R. E. Wagner

Quantum fluctuations in the dressed vacuum of a bosonic model system

Quantum fluctuations and the polarizability of the vacuum state are sometimes interpreted in terms of virtual particles that come into and out of existence for a limited amount of time. We study the spatial and temporal properties of these auxiliary particles on a numerical space-time grid for a one-dimensional model system. This approach permits us to compute the average distance between virtual particles and their lifetime. The creation dynamics of the virtual particles from the bare vacuum state is also examined.

Exponential enhancement of field-induced pair creation from the bosonic vacuum

Using numerical solutions to quantum field theory, the creation of boson-antiboson pairs from the vacuum under a very strong localized external electric field is explored. The simulations reveal that the initial linear increase of the number of particles turns into an exponential growth. This self-amplification can be understood as the result of the interaction of the previously generated particles with the creation process. While the number of particles keeps increasing, the spatial shape of the (normalized) charge density of the created particles reaches a universal form that can be related to the bound states of the supercritical potential well. We accompany the space-time resolved quantum field theoretical simulations with a model calculation that allows us to interpret the numerical simulations in terms of simple classical mechanical concepts.

Spatial Electron Clouds at Fractional and Multiple Magneto-optical Resonances

We solve numerically the relativistic Liouville equation for the phase space density of an atom in a uniform static magnetic field and a laser field. If the cyclotron frequency that is associated with the magnetic field is tuned slightly above a multiple or a fraction of the frequency of the laser field, the electron’s dynamics becomes resonant and its velocity can approach the speed of light. We compare the spatial electron distributions at these resonances with those obtained from the corresponding non-relativistic calculations and find the formation of stable ring-shaped distributions at the multiple resonances. The fractional resonances are characterized by figure-eight or propeller-shaped distributions.

Comparison of mass renormalization schemes for simple model systems

We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on the requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete example of bosonic quadratic and quartic interactions. The results are compared with those obtained by the standard renormalization technique based on a spectral analysis of the usual field-based propagators. We also discuss a potential method for renormalizing a quantum field theory in a non-perturbative way using computational methods.

Absorbing-like boundaries for quantum field theoretical grid simulations

Abstract We introduce a computational method that permits us to increase the interaction time for quantum mechanical and quantum field theoretical simulations of multi-particle states on a finite space–time grid. In contrast to the usual approach where the unwanted portion of the wave function close to the grid boundaries is absorbed by a potential with a negative imaginary part, this method is unitary and therefore conserves the norm of the state. This technique is based on assigning particles close to the boundary a larger effective mass (or slower speed of light) such that the particles slow down and cannot re-enter the interaction zone. The method can therefore be applied to multi-particle states for which imaginary potential methods fail.

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.

Scanning techniques for decomposition based imaging of turbid media

Methods for using laser light to detect multiple hidden objects inside random scattering media are discussed. It is shown that the resolution of objects that are upstream relative to the incoming laser source is lowered by the presence of objects further downstream. A scanning method is introduced which uses weighted shadow patterns of objects at fixed locations to ‘mask’ one section of the detection region, so that objects in the unmasked region can be located by a scanning technique. It is found that the method is very sensitive to random noise, but this noise sensitivity can be reduced through a scanning method where a weighted, double-rod configuration is used for scanning.

Local and nonlocal spatial densities in quantum field theory

We use a one-dimensional model system to compare the predictions of two different yardsticks to compute the position of a particle from its quantum field theoretical state. Based on the first yardstick (defined by the Newton-Wigner position operator), the spatial density can be arbitrarily narrow, and its time evolution is superluminal for short time intervals. Furthermore, two spatially distant particles might be able to interact with each other outside the light cone, which is manifested by an asymmetric spreading of the spatial density. The second yardstick (defined by the quantum field operator) does not permit localized states, and the time evolution is subluminal.

Space-time properties of a boson-dressed fermion for the Yukawa model

We analyze the interaction of fermions and bosons through a one-dimensional Yukawa model. We numerically compute the energy eigenstates that represent a physical fermion, which is a superposition of bare fermionic and bosonic eigenstates of the uncoupled Hamiltonian. It turns out that even fast bare fermions require only low-momentum dressing bosons, which attach themselves to the fast fermion through quantum correlations. We compare the space-time evolution of a physical fermion with that of its bare counterpart and show the importance of using dressed observables. The time evolution of the center of mass as well as the wave packets spatial width suggests that the physical particle has a lower mass than the sum of the masses of its bare constituents. The numerically predicted dressed mass agrees with that from lowest-order perturbation theory as well as with the renormalized mass obtained from the corresponding Feynman graphs. For a given momentum, this lower mass leads to a faster physical particle and a different relativistic spreading behavior of the wave packet.