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Band-diagonal operators

(1996-11-15)

Fong, CK

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Wu, PY

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應用數學系

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Department of Applied Mathematics

We show that there are operators on a five-dimensional Hilbert space which are not tridiagonal, and that there are compact operators and normal operators on separable infinite-dimensional spaces which are not band-diagonal.

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Numerical microcanonical ensemble method for calculation on statistical models with large lattice sizes

(1996-11-15)

Wang, JZ

;

Yang, TJ

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交大名義發表

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電子物理學系

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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.

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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.

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Structure of high resistivity GaAs film grown by low-temperature metalorganic chemical vapor deposition

(1996-11-18)

Chen, WC

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Chang, CS

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Chan, SH

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光電工程學系

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Department of Photonics

The structure of a low-temperature GaAs layer grown by low-pressure metalorganic chemical vapor deposition with precursors of triethylgallium and arsine is reported. Dense particles containing Ga clusters are found in a high resistivity GaAs film grown at 420 degrees C, The size and concentration of particles are about 800-1000 nm and 7X10(11) cm(-3), respectively. (C) 1996 American Institute of Physics.

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