Convection in a gravitational field

We set up a classical stochastic model for the irreversible dynamics of a lattice gas under gravity. We show that for a class of initial states the system converges to equilibrium, which obeys the laws of thermostatics.Dedicated to Oliver Penrose.     

Classical theory of the interaction between a spinor field and the gravitational field: First-order field equations

The classical theory of the interaction of a neutral spin-1/2 Dirac field and the gravitational field is studied. For the purely gravitational part of the Lagrangian, written in terms of a vierbein and the local connection coefficient _ab , (regarded as independent field variables), the usual first-order form is adopted. For the Dirac part, however, a different choice is made, in which the covariant derivative of is built with the aid of the vierbein instead of with _ab . This still yields a first-order formalism, but one in which _ab is related to the vierbein in the same way as it would be in the absence of. This ensures that the global connection remains symmetric in andv in the presence of. The way in which the vierbein field equation leads to a familiar Einstein equation with a symmetric and conserved stress tensor on its right side is also analyzed.     

Evaluation and preliminary measurement of the interaction of a dynamical gravitational near field with a cryogenic gravitational wave antenna

We present a detailed analysis of the effect of the gravitational field generated by a small rotating quadrupole on a graviational wave antenna and we report on the preliminary measurement of this effect on the Explorer 2270 kg cryogenic gravitational wave antenna of the Rome group. The induced signal had an amplitude twenty times larger than the detector noise when the antenna was equipped with an FET amplifier and was easily detected without requiring integration in time. We remark that with this method we were able to make an absolute calibration of a gravitational wave antenna.     

Spin Hall effect induced by a gravitational field

The experiment by Collela et al. (1975) [1] evidenced in a striking manner how the gravitational field appears in quantum mechanics. Within the modern framework of gauge theories, one can ascribe such effect as due to gauge fields originated from fundamental symmetries of spacetime: local transformations of the Lorentz-Poincaré group. When this gauge principle is applied to the Dirac equation, we obtain kinematical correlations between the gravitational field and the spin of the particles. The phenomenon is similar to the spin Hall effect found in condensed matter systems, although much smaller in magnitude. Actual measurements may require highly precision interferometric techniques with spin-polarized neutrons.     

Pair creation by a photon in an electric field

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region of relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than the “vacuum” energy in electric field: ω?eE/m. For smaller photon energies the low energy approximation is developed. At ω?eE/m the found probability describes the absorption of soft photon by the particles created by an electric field.     

Black hole in a gravitational field

An exact solution of the vacuum Einstein field equations representing a Schwarzschild black hole in an external gravitational field is derived using a formalism developed by Ernst.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Relativistic gas in a gravitational field

Equations describing the kinetics and hydrodynamics of a relativistic gas in a gravitational field are obtained using the concept of a gravitational field as a physical field in a pseudo-Euclidean space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1982.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Magnetic field focusing of hyperfine interaction in hydrogen

We find a new correction to hyperfine splitting in the ground state of hydrogen atom in magnetic field. The physical basis for this effect is the reduction of the size of the electron orbit in magnetic field. As a result, the value of the wavefunction at the origin increases which can be called magnetic focusing. Another magnetic-field-induced effect is the appearance of field dependent tensor forces.     

Orbital equations in a weak gravitational field

With the obtainment of the Synge equations of motion in third approximation for a test particle, we determine the relativistic force in the field generated by a massive body obtained previously in terms of its potentials. Afterwards, in order to study the motion, we obtain the integral of energy and the integral of angular momentum. By means of them, the general form for the trajectory of an equatorial orbit and for the advance of its apsidal line are obtained. As we will see, the known diverse contributions for this advance appears in the general form after strong supplementary conditions on the potentials. As application, with such assumptions these contributions are derived in a unified way.     

Phase ordering dynamics in a gravitational field

We study the dynamics of phase ordering in the presence of an external gravitational field, namely a field that varies linearly with distance in one direction. Starting from microscopic considerations, we motivate reasonable phenomenological models for cases with nonconserved and conserved order parameter. We present detailed numerical results from our model for the case with conserved order parameter.     

Trapped Bose condensate in a gravitational field

The Bose condensation of atoms in finite 1D and 2D parabolic traps placed in a gravitational field is considered. The distortion of the trap potential in this field is modeled by a combination of two rectangular 1D and 2D traps. The change in the critical temperature T _c is found with regard to the cutoff and renormalization of the spectrum of these model potentials. The shift of the critical temperature T _c in the gravitational field is calculated. The shift sign and magnitude depend on the way of introducing the gravitational field. For a certain choice, three critical temperatures can be sequentially observed. These temperatures can be attributed to three Bose condensations that occur in the cyclic motion of the trap along the Earth (I)-space (II)-Earth (III) route.     

Hard thermal loops in a gravitational field

We calculate the high-temperature (T ⁴) limit of the 3-graviton vertex function, with a single loop of internal scalar particles in thermal equilibrium. We use the analytically continued imaginary-time formalism. We verify a particular case of the Ward identity connecting the 3- and 2-graviton functions. This confirms that there is covariance under general coordinate transformations (which reduce to the identity at infinity). We remark that the ghost-ghost-graviton vertex (with ghost and graviton internal lines) has noT ⁴ term. This implies that the 3-graviton function with internal graviton (and ghost) lines must satisfy the Ward identity too, so it is possible for it to be proportional to the scalar contribution. We have verified this for that part of the vertex function which is manifestly symmetric and traceless in the six Lorentz indices.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Chaos in a gravitational field with dipoles

In this paper we investigate the dynamics of a test particle in the gravitational field with dipoles. At first we study the gravitational potential by numerical simulations, we find that, for appropriate parameters, there are two different cases in the potential curve: one is the one-well case with a stable critical point, and the other is the three-well case with three stable critical points and two unstable critical points. By performing Poincare sections for different values of the parameters and initial conditions, we find a regular motion and a chaotic motion. From these Poincar6 sections,we further confirm that the chaotic motion of the test particle originates mainly from the dipoles.