Neutrino oscillations in de Sitter space-time

We try to understand flavor oscillations and to develop the formulae for describing neutrino oscillations in de Sitter space-time. First, the covariant Dirac equation is investigated under the conformally flat coordinates of de Sitter geometry. Then, we obtain the exact solutions of the Dirac equation and indicate the explicit form of the phase of wave function. Next, the concise formulae for calculating the neutrino oscillation probabilities in de Sitter space-time are given. Finally, The difference between our formulae and the standard result in Minkowski space-time is pointed out.Comment: 13 pages, no figure

Engineering the accurate distortion of an object's temperature-distribution signature

It is up to now a challenge to control the conduction of heat. Here we develop a method to distort the temperature distribution signature of an object at will. As a result, the object accurately exhibits the same temperature distribution signature as another object that is predetermined, but actually does not exist in the system. Our finite element simulations confirm the desired effect for different objects with various geometries and compositions. The underlying mechanism lies in the effects of thermal metamaterials designed by using this method. Our work is of value for applications in thermal engineering.Comment: 11 pages, 4 figure

Hermitian symmetric polynomials and CR complexity

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.Comment: 19 pages, latex, fixed typos, to appear in Journal of Geometric Analysi

Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE

Entropy and specific heat for open systems in steady states

The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general can not describe the steady state of open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.Comment: 4 pages, 7 figure

Warm Jupiters are less lonely than hot Jupiters: close neighbours

Exploiting the Kepler transit data, we uncover a dramatic distinction in the prevalence of sub-Jovian companions, between systems that contain hot Jupiters (periods inward of 10 days) and those that host warm Jupiters (periods between 10 and 200 days). Hot Jupiters, with the singular exception of WASP-47b, do not have any detectable inner or outer planetary companions (with periods inward of 50 days and sizes down to $2 R_{\rm Earth}$). Restricting ourselves to inner companions, our limits reach down to $1 R_{\rm Earth}$. In stark contrast, half of the warm Jupiters are closely flanked by small companions. Statistically, the companion fractions for hot and warm Jupiters are mutually exclusive, particularly in regard to inner companions. The high companion fraction of warm Jupiters also yields clues to their formation. The warm Jupiters that have close-by siblings should have low orbital eccentricities and low mutual inclinations. The orbital configurations of these systems are reminiscent of those of the low-mass, close-in planetary systems abundantly discovered by the Kepler mission. This, and other arguments, lead us to propose that these warm Jupiters are formed in-situ. There are indications that there may be a second population of warm Jupiters with different characteristics. In this picture, WASP-47b could be regarded as the extending tail of the in-situ warm Jupiters into the hot Jupiter region, and does not represent the generic formation route for hot Jupiters.Comment: 12 pages, 7 figures, accepted by Ap

Neutrino oscillations in Kerr-Newman space-time

The mass neutrino oscillation in Kerr-Newman(K-N) space-time is studied in the plane $\theta=\theta_{0}$, and the general equations of oscillation phases are given. The effect of the rotation and electric charge on the phase is presented. Then, we consider three special cases: (1) The neutrinos travel along the geodesics with the angular momentum $L=aE$ in the equatorial plane. (2) The neutrinos travel along the geodesics with L=0 in the equatorial plane. (3) The neutrinos travel along the radial geodesics at the direction $\theta=0$. At last, we calculate the proper oscillation length in the K-N space time. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. When the neutrino travels out of the gravitational field, the blue shift of the oscillation length takes place. We discussed the variation of the oscillation length influenced by the gravitational field strength, the rotation $a^{2}$ and charge $Q$.Comment: 20 pages, no figure