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

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

Remark on approximation in the calculation of the primordial spectrum generated during inflation

We re-examine approximations in the analytical calculation of the primordial spectrum of cosmological perturbation produced during inflation. Taking two inflation models (chaotic inflation and natural inflation) as examples, we numerically verify the accuracy of these approximations.Comment: 10 pages, 6 figures, to appear in PR

Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use dynamical network approach to evaluate the collective financial failure---systemic risk---quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided on sub-periods, where within each sub-period banks may contiguously fail due to links to either (i) assets or (ii) other banks, controlled by two parameters, probability of internal failure $p$ and threshold $T_h$ ("solvency" parameter). The systemic risk non-linearly increases with $p$ and decreases with average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller $T_h$), the smaller the systemic risk---for some $T_h$ values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic (ii) controlled by probability $p_2$---a condition for the bank to be solvent (active) is stochastic---the systemic risk decreases with decreasing $p_2$. We analyse asset allocation for the U.S. banks.Comment: 7 pages, 7 figure

Non-Thermal Production of WIMPs and the Sub-Galactic Structure of the Universe

There is increasing evidence that conventional cold dark matter (CDM) models lead to conflicts between observations and numerical simulations of dark matter halos on sub-galactic scales. Spergel and Steinhardt showed that if the CDM is strongly self-interacting, then the conflicts disappear. However, the assumption of strong self-interaction would rule out the favored candidates for CDM, namely weakly interacting massive particles (WIMPs), such as the neutralino. In this paper we propose a mechanism of non-thermal production of WIMPs and study its implications on the power spectrum. We find that the non-vanishing velocity of the WIMPs suppresses the power spectrum on small scales compared to what it obtained in the conventional CDM model. Our results show that, in this context, WIMPs as candidates for dark matter can work well both on large scales and on sub-galactic scales.Comment: 6 pages, 2 figures; typo corrected; to appear in PR

Quantum Brayton cycle with coupled systems as working substance

We explore the quantum version of Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process, one corresponds to the external magnetic field (characterized by $F_x$) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by $F_y$). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by $F_x$), whereas the subsystem's cycle is of quantum Otto in another Brayton cycle (characterized by $F_y$). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system are usually larger than the sum of work done by the two subsystems. The other interesting finding is that for the cycle characterized by $F_y$, the subsystem can be a refrigerator while the total system is a heat engine. The result in the paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.Comment: 7 pages, 3 figures, accepted by Phys. Rev.

Dust-to-gas ratio, XCOX_{\rm CO} factor and CO-dark gas in the Galactic anticentre: an observational study

We investigate the correlation between extinction and H~{\sc i} and CO emission at intermediate and high Galactic latitudes (|b|>10\degr) within the footprint of the Xuyi Schmidt Telescope Photometric Survey of the Galactic anticentre (XSTPS-GAC) on small and large scales. In Paper I (Chen et al. 2014), we present a three-dimensional dust extinction map within the footprint of XSTPS-GAC, covering a sky area of over 6,000\,deg$^2$ at a spatial angular resolution of 6\,arcmin. In the current work, the map is combined with data from gas tracers, including H~{\sc i} data from the Galactic Arecibo L-band Feed Array H~{\sc i} survey and CO data from the Planck mission, to constrain the values of dust-to-gas ratio $DGR=A_V/N({\rm H})$ and CO-to-$\rm H_2$ conversion factor $X_{\rm CO}=N({\rm H_2})/W_{\rm CO}$ for the entire GAC footprint excluding the Galactic plane, as well as for selected star-forming regions (such as the Orion, Taurus and Perseus clouds) and a region of diffuse gas in the northern Galactic hemisphere. For the whole GAC footprint, we find $DGR=(4.15\pm0.01) \times 10^{-22}$\,$\rm mag\,cm^{2}$ and $X_{\rm CO}=(1.72 \pm 0.03) \times 10^{20}$\,$\rm cm^{-2}\,(K\,km\,s^{-1})^{-1}$. We have also investigated the distribution of "CO-dark" gas (DG) within the footprint of GAC and found a linear correlation between the DG column density and the $V$-band extinction: $N({\rm DG}) \simeq 2.2 \times 10^{21} (A_V - A^{c}_{V})\,\rm cm^{-2}$. The mass fraction of DG is found to be $f_{\rm DG}\sim 0.55$ toward the Galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and CO-traced molecular gas in the same region. This result is consistent with the theoretical work of Papadopoulos et al. but much larger than that expected in the $\rm H_2$ cloud models by Wolfire et al.Comment: 11 pages, 7 figures, accepted for publication in MNRA

A Two-Component Explosion Model for the Giant Flare and Radio Afterglow from SGR1806-20

The brightest giant flare from the soft $\gamma$-ray repeater (SGR) 1806-20 was detected on 2004 December 27. The isotropic-equivalent energy release of this burst is at least one order of magnitude more energetic than those of the two other SGR giant flares. Starting from about one week after the burst, a very bright ($\sim 80$ mJy), fading radio afterglow was detected. Follow-up observations revealed the multi-frequency light curves of the afterglow and the temporal evolution of the source size. Here we show that these observations can be understood in a two-component explosion model. In this model, one component is a relativistic collimated outflow responsible for the initial giant flare and the early afterglow, and another component is a subrelativistic wider outflow responsible for the late afterglow. We also discuss triggering mechanisms of these two components within the framework of the magnetar model.Comment: 7 pages including 3 figures, emulateapj5.sty, accepted for publication in ApJ Letter