If the magnetic flux trapped in a superconducting quantum-interference device has observable values $\pm \frac{h}{2e}$, which alternate in time, and if the value at a given moment is unknown, it is in general impossible to determine that value without affecting the results of subsequent observations.

We present new results of Monte Carlo simulations for self-avoiding walks on randomly diluted square and simple-cubic lattices performed very close to the percolation thresholds. Our results indicate the asymptotic behavior of the walk dimension to be rather similar to the undiluted lattice even at critical dilution.

A general cluster updating algorithm for Monte Carlo simulations is presented. The method contains arbitrary probability functions which can be used to minimize the relaxation time. It is applicable to systems where the interaction energy has a global (discrete or continuous) symmetry. Special cases cover standard site-by-site updating as well as the cluster updating method proposed by Swendsen and Wang for Ising and Potts models.

Using stored spin-polarized ultracold neutrons subjected to a temporally varying magnetic field, we have demonstrated a manifestation of Berry's phase. We verified several properties of Berry's phase which include its solid-angle dependency and additivity for multiple excursions along the same path in parameter space.

Experiments are presented which demonstrate the conversation of certain integrals of motion during Hamiltonian chaos where the conservation of some of the integrals has been broken by the overlap of resonances. Experimentally, conservation laws are demonstrated through the observation of restrictions on transport, in phase space, of chaotic trajectories. Transport of plasma ions during stochastic motion in an electrostatic wave is followed by means of laser-induced fluorescence on metastable "test particles" produced by optical pumping.

We propose that the $r$-process elements may be synthesized in the helium zones surrounding a newly forming neutron star. Neutrinos released from a cooling neutron star produce neutrons (and other nuclides) by neutral-current excitations of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. If the neutron-star progenitor is metal-poor, compact, or both, the flux of free neutrons is sufficiently intense and of long enough duration to generate an $r$ process.

We solve Einstein's field equation via null-strut calculus (NSC). This working version of Regge calculus makes maximal use of light rays. We model the Kasner universe—prototype of the Belinsky-Khalatnikov-Lifshitz mixmaster oscillation generic to all crunch cosmologies. We demonstrate that in evolution NSC (1) conserves energy to a degree comparable to the standard finite difference method, and (2) is free of the Courant instability. NSC handles successfully both the dynamics and the manufacture of the initial-value data, in full conformity with the York initial-value prescription.

A new three-parameter family of radiative, cylindrically symmetric solutions of the Einstein vacuum equations is presented. Its members represent analytic models of a cylindrical pulse of gravitational radiation reflecting off a straight-line cosmic string.

We link the moments of the vertex operator describing photon emission to a vielbein satisfying Maurer-Cartan structure equations connected with the Virasoro algebra. We also discuss string theory in terms of the Abelianized Virasoro operators and describe the consequences of our approach for the structure of the spectrum-generating algebra.

A new method of simulating systems with a complex action which was recently introduced is applied to lattice QCD at finite density. At infinite gauge coupling I obtain a phase diagram which, in nice agreement with mean-field theory, gives a critical value of the chemical potential unrelated to the baryon mass. At the same time we demonstrate explicitly the failure of the quenched approximation.

Monte Carlo calculations on lattices with large spatial volume show that the SU(3) deconfining phase transition is more weakly first order than previously thought. We have studied the transition for $N_T=4\mathrm{} \mathrm{and} 6$ on lattices of spatial volumes ${16}^3$, ${20}^3$, and ${24}^3$. The ${24}^3$×4 calculations show a sharp first-order phase transition, yielding a latent heat $\frac{\Delta \mathcal{E}}{T^4}$ of 2.54±0.12. The ${24}^3$×6 calculations suffer greater finite-volume smearing, but suggest that $\frac{\Delta \mathcal{E}}{T^4}=2.48\mathrm{}\pm 0.24$. Correlation lengths increase significantly near the transition, and the energy plus pressure of the ordered phase depends strongly on $\beta$.

We report here on a search for the lepton-family-number-violating decay $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$. We found no evidence for this decay mode and we establish an upper limit on its branching ratio of 1.1×${10}^{-9\mathrm{}}$ at the 90% confidence level (C.L.) for a uniform phase-space decay distribution. We also use this result to establish an upper limit for the branching ratio of the decay ${\pi }^0\to {\mu }^{+}{e}^{-}$ of 7.8×${10}^{-8\mathrm{}}$ (90% C.L.).

In (2+1)-dimensional models with a Chern-Simons term, there is a periodicity in the parameter $\frac{e^2}{2\mu }$, where $e$ is the smallest charge in the theory and $\frac{\mu }{2}$ is the coefficient of the Chern-Simons term. Since $\mu \to -\mu$ under the action of time reversal $T$, in such a theory the question of $T$ invariance becomes involved with the dynamical issue of what are the allowable values of the charge. We show how cross sections develop $T$-violating terms for "forbidden" values of the charge. Connections are made with some recent ideas concerning the mechanism of high-temperature superconductivity.

The analysis of the cross section and the tensor analyzing power of the reaction $p+\overrightarrow{d}\to {}_{}{}^3{}_{}{}^{}\mathrm{He}+\eta$ provides us with the most direct, and the strongest, signature of the meson double-scattering three-body mechanism in $\mathrm{pd}$ capture reactions.

Evidence is presented for a $\pi h_{\frac{9}{2}}$ band crossing at surprisingly low rotational frequency in the odd-neutron ${}_{}{}^{185}{}_{}{}^{}\mathrm{Pt}$ and odd-proton ${}_{}{}^{183}{}_{}{}^{}\mathrm{Ir}$ nuclei. The proton nature of the crossing is indicated by measured $\frac{B(M1;I\to I-1)}{B(E2;I\to I-2)}$ ratios, strongly supported by theoretical values from both the semi-classical Dönau and Frauendorf approach and a variable-core particle-rotor calculation employing cranked-shell-model matrix elements. However, the actual crossing frequency is greatly overestimated by the cranking method using generally accepted model parameters.

A new formula for the neutron separation energy at high nuclear excitations and nuclear spin is derived. The statistical theory of the superfluid nucleus is used to obtain the neutron emission probability at high spins $>50\mathrm{}\hslash$. The results obtained here agree very well with the recent experimental data of Henss et al. for ${}_{68}{}^{156}{}_{}{}^{}\mathrm{Er}$. The nature and consequences of the structural transitions for the isotones $N=88\mathrm{}$ have been investigated comprehensively. A shape transition from prolate to oblate at $I\simeq 47\hslash$ is predicted for ${}_{68}{}^{156}{}_{}{}^{}\mathrm{Er}$.

We channeled 405-MeV/nucleon uranium ions in Si single crystals to determine the electron impact ionization cross section for berylliumlike-hydrogenlike uranium by 222-keV electrons, Our cross sections are 3.9, 11.0, 16.0, and 31.0 b (+100%, -50%), respectively, for ionizing $1s$, ${1s}^2$, $2s$, and ${2s}^2$ electrons. Our $1s$ and ${1s}^2$ results disagree with present theory. Our $2s$ and ${2s}^2$ results are not accurate enough to distinguish between theories.

The relationship between the velocity vectors of a gas-phase molecule before and after a collision is given by the differential cross section. Optical-optical double-resonance experiments using highly coherent sources can be used to obtain this information. Predictions and experimental considerations are discussed, and data are presented for elastic scattering in the $\upsilon =18\mathrm{}$, $j=13\mathrm{}$ level of $A{}_{}{}^1{}_{}{}^{}\Sigma _{\mathrm{u}}^{}{}_{}{}^{+}$-state ${\mathrm{Li}}_2$ by Xe atoms.

Rydberg-atom-Rydberg-atom associative ionization was measured in lithium at 85 K for principal quantum numbers 3, 5, and 9. The very high rate constants, up to ${10}^{-7\mathrm{}}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{-1\mathrm{}}$, were modeled by considering the binding between the ion and the Rydberg atom which result from an initial ionizing collision. A search for evidence of ion pair production yielded an upper bound on its rate constant of 3 × ${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{-1\mathrm{}}$ for $n=9\mathrm{}$. Lithium negative ions observed in the experiment were produced by attachment.

A new method to suppress one of the two recoil components in saturation and Ramsey spectroscopy is presented. It is applied to the calcium intercombination line ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ ($\lambda \cong 675$ nm) by optical pumping of the calcium atoms from the metastable ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state through the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state into the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ or the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states. The suppression of the low-frequency recoil component could be deduced in saturated absorption from a narrowing and shift of the Lamb dip as well as observed directly in Ramsey fringe spectroscopy when the recoil doublet was resovled.