Roy J. Glauber

Time‐Dependent Statistics of the Ising Model

The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for any one spin depend on the values of the neighboring spins. This dependence is determined, in part, by the detailed balancing condition obeyed by the equilibrium state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N‐member chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different time, are found explicitly. The influence of a uniform, time‐varying magnetic field upon the model is discussed, and the frequency‐dependent magnetic susceptibility is found in the weak‐field limit. Some fluctuation‐dissipation theorems are derived which relate the susceptibility to the Fourier transform of the time‐dependent correlation function of the magnetization at equilibrium.

High-energy scattering of protons by nuclei

The theory of high-energy hadron-nucleus collisions is discussed by means of the multiple-diffraction theory. Effects of the Coulomb field are accounted for in elastic scattering by light and heavy nuclei. Inelastic scattering is treated by means of the shadowed single collision approximation at small momentum trans- fer and the corresponding multiple collision expansion at large momentum trans- fers. The theory is compared with the measurements of Bellettini et al. on pro- ton-nucleus scattering at 20 GeV/c by finding density distributions for the nuclei which provide least-squares fits to the data. The nucleon densities found are closely comparable in dimensions to the known charge densities. The predicted sums of the angular distributions of elastic and inelastic scattering reproduce the experimental angular distributions fairly closely.

Spatial coherence and density correlations of trapped Bose gases

We study first- and second-order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second-order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first- and second-order coherence are therefore functions of temperature, chemical potential, and position. The second-order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasiparticle excitations. The results of some recent experiments on second- and third-order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed.

Classical behavior of systems of quantum oscillators

Abstract We show that if the equations of motion of a system of coupled oscillators assume a certain general form, states of the system which are initially coherent remain coherent at all times. It follows that the motion of the system is nearly classical in nature.

The initiation of superfluorescence

The early stages of a superfluorescent pulse are described with full account of both quantum and propagation effects. The pulse is triggered by zero point fluctuations of the atomic polarization field. If the number of atoms N is large these zero point fluctuations, and the electric field radiated at early times as well, have a gaussian distribution with width 4/N. An equivalent classical stochastic process is found in terms of which the later, intrinsically nonlinear part of the radiation problem can be analyzed.

Polarization in elastic proton-nucleus scattering

Abstract The polarizations which result from the elastic scattering of protons by spin-zero nuclei are discussed by means of the multiple-diffraction approximation. They are found to depend largely on the elementary proton-nucleon central-force and spin-orbit scattering amplitudes and, at least for heavy nuclei, to depend very little upon the remaining proton-nucleon amplitudes which are proportional to the spins of the target nucleons. In particular, the values of the polarization measured at small angles can be used to determine the imaginary part of the forward proton-nucleon spin-orbit scattering amplitude. The real part of that amplitude, on the other hand, is much less sensitively determined by the polarization distributions. Its evaluation will probably require more detailed measurements on the proton spin distribution. We show that the effects of the Coulomb field on the polarization distributions are significant at all scattering angles. Included among these electromagnetic effects is the relativistic interaction of the proton magnetic moment with the Coulomb field.

Mass formulas for static solitons

Abstract General explicit formulas are derived for the first quantum-mechanical correction to the mass of a static soliton in a weakly-coupled two-dimensional scalar field theory.

Spin-rotation effects in elastic proton-nucleus scattering

Abstract We discuss a particular form of spin-rotation distribution in the context of proton-nuclear scattering and indicate its behaviour as a function of momentum transfer. We point out that besides effectively completing our knowledge of the nuclear scattering amplitudes the measurement of this function would furnish information both about the nuclear density distribution and about parts of the fundamental proton-nucleon spin-orbit scattering amplitudes. The latter are terms of the amplitudes which have been left undetermined by existing polarization data.

On momentum-loss spectra in proton scattering on deuterium

The multtple scattering formalmm ts used m an mvest~gatmn of the mo- mentum-loss spectra of protons scattered on deutermm at high energms. The results can be used to set hm~ts on the strength of mtermedmte N* states m h~gh-energy scattering of protons from nucle~ as well as to provide mformatmn on neutron-proton scattering.

Quantum Theory of Particle Trapping by Oscillating Fields

The technique of trapping atomic particles in electromagnetic fields has opened the possibility of dramatic advances in high-precision spectroscopy. Most theoretical analyses of trapping have thus far been carried out in classical terms, but since the very purpose of such techniques is to minimize the energy of particle motion, it is clear that their success implies a need for quantum mechanical analysis. Only by treating such systems quantum mechanically can we hope to understand the influence of residual particle motions on radiative interactions, or any fundamental limits on the lowest attainable particle temperatures.