A study of local and non-local 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.Comment: 29 pages, 3 figure

Matched Optical Solitary Waves for 3-Level and 5-Level Systems

Exact analytic results are presented that give a general solution for a pair of solitary waves which can propagate through a three- and a five-level system with their shapes invariant. These solitary waves vary widely in shape and form: from ones for which the pulses have similar shape to ones which have very different but \u27\u27complementary\u27\u27 shapes. A general type of solitary-wave pair which is insensitive to small perturbations is identified

Progressive photon mapping for daylight redirecting components

AbstractDaylight redirecting components (DRCs) are characterised by complex transmissive and reflective behaviour that is difficult to predict accurately largely due to their highly directional scattering, and the caustics this produces. This paper examines the application of progressive photon mapping as a state of the art forward raytracing technique to efficiently simulate the behaviour of such DRCs, and how this approach can support architects in assessing their performance.Progressive photon mapping is an iterative variant of static photon mapping that effects noise reduction through accumulation of results, as well as a reduction in bias inherent to all density estimation methods by reducing the associated bandwidth at a predetermined rate. This not only results in simplified parametrisation for the user, but also provides a preview of the progressively refined simulation, thus making the tool accessible to non-experts as well.We demonstrate the effectiveness of this technique with an implementation based on the Radiancephoton mapping extension and a case study involving retroreflecting prismatic blinds as a representative DRC

Quantum chaos and QCD at finite chemical potential

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex. We discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(3) simulation with staggered fermions are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $\mu\approx 0.7$.Comment: LATTICE98(hightemp), 3 pages, 10 figure

Computational renormalization scheme for quantum field theories

We propose an alternative technique for numerically renormalizing quantum field theories based on their Hamiltonian formulation. This method is nonperturbative in nature and, therefore, exact to all orders. It does not require any correlation functions or Feynman diagrams. We illustrate this method for a model Yukawa-like theory describing the interaction of electrons and positrons with model photons in one spatial dimension. We show that, after mass renormalization of the fermionic and bosonic single-particle states, all other states in the Fock space have finite energies, which are independent of the momentum cutoff

Magnetic control of the pair creation in spatially localized supercritical fields

We examine the impact of a perpendicular magnetic field on the creation mechanism of electron-positron pairs in a supercritical static electric field, where both fields are localized along the direction of the electric field. In the case where the spatial extent of the magnetic field exceeds that of the electric field, quantum field theoretical simulations based on the Dirac equation predict a suppression of pair creation even if the electric field is supercritical. Furthermore, an arbitrarily small magnetic field outside the interaction zone can bring the creation process even to a complete halt, if it is sufficiently extended. The mechanism for this magnetically induced complete shutoff can be associated with a reopening of the mass gap and the emergence of electrically dressed Landau levels

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