapped Bose-Einstein condensate is discussed.