Anomalous Paths in Quantum Mechanical Path-Integrals

We investigate modifications of the discrete-time lattice action, for a quantum mechanical particle in one spatial dimension, that vanish in the na\"ive continuum limit but which, nevertheless, induce non-trivial effects due to quantum fluctuations. These effects are seen to modify the geometry of the paths contributing to the path-integral describing the time evolution of the particle, which we investigate through numerical simulations. In particular, we demonstrate the existence of a modified lattice action resulting in paths with any fractal dimension, d_f, between one and two. We argue that d_f=2 is a critical value, and we exhibit a type of lattice modification where the fluctuations in the position of the particle becomes independent of the time step, in which case the paths are interpreted as superdiffusive L\'{e}vy flights. We also consider the jaggedness of the paths, and show that this gives an independent classification of lattice theories.Comment: 7 pages,6 figure

Noise and Order in Cavity Quantum Electrodynamics

In this paper we investigate the various aspects of noise and order in the micromaser system. In particular, we study the effect of adding fluctuations to the atom cavity transit time or to the atom-photon frequency detuning. By including such noise-producing mechanisms we study the probability and the joint probability for excited atoms to leave the cavity. The influence of such fluctuations on the phase structure of the micromaser as well as on the long-time atom correlation length is also discussed. We also derive the asymptotic form of micromaser observables.Comment: 31 pages and 8 figure

Quantum Field Theory with Classical Sources - Linearized Quantum Gravity

In a previous work and in terms of an exact quantum-mechanical framework, $\hbar$-independent causal and retarded expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge were derived in the presence of a conserved classical electric current. The classical $\hbar$-independent Maxwell's equations then naturally emerged. In the present work, we extend these considerations to linear gravitational quantum deviations around a flat Minkowski space-time in a Coulomb-like gauge. The emergence of the classical causal and properly retarded linearized classical theory of general relativity with a conserved classical energy-momentum tensor is then outlined. The quantum-mechanical framework also provides for a simple approach to classical quadrupole gravitational radiation of Einstein and microscopic spontaneous graviton emission and/or absorption processes