Two Phases of the Non-Commutative Quantum Mechanics with the Generalized Uncertainty Relations

We consider the quantum mechanics on the noncommutative plane with the generalized uncertainty relations \({\Delta } x_{1} {\Delta } x_{2} \ge \frac {\theta }{2}, {\Delta } p_{1} {\Delta } p_{2} \ge \frac {\bar {\theta }}{2}, {\Delta } x_{i} {\Delta } p_{i} \ge \frac {\hbar }{2}, {\Delta } x_{1} {\Delta } p_{2} \ge \frac {\eta }{2}\). We show that the model has two essentially different phases which is determined by \(\kappa = 1 + \frac {1}{\hbar ^{2} } (\eta ^{2} - \theta \bar {\theta })\). We construct a operator \(\hat {\pi }_{i}\) commuting with \(\hat {x}_{j} \) and discuss the harmonic oscillator model in two dimensional non-commutative space for three case κ > 0, κ = 0, κ < 0. Finally, we discuss the thermodynamics of a particle whose hamiltonian is related to the harmonic oscillator model in two dimensional non-commutative space.     

Transmission of 40 Gb/s × 8 WDM channels with 100 GHz spacing using short-period dispersion-managed fiber

We report on the 320 Gb/s (40 Gb/s × 8 channels) WDM transmission experiment using short-period dispersion-managed fiber. After 320-km transmission, the average Q-factor was measured to be better than 20.4 dB. In addition, we compared the performances of various types of fibers in 40-Gb/s based systems. The results show that the SPDMF was robust to both the intra-channel and inter-channel nonlinearities due to its small average dispersion and large local dispersion.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

Calculation of transport parameters in KT-1 tokamak edge plasma

The radial profiles of KT-1 tokamak (major radius of 27 cm, minor radius of 4.25 cm, two poloidal stainless-steel limiters) edge plasma parameters are measured using single and triple electric probes. The particle transport parameters are calculated from the measured edge plasma parameters, and the results are analyzed by the simple fluid approximations. The cross-field particle diffusion coefficient (D) in the boundary plasma of the KT-1 is calculated from the density scrape-off length (λ_n) measured by using a triple probe. The particle density and electron temperature fall exponentially in the radial direction with the e-folding length of λ_n=0.13 cm and λ_e=0.41 cm, respectively. From the scrape-off layer (SOL) model, the experimental values of scrape-off length (λ_n) is used to calculate the cross-field diffusion coefficient (D=1.2×10³cm²/s), roughly corresponding to one third of the typical Bohm value. A simple SOL model with the contribution of recombination is introduced to evaluate the Bohm diffusion in the KT-1 tokamak edge plasma. Cross-field heat conductivity calculated from these deduced values is 5.2D in the SOL of KT-1 edge plasma. These results provide the finally certain information for edge particle transport in the KT-1 boundary plasmas.     

Simplified power supply for long pulse CO2 laser using zero cross switching technique

We propose a simple power supply for a longitudinally pulsed CO₂ laser with long pulse duration by the switching control of AC line (60 Hz) on HV leakage transformer primary, which can generate long pulse of about 3 ms compared to a typical pulsed power supply. In this power supply, a low voltage open loop control for high voltage discharge circuit is employed to avoid the HV sampling or switching, and AC line voltage switched directly by a SCR is applied to the leakage transformer primary. Thus, there is no need of a rectified bridge and an energy-storage capacitor in the discharge circuit, and the leakage transformer allows one to omit a current-limiting resistor. In order to control the laser output power, the pulse repetition rate is adjusted up to 60 Hz. A ZCS circuit and a PIC one-chip microprocessor are used to control the gate signal of SCR precisely.     

Directed flow of lambda hyperons in (2-6 )A GeV Au+Au collisions

Directed flow measurements for Lambda hyperons are presented and compared to those for protons produced in the same Au+Au collisions (2A, 4A, and 6A GeV; b<5-6 fm). The measurements indicate that Lambda hyperons flow consistently in the same direction but with smaller magnitudes. A strong positive flow [for Lambdas] has been predicted in calculations which include the influence of the Lambda-nucleon potential. The experimental flow ratio Lambda/p is in qualitative agreement with expectations (approximately 2/3) from the quark counting rule at 2A GeV but is found to decrease with increasing beam energy.     

Source breakup dynamics in Au + Au collisions at sqrt[s(NN)]=200 GeV via three-dimensional two-pion source imaging

A three-dimensional correlation function obtained from midrapidity, low p(T), pion pairs in central Au+Au collisions at sqrt[s(NN)]=200 GeV is studied. The extracted model-independent source function indicates a long range tail in the directions of the pion pair transverse momentum (out) and the beam (long). A proper breakup time tau(0) ~ 9 fm/c and a mean proper emission duration Delta tau ~ 2 fm/c, leading to sizable emission time differences ({|Delta t(LCM)|} approximately 12 fm/c), are required to allow models to be successfully matched to these tails. The model comparisons also suggest an outside-in "burning" of the emission source reminiscent of many hydrodynamical models.