Gaussian elimination and numerical instability /

"UILU-ENG 77 1714."

Deposition and washout computations based on the generalized Gaussian plume model /

"September 30, 1963."

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

Orientation of biological cells using plane-polarized gaussian beam optical tweezers

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of the trapped cells. We show that it is possible to controllably align or rotate disc-shaped cells-chloroplasts of Spinacia oleracea-in a plane-polarized Gaussian beam trap, using optical torques resulting predominantly from circular polarization induced in the transmitted beam by the non-spherical shape of the cells.

Gaussian quantum Monte Carlo methods for fermions and bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Nonclassicality of a photon-subtracted Gaussian field

We investigate the nonclassicality of a photon-subtracted Gaussian field, which was produced in a recent experiment, using negativity of the Wigner function and the nonexistence of well-behaved positive P function. We obtain the condition to see negativity of the Wigner function for the case including the mixed Gaussian incoming field, the threshold photodetection and the inefficient homodyne measurement. We show how similar the photon-subtracted state is to a superposition of coherent states.

Normalized Gaussian Networks with Mixed Feature Data

With mixed feature data, problems are induced in modeling the gating network of normalized Gaussian (NG) networks as the assumption of multivariate Gaussian becomes invalid. In this paper, we propose an independence model to handle mixed feature data within the framework of NG networks. The method is illustrated using a real example of breast cancer data.

Gaussian operator bases for correlated fermions

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.