R.F. O'Connell

Distribution functions in physics: Fundamentals

This is the first part of what will be a two-part review of distribution functions in physics. Here we deal with fundamentals and the second part will deal with applications. We discuss in detail the properties of the distribution function defined earlier by one of us (EPW) and we derive some new results. Next, we treat various other distribution functions. Among the latter we emphasize the so-called P distribution, as well as the generalized P distribution, because of their importance in quantum optics.

Quantum-Mechanical Distribution Functions: Conditions for Uniqueness

Abstract We add to the postulate, that the distribution function give the proper probabilities for the position and momentum variables (actually only the former is needed) and that its connection with the wave function which it represents have the natural invariances, another one. This is that the integral of the product of two distribution functions be equal, except for a universal constant (which turns out to be 2πħ), to the transition probability between the two states they represent. We then show that it follows from these conditions that the distribution function is the one defined earlier by one of us (E.W.).

Analytical inversion of symmetric tridiagonal matrices

In this paper we present an analytical formula for the inversion of symmetrical tridiagonal matrices. The result is of relevance to the solution of a variety of problems in mathematics and physics. As an example, the formula is used to derive an exact analytical solution for the one-dimensional discrete Poisson equation with Dirichlet boundary conditions.

Some properties of a non-negative quantum-mechanical distribution function

We consider the distribution function obtained by smoothing the original distribution function, defined in an earlier publication, with a ground-state harmonic oscillator wave function. We derive its time dependence and show that, in par- ticular, the field-free result does not correspond to the classical result. We point out that the non-negative property of the smoothed function follows immediately from the fact that the integral of the product of two of the original distribution functions is equal, except for a factor 2πh, to the transition probability between the two states they represent.

Radiation reaction in electrodynamics and the elimination of runaway solutions

pole approximation, as a result of which the Compton wavelength comes into play in the role of a size parameter for the extended electron. By contrast, our considerations will be restricted to the dipole interaction with the goal of carrying out the analysis in an exact manner and analyzing carefully the role of the cutoff frequency, ~2, (which enters into the electron form-factor and, in essence, defines the type of extended model used for the electron) in the equation of motion. The most general quantum equation obtained in our analysis, eq. ( 5 ) below, is a new result and it reduces in the classical limit to (7). Both equations contain I2. We point out that a particular choice for I2 (viz. 12-.c¢, corresponding to a point electron) leads to the AL equation of motion but we argue on physical grounds why this choice should be discarded. We then go on tO deduce that an equation independent of 12 may bel achieved by working to or

Relativistic form of radiation reaction

Abstract We present a relativistic extension of the new form which we have recently obtained for the equation of motion of a radiating electron.

The gravitational interaction: Spin, rotation, and quantum effects-a review

Previous work on spin, rotation, and quantum effects in gravitation is surveyed, with particular emphasis on the gravitational two-body interaction, both for elementary particles and for macroscopic bodies. Applications considered include (a) the precession of a gyroscope, (b) rotational effects on the equations of motion for the orbit, (c) binary systems, particularly the binary pulsar PSR 1913+16, and (d) the prospects of measuring spin-orbit and spin-spin forces in the laboratory. In addition, we discuss quantum effects that arise in the interaction between elementary particles. In particular, we point out the potentially decisive role of these forces in high-density matter, with emphasis on the fact that repulsive forces arise that may prevent gravitational collapse. All of the above considerations are within the framework of Einsteins theory of general relativity, albeit extended to treat spin-dependent and quantum forces. Finally, we consider the additional quantum terms that are present if one works with a generalization of Einsteins theory, the Einstein-Cartan-Sciama-Kibble theory of gravitation, in which the spin of matter, as well as its mass, plays a dynamical role.

Quantum oscillator in a blackbody radiation field II. Direct calculation of the energy using the fluctuation-dissipation theorem

Abstract An earlier exact result ( Phys. Rev. Lett. 55 (1985), 2273) for the free energy of an oscillatordipole interacting with the radiation field is obtained using the fluctuation-dissipation theorem. A key feature of the earlier calculation, a remarkable formula for the free energy of the oscillator, is obtained in the form of a corresponding formula for the oscillator energy. This confirms, by a longer, more conventional proof, the earlier result. An advantage of this present method is that separate contributions to the energy can be isolated and discussed. Explicit, closed-form expressions are given and the high-temperature limit is discussed.

Comment on "Quantum measurement and decoherence"

The prototypical Schrodinger cat state, i.e., an initial state corresponding to two widely separated Gaussian wave packets, is considered. The decoherence time is calculated solely within the framework of elementary quantum mechanics and equilibrium statistical mechanics. This is at variance with common lore that irreversible coupling to a dissipative environment is the mechanism of decoherence. Here, we show that, on the contrary, decoherence can in fact occur at high temperature even for vanishingly small dissipation.  2001 Elsevier Science B.V. All rights reserved.

Nongeodesic motion in general relativity

The equations of motion of a spinning body in the gravitational field of a much larger mass are found using both the Corinaldesi-Papapetrou spin supplementary condition (SSC) and the Pirani SSC. These equations of motion are compared with our previous result derived from Guptas quantum theory of Gravitation. It is found that the spin-dependent terms differ in each of the above three results due to a different location of the center of mass of the spinning body. As expected, these terms are not affected by the choice of either Schwarzschild or isotropic coordinates. Finally, for the presently planned Stanford gyroscope experiment, we find the maximum secular displacement of the orbit of the gyro with respect to the orbit of its non-rotating housing to be of the order of (10−7 cm/year)t, a result much smaller than Schiffs result which is proportional to time squared.