Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation

The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.     

Time Evolution of Spontaneous Emission Rate of Two Undistinguished Radiators

The behavior of the system of radiators at short and long time intervals in comparison with the retardation between them is studied. The entanglement behavior of atomic states in the process of spontaneous emission is determined. It is demonstrated that at a short time interval the rate of spontaneous emission in an oscillatory manner tends to the exponential law of spontaneous emission. The simple kinetic equation, which describes this stage of system evolution, is obtained.     

Grafting of PMMA brushes on titania nanoparticulate surface via surface-initiated conventional radical and “controlled” radical polymerization (ATRP)

Stable dispersion of titania nanoparticles in organic solvents are obtained by grafting poly(methyl methacrylate) layer on to the surface. Titania nanoparticles are synthesized through the hydrolysis of titanium (IV) isopropoxide. The average size of the titania particles is found to be 15 ± 2 nm. The polymer layer was introduced onto the surface by immobilizing the initiating moiety. Azo initiator moiety required for surface-initiated conventional free radical polymerization and a tertiary bromide initiator moiety required for ATRP are attached covalently to the titania nanoparticulate surface through the surface hydroxyl groups. The “encapsulation” of PMMA layer results in the steric stabilization of the titania nanoparticles. Another important finding is that it is possible to grow polymer layer in a controlled fashion.     

Evolution in shapes of a series of (111)-based In<Subscript>2</Subscript>O<Subscript>3</Subscript> particles

In₂O₃ particles with different morphology were controllably synthesized on silicon substrates by thermal evaporation of In grains at 900 °C. The structure and morphology of the In₂O₃ particles were evaluated using X-ray diffraction, and scanning and transmission electron microscopies. The evolution in shapes as the ratio of {100} relative to {111} increases is clearly observed. The photoluminescence spectrum of the obtained In₂O₃ structures exhibits UV emission centered at about 378 nm and wide-band emission covering the green and orange regions with three peaks around 525, 572, and 604 nm. PACS 81.05.Hd; 81.07.Bc; 81.16.-c; 61.46.-w; 81.40.Gh     

On the Problem of Initial Conditions for Inflation

I review the present status of the problem of initial conditions for inflation and describe several ways to solve this problem for many popular inflationary models, including the recent generation of the models with plateau potentials favored by cosmological observations.     

Extreme gravity tests with gravitational waves from compact binary coalescences: (I) inspiral–merger

The observation of the inspiral and merger of compact binaries by the LIGO/Virgo collaboration ushered in a new era in the study of strong-field gravity. We review current and future tests of strong gravity and of the Kerr paradigm with gravitational-wave interferometers, both within a theory-agnostic framework (the parametrized post-Einsteinian formalism) and in the context of specific modified theories of gravity (scalar–tensor, Einstein–dilaton–Gauss–Bonnet, dynamical Chern–Simons, Lorentz-violating, and extra dimensional theories). In this contribution we focus on (i) the information carried by the inspiral radiation, and (ii) recent progress in numerical simulations of compact binary mergers in modified gravity.     

Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh–Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein–Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter (\(\rho _{0}\)) were explicitly plotted. The results show that, when the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter at \(r=1\) (\(\rho _{0}\)) vanish \((\rho _{0}=\epsilon =0)\), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing \(\rho _{0}\), the transition points are shifted to lower entropies. The same thing is observed when increasing \(\epsilon ^{2}\). In the absence of quintessence-like matter (\(\rho _{0}=0\)), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing \(\rho _{0}\) or \((\epsilon ^2)\).     

Improving the Teleportation Scheme of Three-Qubit State with a Four-Qubit Quantum Channel

Recently, Zhao-Hui Wei et al. (Int. J. Theor. Phys. 55, 4687, 2016) proposed an improved quantum teleportation scheme for one three-qubit unknown state with a four-qubit quantum channel based on the original one proposed by Binayak S. Choudhury and Arpan Dhara (Int. J. Theor. Phys. 55, 3393, 2016). According to their schemes, the three-qubit entangled state could be teleported with one four-qubit cluster state and five-qubit joint measurements or four-qubit joint measurements. In this paper, we present an improved protocol only with single-qubit measurements and the same four-qubit quantum channel, lessening the difficulty and intensity of necessary operations.     

Bidirectional Quantum Teleportation of a Class of <Emphasis Type="Italic">n</Emphasis>-Qubit States by Using (2<Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Bold">2</Emphasis>)-Qubit Entangled States as Quantum Channel

A new protocol of bidirectional quantum teleportation (BQT) is proposed in which the users can transmit a class of n-qubit state to each other simultaneously, by using (2n + 2)-qubit entangled states as quantum channel. The state of the art approaches can only transmit two-qubit states in each round. This scheme is based on control-not operation, single-qubit measurements and appropriate single-qubit unitary operations. It is shown that the protocol is secure in preparation phase.