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The eigenvalue problem of the operator a + zeta(boson creation operator) is solved for arbitrarily complex zeta by applying a nonunitary operator to the vacuum state. This nonunitary approach is compared with the unitary approach leading for the absolute value of zeta less than 1 to squeezed coherent states.
In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.
We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.
A finite element analysis using hybrid triangular-rectangular elements is developed to estimate eigenvalues of a rectangular waveguide. Use of rectangular vector-edge finite elements in the vicinity of the PEC boundary and triangular elements in the interior region more accurately models the physical nature of the electromagnetic field, and consequently quicken the convergence.
Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speedup is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.
The equations of motion of thin circular rings are derived and solved for in-plane in-extensional deformation. Modal characteristics are tabulated for the five lowest flexural modes of vibration of semicircular ring segments for the possible combinations of homogeneous boundary conditions that can occur.
Orthogonal function and wave equation of inverse scattering problem in quantum mechanics
Critical volume of cylindrical reactors calculated using n-group diffusion theory
Explicit numerical methods for integrating coupled nonlinear ordinary differential equations with parasitic eignevalues
Eigenvalves of dynamic spin Hamiltonian for trivalent iron ion in titanium dioxide host crystals - tables
Optimum lower bounds to excited states of Hamiltonian having known set of eigenfunctions
Lower bounds of low lying levels of Li ion and helium calculated using partitioning technique with multivalued bracketing function
Criticism of Choi-Smith extension of Lowdin lower bounds formalism to multidimensional reference manifold
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Resonant frequencies in thin circular conical shells
Expectation values and kinetic energy for vibrational-rotational levels of ground states of H2, HD, and D2
Existence and extendability of continuous eigenvector branches and application of nonlinear programming algorithms to nonlinear heat generation and rotating string problems
Effect of rotation on structural and dynamic behavior of spinning body with flexible appendages, and application to Skylab Apollo telescope mount and orbital workshop