An embedding scheme for the Dirac equation

An embedding scheme is developed for the Dirac Hamiltonian H. Dividing space into regions I and II separated by surface S, an expression is derived for the expectation value of H which makes explicit reference to a trial function defined in I alone, with all details of region II replaced by an effective potential acting on S and which is related to the Green function of region II. Stationary solutions provide approximations to the eigenstates of H within I. The Green function for the embedded Hamiltonian is equal to the Green function for the entire system in region I. Application of the method is illustrated for the problem of a hydrogen atom in a spherical cavity and an Au(001)/Ag/Au(001) sandwich structure using basis sets that satisfy kinetic balance.Comment: 16 pages, 5 figure

Exact Green Function for Neutral Pauli-Dirac Particle with Anomalous Magnetic Momentum in Linear Magnetic Field

We consider Pauli--Dirac fermion submitted to an inhomogeneous magnetic field. It is showed that the propagator of the neutral Dirac particle with an anomalous magnetic moment in an external linear magnetic field is the causal Green function $S^{c}(x_{b},x_{a})$ of the Pauli--Dirac equation. The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinors expressions. The neutral particle creation probability corresponding to our system is analyzed, which is obtained as function of the introduced field $B'$ and the additional spin magnetic moment $\mu$.Comment: 12 page

An application of Green-function methods to gravitational radiation theory

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is here analyzed by studying the corresponding second-order hyperbolic operator with variable coefficients, instead of using the reduction method from the retarded flat-space Green function in four dimensions. After reduction to canonical form of this hyperbolic operator, the integral representation of the solution in terms of the Riemann function is obtained. The Riemann function solves a characteristic initial-value problem for which analytic formulae leading to the numerical solution are derived.Comment: 18 pages, Revtex4. Submitted to Lecture Notes of S.I.M., volume edited by D. Cocolicchio and S. Dragomir, with kind permission by IOP to use material in Ref. [12]. arXiv admin note: substantial text overlap with arXiv:gr-qc/010107

A Pedestrian Introduction to Gamow Vectors

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrodinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles of the S matrix are the same as the poles of the Green function and are the complex eigenvalues of the Schrodinger equation subject to a purely outgoing boundary condition. The intrinsic time asymmetry of the purely outgoing boundary condition is discussed. Finally, we show that the probability of detecting the decay within a shell around the origin of the decaying state follows an exponential law if the Gamow vector (resonance) contribution to this probability is the only contribution that is taken into account.Comment: 25 RevTex pages, 3 figure

Coupled Chemistry-Emission Model for Atomic Oxygen Green and Red-doublet Emissions in Comet C/1996 B2 Hyakutake

The green (5577 \AA) and red-doublet (6300, 6364 \AA) lines are prompt emissions of metastable oxygen atoms in the $^1$S and $^1$D states, respectively, that have been observed in several comets. The value of intensity ratio of green to red-doublet (G/R ratio) of 0.1 has been used as a benchmark to identify the parent molecule of oxygen lines as H$_2$O. A coupled chemistry-emission model is developed to study the production and loss mechanisms of O($^1$S) and O($^1$D) atoms and the generation of red and green lines in the coma of C/1996 B2 Hyakutake. The G/R ratio depends not only on photochemistry, but also on the projected area observed for cometary coma, which is a function of the dimension of the slit used and geocentric distance of the comet. Calculations show that the contribution of photodissociation of H$_2$O to the green (red) line emission is 30 to 70% (60 to 90%), while CO$_2$ and CO are the next potential sources contributing 25 to 50% ($<$5%). The ratio of the photo-production rate of O($^1$S) to O($^1$D) would be around 0.03 ($\pm$ 0.01) if H$_2$O is the main source of oxygen lines, whereas it is $\sim$0.6 if the parent is CO$_2$. Our calculations suggest that the yield of O($^1$S) production in the photodissociation of H$_2$O cannot be larger than 1%. The model calculated radial brightness profiles of the red and green lines and G/R ratios are in good agreement with the observations made on comet Hyakutake in March 1996

Pion loops in quenched Quantum Chromodynamics

We calculate the divergences of the generating functional of quenched Chiral Perturbation Theory to one loop for a generic number of flavours. The flavour number dependence of our result enlightens the mechanism of quark loop cancellation in the quenched effective theory for any Green function or S matrix element. We also apply our results to $\pi \pi$ scattering and evaluate the coefficient of the chiral log in the S-wave scattering lengths for the quenched case.Comment: Latex, 10 pages, 1 figur

Ratio of shear viscosity to entropy density in multifragmentation of Au + Au

The ratio of the shear viscosity ($\eta$) to entropy density ($s$) for the intermediate energy heavy-ion collisions has been calculated by using the Green-Kubo method in the framework of the quantum molecular dynamics model. The theoretical curve of $\eta/s$ as a function of the incident energy for the head-on Au+Au collisions displays that a minimum region of $\eta/s$ has been approached at higher incident energies, where the minimum $\eta/s$ value is about 7 times Kovtun-Son- Starinets (KSS) bound (1/4$\pi$). We argue that the onset of minimum $\eta/s$ region at higher incident energies corresponds to the nuclear liquid gas phase transition in nuclear multifragmentation.Comment: 6 pages, 8 figure