This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equ...This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of Shil＇nikov＇s type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The Shil＇nikov＇s theorem guarantees that this system has Smale horseshoes and the horseshoe chaos.展开更多
Gravitation is one of the basic phenomena of the world. Tremendous number of theoretical works on origin, nature, essentials, consequences, etc. of the gravitation and related phenomena were published so far. The most...Gravitation is one of the basic phenomena of the world. Tremendous number of theoretical works on origin, nature, essentials, consequences, etc. of the gravitation and related phenomena were published so far. The most prominent ones are based on the Albert Einstein＇s general theory of relativity. The author of this communication based his approach to the gravitation on Isaac Newton＇s law of the universal gravitation and related quantities, i.e. gravitational forces of matter objects, distance and motion. Namely on the fact, that the gravitation force is - as well as the inertia, mass, space ＂occupied＂ and other properties are - principal features/attributes/properties of matter objects. Gravitation is an additive property of matter objects. Taking into account other positivistic quantities like mass of the Earth, standard acceleration of gravity, and the value of the atomic unit of mass, the author defined a gravitational force of atomic unit （or ＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of Earth＇s mass on 1 kilogram of a mass on Earth＇s surface, and he calculated its value： GFO = 1.4958 × 10^-54 N. This quantity can be useful for further development of the ＂quantum mechanical＂ approach to the description and general notion about the world.展开更多
Integer numbers of natural units （Planck units） to express Newton＇s inverse square law of gravitation in terms of quantum mechanical probabilities are used. The strong nuclear force between two coupled nucleons is ...Integer numbers of natural units （Planck units） to express Newton＇s inverse square law of gravitation in terms of quantum mechanical probabilities are used. The strong nuclear force between two coupled nucleons is derived, the minds of giants such as Newton and Einstein are met. There is a considerable continuing effort directed for the understanding of gravity and the constants of nature, last century＇s legacy of Arthur Stanley Eddington.展开更多
The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eig...The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.展开更多
The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the lo...The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.展开更多
In this paper, we consider the relativistic Harnilton-Jacobi （HJ） equation and study Hawking radiation （HR） of scalar particles from uncharged Grumiller black hole （GBH） which is affordable for testing in astrop...In this paper, we consider the relativistic Harnilton-Jacobi （HJ） equation and study Hawking radiation （HR） of scalar particles from uncharged Grumiller black hole （GBH） which is affordable for testing in astrophysics. It is a/so known as Rindler modified Schwarzschild BH. Our aim is not only to investigate the effect of the Rindler parameter a on the Hawking temperature （TH ）, but to examine whether there is any discrepancy between the computed horizon temperature and the standard TH as well. For this purpose, in addition to its naive coordinate system, we study on the three regular coordinate systems, which are Painlevd--Gullstrand （PG）, ingoing Edding^on-Finkelstein （IEF）, and Kruskal-Szekeres （KS） coordinates. In o21 coordinate systems, we calculate the tunneling probabilities of incoming and outgoing scalar particles from the event horizon by using the HJ equation. It has been shown in detail that the considered HJ method is concluded with the conventional T~ in all these coordinate systems without giving rise to the famous factor-2 problem. Filrthermore, in the PG coordinates Parikh-Wilczek＇s tunneling （PWT） method is employed in order to show how one can integrate the quantum gravity （QG） corrections to the semiclassical tunneling rate by including the effects of self-gravitation and back reaction. We then show how this yields a modification in the TH.展开更多
In the standard model of particle physics, photons are massless particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory lab...In the standard model of particle physics, photons are massless particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory labs and several exterritorial tests have put some upper limits on photon mass, e.g., torsion balance experiment in the lab shows that photon mass should be smaller than 1.2 x 10-51g. In this work, this claim is tested at a cosmological scale by looking at strong gravitational lensing data available and an upper limit of 8.71 x 10-39g on photon mass is given. Observations of energy-dependent gravitational lensing with not yet available higher accuracy astrometry instruments may constrain photon mass better.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos. 60074034 and 70271068
文摘This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of Shil＇nikov＇s type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The Shil＇nikov＇s theorem guarantees that this system has Smale horseshoes and the horseshoe chaos.
文摘Gravitation is one of the basic phenomena of the world. Tremendous number of theoretical works on origin, nature, essentials, consequences, etc. of the gravitation and related phenomena were published so far. The most prominent ones are based on the Albert Einstein＇s general theory of relativity. The author of this communication based his approach to the gravitation on Isaac Newton＇s law of the universal gravitation and related quantities, i.e. gravitational forces of matter objects, distance and motion. Namely on the fact, that the gravitation force is - as well as the inertia, mass, space ＂occupied＂ and other properties are - principal features/attributes/properties of matter objects. Gravitation is an additive property of matter objects. Taking into account other positivistic quantities like mass of the Earth, standard acceleration of gravity, and the value of the atomic unit of mass, the author defined a gravitational force of atomic unit （or ＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of Earth＇s mass on 1 kilogram of a mass on Earth＇s surface, and he calculated its value： GFO = 1.4958 × 10^-54 N. This quantity can be useful for further development of the ＂quantum mechanical＂ approach to the description and general notion about the world.
文摘Integer numbers of natural units （Planck units） to express Newton＇s inverse square law of gravitation in terms of quantum mechanical probabilities are used. The strong nuclear force between two coupled nucleons is derived, the minds of giants such as Newton and Einstein are met. There is a considerable continuing effort directed for the understanding of gravity and the constants of nature, last century＇s legacy of Arthur Stanley Eddington.
文摘The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No. 11175019the Fundamental Research Funds for the Central Universities
文摘The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.
文摘In this paper, we consider the relativistic Harnilton-Jacobi （HJ） equation and study Hawking radiation （HR） of scalar particles from uncharged Grumiller black hole （GBH） which is affordable for testing in astrophysics. It is a/so known as Rindler modified Schwarzschild BH. Our aim is not only to investigate the effect of the Rindler parameter a on the Hawking temperature （TH ）, but to examine whether there is any discrepancy between the computed horizon temperature and the standard TH as well. For this purpose, in addition to its naive coordinate system, we study on the three regular coordinate systems, which are Painlevd--Gullstrand （PG）, ingoing Edding^on-Finkelstein （IEF）, and Kruskal-Szekeres （KS） coordinates. In o21 coordinate systems, we calculate the tunneling probabilities of incoming and outgoing scalar particles from the event horizon by using the HJ equation. It has been shown in detail that the considered HJ method is concluded with the conventional T~ in all these coordinate systems without giving rise to the famous factor-2 problem. Filrthermore, in the PG coordinates Parikh-Wilczek＇s tunneling （PWT） method is employed in order to show how one can integrate the quantum gravity （QG） corrections to the semiclassical tunneling rate by including the effects of self-gravitation and back reaction. We then show how this yields a modification in the TH.
文摘In the standard model of particle physics, photons are massless particles with a particular dispersion relation. Tests of this claim at different scales are both interesting and important. Experiments in territory labs and several exterritorial tests have put some upper limits on photon mass, e.g., torsion balance experiment in the lab shows that photon mass should be smaller than 1.2 x 10-51g. In this work, this claim is tested at a cosmological scale by looking at strong gravitational lensing data available and an upper limit of 8.71 x 10-39g on photon mass is given. Observations of energy-dependent gravitational lensing with not yet available higher accuracy astrometry instruments may constrain photon mass better.
