arXiv subjects
Publications and source records attributed to J. C. Wells.
It is shown how initial conditions can be appropriately defined for the integration of Lorentz-Dirac equations of motion. The integration is performed \QTR{it}{forward} in time. The theory is applied to the case of the motion of an electron in an intense laser pulse, relevant to nonlinear Compton scattering.
We investigate the thermal properties of circular semiconductor quantum dots in high magnetic fields using finite temperature Hartree-Fock techniques. We demonstrate that for a given magnetic field strength quantum dots undergo various shape phase transitions as a function of temperature, and we outline possible observable consequences.
We describe computational methods for the theoretical study of explicit correlations beyond the mean field in excitons confined in semiconductor quantum dots in terms of the Auxiliary-Field Monte Carlo (AFMC) method. Using AFMC, the many-body problem is formulated as a Feynman path integral at finite temperatures and evaluated to numerical precision. This approach is ideally suited for implementation on high-performance parallel computers. Our strategy is to generate a set of mean-field states via the Hartree-Fock method for use as a basis for the AFMC calculations. We present preliminary results.
We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.
The two-center Dirac equation for an electron in the external electromagnetic field of two colliding heavy ions in the limit in which the ions are moving at the speed of light is exactly solved and nonperturbative amplitudes for free electron-positron pair production are obtained. We find the condition for the applicability of this solution for large but finite collision energy, and use it to explain recent experimental results. The observed scaling of positron yields as the square of the projectile and target charges is a result of an exact cancellation of a nonperturbative charge dependence and holds as well for large coupling. Other observables would be sensitive to nonperturbative phases.
We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using light-front variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic charges of the ions.
Presented here is a description of the ionization of hydrogen and hydrogenic ions by antiproton-impact, based on very large scale numerical solutions of the time-dependent Schrödinger equation in three spatial dimensions and on analysis of the topology of the electronic eigenenergy surfaces in the plane of complex internuclear distance. Comparison is made with other theories and very recent measurements.
In relativistic heavy-ion collisions, the strong Lorentz-contracted electromagnetic fields are capable of producing copious numbers of lepton pairs through the two-photon mechanism. Monte Carlo techniques have been developed that allow the exact calculation of production by this mechanism when a semi-classical approximation is made to the motion of the two ions. Here, we develop a hybrid Monte Carlo technique that enables us to calculate the impact parameter dependence of the two-photon mechanism for lepton-pair production, and by using this result, we obtain the probability distribution for multiple-pair production as a function of impact parameter. Computations are performed for S$+$Au and Pb$+$Pb systems at 200 A GeV and 160 A GeV, respectively. We also compare our results with the equivalent photon approximation and elucidate the differences.