Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

Quantum Tunneling of Massive Particles from a Garfinkle-Horowitz-Strominger Dilatonic Black Hole

Hawking radiation is viewed as a process of quantum tunneling. The massive particles‘ tunneling from Garfinkle-Horowitz-Strominger black hole is investigated. Using Jingyi Zhang‘s de Broglie wave method, we get the unthermal spectrum, and the result is consistent with the underlying unitary theory.     

椭圆强非局域空间光孤子

对傍轴椭圆高斯光束在具有椭圆对称响应特性的强非局域非线性介质中的演化规律进行研究，得到了光束各参量演化的精确解析解，分析了单向空间光孤子和强非局域椭圆空间光孤子的形成条件，发现了椭圆光孤子的相移与介质响应函数的椭圆率有关. 关键词： 椭圆对称强非局域响应介质 椭圆强非局域空间光孤子 相移     

Hawking Radiation of Dirac Particles in a Nonuniformly Rectilinearly Accelerating Black Hole

The Hawking radiation of Dirac particles on the event horizon of a nonuniformly rectilinearly accelerating black hole is studied in this paper. First, we construct the symmetrized null tetrad from which the spin coefficients and Dirac equation are derived. Next, by proposing generalized tortoise coordinate transformation, the decoupling problem of the Dirac equation with nonzero rest mass is solved. Finally, by analytic continuation, the Hawking thermal spectrum formula of Dirac particle for nonuniformly rectilinearly accelerating black hole is obtained.     

Study of the pulsed laser vapor doping of Si(1 0 0) with KrF excimer laser and BCl3 gas

The properties of pulsed laser vapor doping on p-Si(1 0 0) with a KrF (248 nm) excimer pulsed laser (248 nm) and BCl₃ gas are reported in this paper. The doped samples are characterized by the resistance measured using a four-probe method, since the sheet resistance changes with the carrier concentration of the sample. The doping effects with the variation of laser energy density, pulse number, and the pressure of BCl₃ were investigated in terms of the sheet resistance. In this way, the optimized parameters were obtained and used for the positive heavy doping on p-Si(1 0 0) and p-Si(1 1 1). Then, using a square mesh under the above conditions, an image doping was completed. Finally, the metal–semiconductor Ohmic contacts were realized by plating Ag and Cu films on the doped surface.     

Tunneling radiation of a Gibbons-Maeda dilaton black hole

We use the Parikh-Wilczek method to treat Hawking radiation as a tunneling process across the event horizon and calculate the emission rate of a Gibbons-Maeda dilaton black hole. We show that if self-gravitation is taken into account, then the radiation deviates from the purely thermal spectrum, and the corrected spectrum is consistent with an underlying unitary theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 172–175, April, 2007.     

Quantum Thermal Effect of Dirac Particles in a Nonuniformly Rectilinearly Accelerating Black Hole with Electric Charge, Magnetic Charge, and Cosmological Constant

The Hawking radiation of Dirac particles in an arbitrarily rectilinearly accelerating Kinnersley black hole with electromagnetic charge and cosmological constant is investigated by using the generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time and the polar angle. The Hawking thermal radiation spectrum of Dirac particles is also derived.     

斜孔气膜冷却数值模拟分析

本文通过数值模拟分析圆柱孔和扩散孔的单斜孔气膜冷却特性,考察复合角、孔型和吹风比对流场和气膜冷却效果的影响。结果表明,复合角的引入使气膜侧向分布更宽,但冷却效果沿主流方向衰减更快。适中吹风比得到的气膜能更有效的保护壁面。在相同吹风比和复合角条件下,扩散孔的气膜冷却效率比圆柱孔更好,且冷却更为均匀持久。     

Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.