Jürgen Audretsch

Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction

We consider an atom in interaction with a massless scalar quantum field. We discuss the structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom through the quantum vacuum. Our main intention is to identify and to analyze quantitatively the distinct contributions of vacuum fluctuations and radiation reaction to the spontaneous excitation of a uniformly accelerated atom in its ground state. This gives an understanding of the role of the different physical processes underlying the Unruh effect. The atoms evolution into equilibrium and the Einstein coefficients for spontaneous excitation and spontaneous emission are calculated.

Trajectories and spin motion of massive spin-1/2 particles in gravitational fields

From covariant Dirac theory in curved space-time, dynamical equations for the motion of the spin and the spin-induced non-geodesic behaviour of the particle trajectories are deduced. This is done for arbitrary space-times in a generally covariant and observer- independent way. The procedure is thereby based on a WKB scheme and a Gordon decomposition of the Dirac probability four-current. A complete, correspondence between the quantum mechanical equations of motion and the classical equations for extended isolated bodies or pole-dipole particles is found. This can as well be taken as a confirmation that to the first order of a WKB approximation the gyro-gravitational factors of the classical angular nromentum and of the intrinsic quantum mechanical spin agree.

Constructive axiomatic approach to spacetime torsion

The EPS scheme of constructive axiomatics for the spacetime geometry leads to a Weyl structure. Torsion cannot be introduced by this method but is obtained in the following by enlarging the axiomatics. If spacetime geometry is what prescribes the respective trajectories to the light rays and freely falling particles, and the propagation to the spin of these particles, then spacetime is a manifold with a Weyl-Cartan structure with a totally antisymmetric contorsion. If one combines the non-operational demand for a unified geometrical description of all three types of physical propagation processes into one universal affine geometry, then spacetime reduces to a Weyl-Cartan space with a totally antisymmetric contorsion.

RAMSEY FRINGES IN ATOMIC INTERFEROMETRY : MEASURABILITY OF THE INFLUENCE OF SPACE-TIME CURVATURE

The influence od space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyse in detail the suitability of the Ramsey atom beam interferometer for the measurement of the phase shift caused by the Riemannian curvature of the earth. It appears that the detection should be possible with minor modifications of existing devices within the near future. The paper is divided into two parts. The first one is concerned with the derivation of general relativistic correction terms to the Pauli equation starting from the fully covariant Dirac equation and their physical interpretation. The inertial effects of acceleration and rotation are included. In the second part we calculate the phase shift as seen in a laboratory resting on the rotating earth and examine various possibilities to enlarge the sensitivity of the apparatus to space-time curvature. Some remarks on the Lense-Thirring effect and on gravitational waves are made. Since the two parts may be more or less interesting for physicists with different research fields they are written in such a way that each one may be read without much reference to the other one.

Wave fields in Weyl spaces and conditions for the existence of a preferred pseudo-Riemannian structure

Previous axiomatic approaches to general relativity which led to a Weylian structure of space-time are supplemented by a physical condition which implies the existence of a preferred pseudo-Riemannian structure. It is stipulated that the trajectories of the short wave limit of classical massive fields agree with the geodesics of the Weyl connection and it is shown that this is equivalent to the vanishing of the covariant derivative of a “mass function” of nontrivial Weyl type. This in turn is proven to be equivalent to the existence of a preferred metric of the conformal structure such that the Weyl connection is reducible to a connection of the bundle of orthonormal frames belonging to this distinguished metric.

RADIATIVE ENERGY SHIFTS OF AN ACCELERATED TWO-LEVEL SYSTEM

We consider the influence of acceleration on the radiative energy shifts of atoms in Minkowski space. We study a two-level atom coupled to a scalar quantum field. Using a Heisenberg picture approach, we are able to separate the contributions of vacuum fluctuations and radiation reaction to the Lamb shift of the two-level atom. The resulting energy shifts for the special case of a uniformly accelerated atom are then compared with those of an atom at rest.

Neutrino Radiation in Gravitational Fields

A differential equation representing radiation solutions of the general relativistic Weyl equation is derived. Their optical properties and the group of motion of the corresponding energy-momentum tensor are studied. If there exists neutrino radiation the Riemann space must be algebraically special and the propagation of the neutrinos occurs only along one of the principal null directions. Gravitational- and neutrinopp-waves taken together, represent an exact solution of the Weyl-Einstein system of field equations.

Matter wave interferometry and why quantum objects are fundamental for establishing a gravitational theory

More recently, a number of interferonletric experiments with electrons, neutrons, and atones have been performed in the gravitational field of the earth and in non-inertial frames of reference. In atomic interferometry, additional high-precision experiments are expected to be clone ill the near future. The results obtained with electrons, neutrons, and atoms, respectively, can be understood by means of the Schrodinger or, in the polarized case, by means of the Pauli equation, both of which are coupled to the external gravito-inertial field. Based on the characteristic features read off from these experiments, one can scat up a constructive axiomatic approach for establishing an appropriate spacetime geometry and can, independently, develop a gauge theoretical formalism for gravity. Both constructions make the Riemann-Cartan geometry of spacetime manifest. This geometry carries torsion as well as curvature. The Riemannian geometry of Einsteins gravitational theory can be recovered as a limiting case for the motion of classical point particles and light rays. We put the Dirac equation, formulated in a non-inertial frame of reference, into an arbitrary gravitational field represented by the spacetime geometry obtained. We compute the consequences for interferometric experiments and provide thereby a theoretical basis for future experiments.

Neutron interference: general theory of the influence of gravity, inertia and space-time torsion

The general theory of the influence of gravity, inertia (i.e. interferometer motion) and space-time torsion on the outcome of neutron interference experiments is presented. The exact results are obtained in a general relativistic treatment based on the description of a stationary working interferometer in Riemann-Cartan space-time and on the WKB approximation for the neutron waves. Particular attention is paid to the influence on the spinor amplitude. There are two types of resulting amplitude effects; one originates in the non-integrability of the spinor connection and represents the influence of a modified Riemann-Cartan curvature; the other is caused by the influence of the interferometer rotation and acceleration and of space-time torsion during the time interval between the emission of the two coherent neutron waves. For practical purposes small effects are treated in an approximation. Two examples of a global evaluation of the expressions are given. Applications including a gravitational Aharonov-Bohm effect are discussed.

Thermal particle production in a contracting and expanding universe without singularity

The creation of massive spin-0 particles described by the conformally coupled Klein-Gordon equation in a 3-flat Robertson-Walker universe ds2 = R2(η)(dη2 − dx2 − dy2 − dz2 with contraction-expansion law R2 = b2η2 + R20 for −∞ < η < +∞ is studied. It represents a time-symmetric universe for which the singularity is avoided. Particles are created in the out-region with a nonrelativistic thermal spectrum with temperature T = b(2πR2kB)−1 and chemical potential μ = −12mR20R−2. The latter implies an expotential damping for large m.