The analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the single pencil beam (SPB) algorithm for the calculation of dose distributions for photon beams. AAA was developed to improve the dose calculation accuracy, especially in heterogeneous media. The total dose deposition is calculated as the superposition of the dose deposited by two photon sources (primary and secondary) and by an electron contamination source. The photon dose is calculated as a three-dimensional convolution of Monte-Carlo precalculated scatter kernels, scaled according to the electron density matrix. For the configuration of AAA, an optimization algorithm determines the parameters characterizing the multiple source model by optimizing the agreement between the calculated and measured depth dose curves and profiles for the basic beam data. We have combined the acceptance tests obtained in three different departments for 6, 15, and 18 MV photon beams. The accuracy of AAA was tested for different field sizes (symmetric and asymmetric) for open fields, wedged fields, and static and dynamic multileaf collimation fields. Depth dose behavior at different source-to-phantom distances was investigated. Measurements were performed on homogeneous, water equivalent phantoms, on simple phantoms containing cork inhomogeneities, and on the thorax of an anthropomorphic phantom. Comparisons were made among measurements, AAA, and SPB calculations. The optimization procedure for the configuration of the algorithm was successful in reproducing the basic beam data with an overall accuracy of 3%, 1 mm in the build-up region, and 1%, 1 mm elsewhere. Testing of the algorithm in more clinical setups showed comparable results for depth dose curves, profiles, and monitor units of symmetric open and wedged beams below dmax. The electron contamination model was found to be suboptimal to model the dose around dmax, especially for physical wedges at smaller source to phantom distances. For the asymmetric field verification, absolute dose difference of up to 4% were observed for the most extreme asymmetries. Compared to the SPB, the penumbra modeling is considerably improved (1%, 1 mm). At the interface between solid water and cork, profiles show a better agreement with AAA. Depth dose curves in the cork are substantially better with AAA than with SPB. Improvements are more pronounced for 18 MV than for 6 MV. Point dose measurements in the thoracic phantom are mostly within 5%. In general, we can conclude that, compared to SPB, AAA improves the accuracy of dose calculations. Particular progress was made with respect to the penumbra and low dose regions. In heterogeneous materials, improvements are substantial and more pronounced for high (18 MV) than for low (6 MV) energies.

We study a two-electron quantum dot molecule in a magnetic field by the direct diagonalization of the Hamiltonian matrix. The ground states of the molecule with the total spin S = 0 and S = 1 provide a possible realization for a qubit of a quantum computer. Switching between the states is best achieved by changing the magnetic field. Based on an analysis of the wave function, we show that the system consists of composite particles formed by an electron and flux quanta attached to it. This picture can also be used to explain the spin phase diagram.

In this work, a novel three-dimensional superposition algorithm for photon dose calculation is presented. The dose calculation is performed as a superposition of pencil beams, which are modified based on tissue electron densities. The pencil beams have been derived from Monte Carlo simulations, and are separated into lateral and depth-directed components. The lateral component is modeled using exponential functions, which allows accurate modeling of lateral scatter in heterogeneous tissues. The depth-directed component represents the total energy deposited on each plane, which is spread out using the lateral scatter functions. Finally, convolution in the depth direction is applied to account for tissue interface effects. The method can be used with the previously introduced multiple-source model for clinical settings. The method was compared against Monte Carlo simulations in several phantoms including lung- and bone-type heterogeneities. Comparisons were made for several field sizes for 6 and 18 MV energies. The deviations were generally within (2%, 2 mm) of the field central axis d(max). Significantly larger deviations (up to 8%) were found only for the smallest field in the lung slab phantom for 18 MV. The presented method was found to be accurate in a wide range of conditions making it suitable for clinical planning purposes.

A novel, efficient optimization method for physical problems is presented. The method utilizes the noise inherent in stochastic functions. As an application, an algorithm for the variational optimization of quantum many-body wave functions is derived. The numerical results indicate superior performance when compared to traditional techniques. [S0031-9007(97)