Transitions into the negative-energy Dirac continuum

We compare the predictions of the single-particle Dirac equation with quantum field theory for an electron subjected to a space and time dependent field. We demonstrate analytically and numerically that a transition into the negative-energy subspace predicted by the single-particle Dirac equation is directly associated with the degree of suppression of pair-production as described by quantum field theory. We show that the portion of the mathematical wave function that populates the negative-energy states corresponds to the difference between the positron spatial density for systems with and without an electron initially present

Interpretational difficulties in quantum field theory

Based on space-time-resolved solutions to relativistic quantum field theory we illustrate interpretational difficulties in associating field-theoretical quantities with properties of particles. These difficulties are related to the fact that the definition of the spatial probability density of particles depends on the choice of the Hilbert subspace on which the field operator is projected. We illustrate these problems by analyzing pair-production probabilities and spatial densities for the electron-positron dynamics associated with a spatially localized subcritical potential that is turned on and off in time

Effects of relativity on the time-resolved tunneling of electron wave packets

We solve numerically the time-dependent Dirac equation for a quantum wave packet tunneling through a potential barrier. We analyze the spatial probability distribution of the transmitted wave packet in the context of the possibility of effectively superluminal peak and front velocities of the electron during tunneling. Both the Dirac and Schrodinger theories predict superluminal tunneling speeds. However, in contrast to the Dirac theory the Schrodinger equation allows a possible violation of causality. Based on an analysis of the tunneling process in full temporal and spatial resolution, we introduce an instantaneous tunneling speed that can be computed inside the potential barrier

Velocity half-sphere model for multiple scattering in a semi-infinite medium

We show how the velocity half-sphere model [S. Menon, Q. Su, and R. Grobe, Phys. Rev. E 72, 041910 (2005)] recently introduced to predict the propagation of light for an infinite turbid medium can be extended to account for the emission of multiply scattered light for a geometry with a planar boundary. A comparison with exact solutions obtained from Monte Carlo simulations suggests that this approach can improve the predictions of the usual diffusion theory for both isotropic and highly forward scattering media with reflecting interfaces

Creation of multiple electron-positron pairs in arbitrary fields

We examine the spontaneous breakdown of the matter vacuum triggered by an external force of arbitrary strength and spatial and temporal variations. We derive a nonperturbative framework that permits the computation of the complete time evolution of various multiple electron-positron pair probabilities. These time-dependent probabilities can be computed from a generating function as well as from solutions to a set of ratelike equations with coupling constants determined by the single-particle solutions to the time-dependent Dirac equation. This approach might be of relevance to the planned experiments to observe for the first time the laser-induced breakdown process of the vacuum

Klein paradox with spin-resolved electrons and positrons

Using numerical solutions to relativistic quantum field theory with space-time resolution, we illustrate how an incoming electron wave packet with a definite spin scatters off a supercritical potential step. We show that the production rate is reduced of only those electrons that have the same spin as the incoming electron is reduced. This spin-resolved result further clarifies the importance of the Pauli-exclusion principle for the Klein paradox

Critique of the Wigner tunneling speed and a proposed alternative

In the context of superluminal propagation of wave packets through potential barriers, the tunneling speed is usually characterized by the Wigner velocity. We propose an alternative speed that takes into account the interference between the incoming and the reflected waves and leads to a better estimation of arrival time for a wave packet entering the tunneling region. This arrival time is derived by an extrapolation from inside the barrier. The analytical theory is based on the stationary phase approximation whose validity is justified by a comparison with the numerical solution of the time-dependent Dirac equation

Electric-field-induced relativistic Larmor-frequency reduction

Using the numerical solution to the time-dependent Dirac equation we show that the effect of relativity on the usual Larmor period for an electron in a magnetic field can be enhanced drastically if a suitably scaled and aligned static electric field is added to the interaction. This electric field does not change the electron\u27s speed but leads to an elliptical spin precession due to relativity. This spin precession is accompanied by a position-dependent spin distribution

Timing of pair production in time-dependent force fields

We examine the creation and annihilation dynamics for electron-positron pairs in a time-dependent but subcritical electric force using a simplified model system. Numerical and semianalytical solutions to computational quantum field theory show that despite the continuity of the quantum field operator in time, the actual number of created particles can change in a discontinuous way if the field changes abruptly. The number of permanently created particles after the pulse, however, increases continuously with the duration of the electric field pulse, suggesting a transition from an exclusive annihilation to a creation regime

Time-resolved Compton scattering for a model fermion-boson system

We study the scattering of a boson with a fermion with full spatial and temporal resolution based on the one-dimensional Yukawa Hamiltonian. In quantum field theory this interaction is described by the annihilation and creation of bosons with intermediate virtual particle states. We show that this process can be modeled in the center-of-mass frame by a scattering potential, permitting us to interpret the absorption and re-emission processes in quantum mechanical terms of a characteristic force. This Compton force between the fermion and boson is repulsive for large distances and attractive for shorter spacings. We also examine the periodic dynamics of a fermion and a boson that are spatially confined to a ring cavity in which they counterpropagate, enabling us to study interactions independent of the transients that characterize the (one-time) scattering event of two wave packets