Photoelectric Properties of GaS1-xSex (0 ≤ x ≤ 1) Layered Crystals.

In this study, the photoelectric properties of a complete series of GaS1-xSex (0 ≤ x ≤ 1) layered crystals are investigated. The photoconductivity spectra indicate a decreasing bandgap of GaS1-xSex as the Se composition x increases. Time-resolved photocurrent measurements reveal a significant improvement in the response of GaS1-xSex to light with increasing x. Frequency-dependent photocurrent measurements demonstrate that both pure GaS crystals and GaS1-xSex ternary alloy crystals exhibit a rapid decrease in photocurrents with increasing illumination frequency. Crystals with lower x exhibit a faster decrease in photocurrent. However, pure GaSe crystal maintains its photocurrent significantly even at high frequencies. Measurements for laser-power-dependent photoresponsivity and bias-voltage-dependent photoresponsivity also indicate an increase in the photoresponsivity of GaS1-xSex as x increases. Overall, the photoresponsive performance of GaS1-xSex is enhanced with increasing x, and pure GaSe exhibits the best performance. This result contradicts the findings of previous reports. Additionally, the inverse trends between bandgap and photoresponsivity with increasing x suggest that GaS1-xSex-based photodetectors could potentially offer a high response and wavelength-selectivity for UV and visible light detection. Thus, this work provides novel insights into the photoelectric characteristics of GaS1-xSex layered crystals and highlights their potential for optoelectronic applications.

Ehrenfest urn model with interaction.

We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first- or second-order phase transition. The relaxation time to the equilibrium state, the Poincaré cycles of the equilibrium state and the most far-from-equilibrium state, and the duration time of the states during first-order phase transition are calculated. It was shown that the scaling behavior the Poincaré cycles could serve as an indication to the nature of phase transition, and the behavior of the ratio of duration time of the states could be strong evidence of the metastability during first-order phase transition.

Design of multichannel DWDM fiber Bragg grating filters by Lagrange multiplier constrained optimization.

We present the synthesis of multi-channel fiber Bragg grating (MCFBG) filters for dense wavelength-division-multiplexing (DWDM) application by using a simple optimization approach based on a Lagrange multiplier optimization (LMO) method. We demonstrate for the first time that the LMO method can be used to constrain various parameters of the designed MCFBG filters for practical application demands and fabrication requirements. The designed filters have a number of merits, i.e., flat-top and low dispersion spectral response as well as single stage. Above all, the maximum amplitude of the index modulation profiles of the designed MCFBGs can be substantially reduced under the applied constrained condition. The simulation results demonstrate that the LMO algorithm can provide a potential alternative for complex fiber grating filter design problems.

Adomian's decomposition method for eigenvalue problems.

We extend the Adomian's decomposition method to work for the general eigenvalue problems, in addition to the existing applications of the method to boundary and initial value problems with nonlinearity. We develop the Hamiltonian inverse iteration method which will provide the ground state eigenvalue and the explicit form eigenfunction within a few iterations. The method for finding the excited states is also proposed. We present a space partition method for the case that the usual way of series expansion failed to converge.

Adomian's decomposition method for electromagnetically induced transparency.

We developed the Adomian's decomposition method to work for the electromagnetically induced transparency (EIT) problem. The method is general and capable to solve the coupled nonlinear partial differential equations for a light pulse passing through a three-level -type coherent medium. This EIT system is described by the coupled Maxwell-Schrödinger equations and optical Bloch equations. In the weak probe field case, the results agree with perturbation solutions and experimental data. In the stronger probe field case while perturbation may fail, our results reproduce experimental data well. With the techniques of spatial and time partitions, we extend the decomposition method that will be versatile for the investigation of the light pulse propagating through a coherent atomic medium.

Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model.

We study the continuous limit of a multibox Erhenfest urn model proposed before by the authors. The evolution of the resulting continuous system is governed by a differential equation, which describes a diffusion process on a circle with a nonzero drifting velocity. The short time behavior of this diffusion process is obtained directly by solving the equation, while the long time behavior is derived using the Poisson summation formula. They reproduce the previous results in the large M (number of boxes) limit. We also discuss the connection between this diffusion equation and the Schrödinger equation of some quantum mechanical problems.

Poincaré cycle of an Ehrenfest multiurn model in a one-dimensional ring.

We study an Ehrenfest multiurn model of a one-dimensional ring, generalizing the directed transport in the previous model to arbitrary transports. We analytically study the evolution of the system and calculate the Poincaré cycle for given transport probabilities. The result shows that the average number of balls in an urn evolves according to the transport probability, but the Poincaré cycle is only related to the initial configuration.

Poincaré cycle of a multibox Ehrenfest urn model with directed transport.

We propose a generalized Ehrenfest urn model of many urns arranged periodically along a circle. The evolution of the urn model system is governed by a directed stochastic operation. Method for solving an N-ball, M-urn problem of this model is presented. The evolution of the system is studied in detail. We find that the average number of balls in a certain urn oscillates several times before it reaches a stationary value. This behavior seems to be a peculiar feature of this directed urn model. We also calculate the Poincaré cycle, i.e., the average time interval required for the system to return to its initial configuration. The result indicates that the fundamental assumption of statistical mechanics holds in this system.