A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network (QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lat...A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network (QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lattice. An artificial neuron may consist of a cell of a quantum cellular automaton or a quantum dot, which confines a single electron. The Coulomb interaction or the spin-spin interaction between neurons can be used to transmit signals and perform logic operations. The recursive formulas of the eigenvalues and eigenvectors between sub-lattices are obtained explicitly. As the application of the formulations, the eigenvalues and eigenvectors of the Hamiltonian operator for the Sierpinskii gasket are calculated.展开更多
基金Supported by the National Natural Foundation of China (79970121).
文摘A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network (QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lattice. An artificial neuron may consist of a cell of a quantum cellular automaton or a quantum dot, which confines a single electron. The Coulomb interaction or the spin-spin interaction between neurons can be used to transmit signals and perform logic operations. The recursive formulas of the eigenvalues and eigenvectors between sub-lattices are obtained explicitly. As the application of the formulations, the eigenvalues and eigenvectors of the Hamiltonian operator for the Sierpinskii gasket are calculated.
