The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics

We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.     

Similarity Transformations of Hermitian Hamiltonians and Pseudo-Hermitian Coupling Between Two Electromagnetic Modes

Pseudo-Hermitian Hamiltonians and pseudo-Hermitian coupling between two electromagnetic modes are analyzed by using similarity transformations of Hermitian Hamiltonians or of Hermitian operators, including a special metric and biorthogonal relations replacing the usual orthogonal relations used in quantum mechanics. The coupling between two electromagnetic (em) modes including certain decay and amplification processes is related to a coupling matrix G which has parity-time (PT) symmetry and which obeys the pseudo-Hermiticity condition ηGη⁻¹ = G ^† where η is a metric. The linear equations representing the pseudo-Hermitian coupling between the two em modes are diagonalized, in the interaction picture, by introducing ‘dressed’ αˉ and β~ operators which have real or pure imaginary eigenfrequencies. The commutation-relations (CR) for the α~ and β~ operators and for the two-mode operators ā and b~, in the interaction picture and under the condition of real eigenfrequencies are obtained by the use of the pseudo-Hermiticity property of the G matrix. These CR for real eigenfrequencies, are preserved in time without any Langevin noise terms.     

Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Determination of Trace Mercury by Solid Substrate-Room Temperature Phosphorimetry Quenching Method Based on Catalytic Effect of Hg2+on Formation of the Ion Association Complex [Sn(XO)6]4+·[(Fin)4]

A new method for the determination of trace mercury by solid substrate-room temperature phosphorimetry (SS-RTP) quenching method has been established. In glycine-HCl buffer solution, xylenol orange (XO) can react with Sn⁴⁺ to form the complex [Sn(XO)₆]⁴⁺. [Sn(XO)₆]⁴⁺ can interact with Fin⁻ (fluorescein anion) to form the ion associate [Sn(XO)₆]⁴⁺·[(Fin)₄]⁻, which can emit strong and stable room temperature phosphorescence (RTP) on polyamide membrane (PAM). Hg²⁺ can catalyze H₂O₂ oxidizing the ion association complex [Sn(XO)₆]⁴⁺·[(Fin)₄]⁻, which causes the RTP to quench. The ΔIp value is directly proportional to the concentration of Hg²⁺ in the range of 0.016–1.6 fg spot⁻¹ (corresponding concentration: 0.040–4.0 pg ml⁻¹, 0.40 μl spot⁻¹), and the regression equation of working cure is ΔIp=10.03+83.15 m Hg²⁺ (fg spot⁻¹), (r=0.9987, n=6) and the detection limit (LD) is 3.6 ag spot⁻¹(corresponding concentration: 9.0×10^–15 g ml⁻¹, the sample volume: 0.4 μl). This simple, rapid, accurate method is of high selectivity and good repeatability, and it has been successfully applied to the determination of trace mercury in real samples. The reaction mechanism for catalyzing H₂O₂ oxidizing the ion association complex ([Sn(XO)₆]⁴⁺·[(Fin)₄]⁻) SS-RTP quenching method to determine trace mercury is also discussed.     

Theoretical models for the extracavity Raman laser with crystalline Raman medium

The rate equation model of an extracavity Raman laser is deduced for the first time to the best knowledge of the authors. The normalized radiation transfer equations of the extracavity Raman laser are given. The normalized radiation transfer equations and rate equations were solved numerically to find the optimum reflectivity of the output coupler to realize the maximum conversion efficiency at the first Stokes for both the single and double-pass pumping configurations. Also, the pulse duration of the first Stokes was investigated numerically. The rate equations are verified to be a good approximation to the radiation transfer equations for the regime of low Raman gain and long pump pulse duration. Furthermore, it is found that the optimum reflectivity of the first Stokes and the second Stokes threshold are influenced significantly by the minor feedback of the resonator mirror at the second Stokes. PACS 42.55 42.55.Ye; 42.65 42.65.Dr; 02.60 02.60.Lj; 63.20 63.20.-e     

Synthesis of single-crystalline wurtzite aluminum nitride nanowires by direct arc discharge

High-density hexagonal aluminum nitride (h-AlN) nanowires were synthesized through the direct reaction of Al with nitrogen gas without catalyst and template using a direct arc discharge method. The as-grown AlN nanowires were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and Raman spectroscopy. The h-AlN nanowires have a diameter in the range 20–70 nm and a length of several tens of micrometers. Vapor–solid growth mechanisms can be employed to explain the formation of the h-AlN nanowires. PACS 81.05.Ea; 81.10.Bk; 81.16.Dn; 68.65.-k; 81.16.-c     

Bump formation on a glass surface with a transparent coating using femtosecond laser processing

The morphology of a glass surface having a transparent coating processed with focused femtosecond laser pulses is investigated. The transparent coating is formed of poly-methyl methacrylate (PMMA). When the glass was coated with a PMMA film with a thickness of 2.8 μm, bumps were formed over a wide range of axial focus positions. The same laser pulse energy produced cavities when processing bare glass with no coating. The bumps were formed as a result of suppressing material emission from the glass surface by a shielding effect of plasma generated by ablation of the PMMA film and by physical blocking of the PMMA film. A thinner film with a thickness of 0.7 μm produced a reduced shielding effect, forming an exploded bump with a small pit at its center and debris around the periphery. PACS 44.10.+i; 61.80.Ba; 79.20.Ds     

Optical filaments and optical bullets in dispersive nonlinear media

We have investigated the evolution of picosecond and femtosecond optical pulses governed by the amplitude vector equation in the optical and UV domains. We have written this equation in different coordinate frames, namely, in the laboratory frame, the Galilean frame, and the moving-in-time frame and have normalized it for the cases of different and equal transverse and longitudinal sizes of optical pulses or modulated optical waves. For optical pulses with a small transverse size and a large longitudinal size (optical filaments), we obtain the well-known paraxial approximation in all the coordinate frames, while for optical pulses with relatively equal transverse and longitudinal sizes (so-called light bullets), we obtain new non-paraxial nonlinear amplitude equations. In the case of optical fields with low intensity, we have reduced the nonlinear amplitude vector equations governing the light-bullet evolution to the linear amplitude equations. We have solved the linear equations using the method of Fourier transform. An unexpected new result is the relative stability of light bullets and the significant decrease in the diffraction enlargement of light bullets with respect to the case of long pulses in the linear propagation regime.     

Re-hardening of hadron transverse mass spectra in relativistic heavy-ion collisions

We analyze the spectra of pions and protons in heavy-ion collisions at relativistic energies from 2 A GeV to 65+65 A GeV by using a jet-implemented hadron-string cascade model. In this energy region, hadron transverse mass spectra first show softening until SPS energies, and re-hardening may emerge at RHIC energies. Since hadronic matter is expected to show only softening at higher energy densities, this re-hardening of spectra can be interpreted as a good signature of the quark-gluon plasma formation     

Laser-sintered mesoporous TiO2 electrodes for dye-sensitized solar cells

Low-temperature laser sintering has been successfully demonstrated to improve the overall conversion efficiency of dye-sensitized solar cells. Mesoporous TiO₂ electrodes were prepared from a colloidal solution of TiO₂ nanopowders by a laser direct-write technique and then sintered by a quasi-continuous-wave UV laser (λ=355 nm) for the fabrication of dye-sensitized solar cells. The overall conversion efficiency of the cells based on the laser-sintered TiO₂ electrodes was double that of the devices with non-laser-treated TiO₂ electrodes. This enhancement is attributed to both the removal of organic additives and the improved inter-nanoparticle electrical contacts induced by the laser-sintering process, which led to an increase in porosity and dye-absorption sites in the TiO₂ electrodes. PACS 61.80.Ba; 61.46.+w; 73.22.-f; 84.60.Jt