Browsing by Author "Kao, YM"

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Adomian's decomposition method for eigenvalue problems
(2005-03-01)
Kao, YM
;
Jiang, TF
;
應用數學系
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物理研究所
;
Department of Applied Mathematics
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
(2005-12-01)
Kao, YM
;
Jiang, TF
;
Yu, IA
;
應用數學系
;
物理研究所
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 Lambda-type coherent medium. This EIT system is described by the coupled Maxwell-Schrodinger 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
(2004-02-01)
Luan, PG
;
Kao, YM
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物理研究所
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Institute of Physics
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 Schrodinger equation of some quantum mechanical problems.
Low-temperature series expansions for square-lattice Ising model with first and second neighbour interactions
(2002-12-20)
Kao, YM
;
Chen, M
;
Lin, KY
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物理研究所
;
Institute of Physics
We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J(1) and second-neighbour interaction J(2) to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Pade approximants to estimate the critical exponents and the critical temperature for different ratios of R = J(2)/J(1). The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.
Poincare cycle of an Ehrenfest multiurn model in a one-dimensional ring
(2004-02-01)
Kao, YM
;
物理研究所
;
Institute of Physics
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 Poincare 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 Poincare cycle is only related to the initial configuration.
Transition temperature of a weakly interacting Bose gas
(2006-04-01)
Kao, YM
;
Jiang, TF
;
物理研究所
;
Institute of Physics
We report a theoretical study of the transition temperature of a trapped interacting dilute Bose gas. The system is treated like a two-fluid model consisting of a thermal component and a condensate component. Through the calculation of the energy spectra, the origins of various effects on the transition temperature are derived. We found that the interactive shift is affected by both the thermal component and the condensate component. The latter effect, which is about 34% of the former, has never been reported so far. With these two effects, our calculated interactive shift agrees very well with the recent measurement.