Browsing by Author "Wang, JZ"

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Calculation of numerical microcanonical ensemble method on 2D statistical models
(1998-06-01)
Wang, JZ
;
Yang, TJ
;
電子物理學系
;
Department of Electrophysics
In our earlier work, we proposed a new microcanonical ensemble method and showed that the numerical results of this method are correct in 1D models. In this paper, the numerical data in 2D models are presented. One of our calculations is concentrated on fermionic models, because fermionic models behave quite differently from bosonic models when the dimension is larger than two (there may be boson-fermion duality in 1D). Our results come out to be consistent with exact values. To our knowledge, there is no other numerical methods which can present reliable calculation on fermionic models with large lattice, especially when the temperature is low. In addition to the test on fermionic models, we also show our results on quantum 2D XY model. We calculate longitudinal spin-spin correlation, specific heat, vortex density and vortex pair density. These results agree with the calculations by other methods. The data of vortex density and vortex pair density seem to. display directly the unbinding of vortices and antivortices.
Effects of the quantum size and an off-center donor atom on energy levels in a quantum dot
(1998-08-01)
Wang, JZ
;
Yang, TJ
;
電子物理學系
;
Department of Electrophysics
Gorecki and Brown [J. Phys. B 22, 2659 (1989)] proposed a variational theory for the ground state. They assumed the trial wave function in confined systems as f phi, where f acted as a variable contour function to minimize the energy. In practical calculations, it is only possible to calculate electronic energy levels at some shapes of f to decide which f gives the minimal energy. Due to this constraint in the variational calculation of f, their method gives unsatisfactory results in asymmetrical quantum problems, and therefore is rarely used. We generalize their method by assuming the trial wave function as f psi, where psi is a linear combination of basis functions. In our improvement, the use of the linear combination of basis functions acts not only to simulate efficiently the asymmetrical state but also to the give energy levels of the excited state. For the same reason, our method can be applied in open systems and in the problem where a new potential exists. Therefore, the goal of our improvement is to propose a general variational method. As applications, the changes of binding energies and donor states in spherical and ellipsoidal semiconductor quantum dots are studied when the position of the donor is shifted and when the size of the dot is changed.
Numerical microcanonical ensemble method for calculation on statistical models with large lattice sizes
(1996-11-15)
Wang, JZ
;
Yang, TJ
;
交大名義發表
;
電子物理學系
;
National Chiao Tung University
Based on the microcanonical ensemble theory in statistical mechanics, we devise a method that can be used to enhance the capability of numerical calculation on statistical models with large lattice sizes. In our method, we take the expectation value of the energy, as defined in quantum mechanics, instead of the eigenvalue as the energy of a physical system. We show mathematically that the relevant physical quantities obtained in this way are unchanged in the thermodynamical limit and we apply this method to numerical calculations. In this paper, we present our numerical results with the one-dimensional spinless fermionic model as a first test of our method. The numerical calculations are done to a 4096 lattice size using a computer with a speed of about 40 mflops. Our numerical data agree quite well with the exact values. Also, the fluctuation of data is small, in contrast to that obtained using the quantum Monte Carlo method.
Numerical microcanonical ensemble method for calculation on statistical models with large lattice sizes
(1996-11-15)
Wang, JZ
;
Yang, TJ
;
電子物理學系
;
Department of Electrophysics
Based on the microcanonical ensemble theory in statistical mechanics, we devise a method that can be used to enhance the capability of numerical calculation on statistical models with large lattice sizes. In our method, we take the expectation value of the energy, as defined in quantum mechanics, instead of the eigenvalue as the energy of a physical system. We show mathematically that the relevant physical quantities obtained in this way are unchanged in the thermodynamical limit and we apply this method to numerical calculations. In this paper, we present our numerical results with the one-dimensional spinless fermionic model as a first test of our method. The numerical calculations are done to a 4096 lattice size using a computer with a speed of about 40 mflops. Our numerical data agree quite well with the exact values. Also, the fluctuation of data is small, in contrast to that obtained using the quantum Monte Carlo method.