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

Dynamics of quantum-classical hybrid system: effect of matter-wave pressure

Radiation pressure affects the kinetics of a system exposed to the radiation and it constitutes the basis of laser cooling. In this paper, we study {\it matter-wave pressure} through examining the dynamics of a quantum-classical hybrid system. The quantum and classical subsystem have no explicit coupling to each other, but affect mutually via a changing boundary condition. Two systems, i.e., an atom and a Bose-Einstein condensate(BEC), are considered as the quantum subsystems, while an oscillating wall is taken as the classical subsystem. We show that the classical subsystem would experience a force proportional to $Q^{-3}$ from the quantum atom, whereas it acquires an additional force proportional to $Q^{-2}$ from the BEC due to the atom-atom interaction in the BEC. These forces can be understood as the {\it matter-wave pressure}.Comment: 7 pages, 6 figue

CRLBs for Pilot-Aided Channel Estimation in OFDM System under Gaussian and Non-Gaussian Mixed Noise

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of channel estimation in wireless communication is a very important issue. Several CRLBs on channel estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic and stochastic CRLBs for Gaussian and non-Gaussian mixed noise. Due to the use of the non-parametric kernel method to build the PDF of non-Gaussian noise, the proposed CRLBs are suitable for practical channel environments with various noise distributions

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

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

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