The edge of the gap in the distribution of Yang-Lee zeros at $H=i{H}_0\mathrm{}\left(T\right)\mathrm{}$ on the imaginary magnetic field axis in ferromagnets above $T_c$ is essentially a critical point. In terms of the edge exponents $\delta$ and $\eta$, the density of zeros obeys $\mathcal{G}\left(H^{\prime \prime }\right)\sim {[H^{\prime \prime }-H_0\mathrm{}(T\left)\right]}^{\sigma }$, with $\sigma =\frac{1}{\delta }=\frac{(d-2+\eta )}{(d_2-\eta )}$. Classical behavior ($\sigma =\frac{1}{2}$) occurs for $d>\mathrm{}{d}^{\times }=6\mathrm{}$. The appropriate field-theoretic renormalization group entails a $w{\varphi }^3$ coupling and, with $\epsilon =6-d>~0$, yields $\eta \approx -\frac{\epsilon }{9}$ for all $n<\mathrm{}\infty$. This correlates well with refined series estimates for $d=2\mathrm{}$ and $d=3\mathrm{}$ and with exact results for $d=1\mathrm{}$ ($\eta =-1\mathrm{}$).

It is shown that quantum mechanical barrier penetration (tunneling) is related to classical escape over a related potential barrier, and that therefore the WKB approximation for the former and Kramers approximation for the latter are equivalent.

I construct an entropy function $S\left(t\right)\mathrm{}$ suitable for a system of hard spheres satisfying the (modified) nonlinear Enskog equation, and show that ${\partial }_{t}S\left(t\right)\mathrm{}>~0$. The equality sign holds only when the system has reached absolute equilibrium, in which case $S$ becomes the exact equilibrium entropy of the hard-sphere fluid.

We compare the results of precision electron $g$-factor experiments at low energy and at 110 keV. The agreement between these measurements constitutes the most precise laboratory confirmation to date of the predictions of special relativity. Relativistic electromagnetic theory and Thomas precession are verified in this test. We also consider limits on possible effects of acceleration.

We present a new unified method of coupling matter to both Poincaré and conformal supergravity. As an example we construct the coupled Maxwell-Weyl and the coupled Maxwell-Einstein supergravity theories. We also discuss the close connection with a recent auxiliary-field formulation of supergravity.

Approximate real-space (cell-type) renormalization-group methods are used to calculate the surface tension between coexisting phases in two- and three-dimensional Ising models. The results are physically reasonable and show the expected scaling properties near a critical point. However, there are some problems in reconciling the three-dimensional results with the existence of a roughening transition.

A mechanism for spontaneous symmetry breaking and related phenomena and the corresponding blocking of metastable states is discussed. It is based on the interaction of an object with a background of "probes" like photons or particles, etc., in its natural surrounding. Applications include quasilocalization of macroscopic bodies, spontaneous parity nonconservation of sugar crystals, localization of atoms in molecules (Born-Oppenheimer approximation), stability of metastable compounds, and perhaps also intrinsic symmetries of elementary particles.

Measurements of statistical quantities other than the spectrum can distinguish between different $\frac{1}{f}$ noise mechanisms. One such quantity, the average behavior before and after a given fluctuation amplitude, is used to determine if the noise mechanism is linear. Measurements on different sources show that $\frac{1}{f}$ noise in some systems, such as carbon resistors and field-effect transistors, is due to a linear mechanism, while other systems, such as $p-n$ junction devices, require a nonlinear mechanism.

A method of stably trapping, cooling, and manipulating atoms on a continuous-wave basis is proposed using resonance radiation pressure forces. Use of highly focused laser beams and atomic beam injection should give a very deep trap for confining single atoms or gases at temperatures ∼ ${10}^{-6\mathrm{}}$ °K. An analysis of the saturation properties of radiation pressure forces is given.

We use the renormalization-group method of Kosterlitz to study the dynamics of a purely relaxational model for the roughening transition. Implications of our results for the behavior of spatial and temporal correlation functions of a crystal-vapor interface and for the crystal growth rate are discussed.

By adopting Nelson's stochastic framework of quantum mechanics (i.e., the stochastic quantization), a time-dependent description of tunneling phenomena is developed. As a simple model, tunnel effect of a one-dimensional quantum mechanical system with bistable potential is analyzed in much detail.

The complex amplitude $X_1+i{X}_2\equiv (x+\frac{\mathrm{ip}}{m\omega })e^{i\omega t}$ of a harmonic oscillator is constant in the absence of driving forces. Although the uncertainty principle forbids precise measurements of $X_1$ and $X_2$ simultaneously ($\Delta X_1\Delta X_2>~\frac{\hslash }{2m\omega }$), $X_1$ alone can be measured precisely and continuously ("quantum nondemolition measurement"). Examples are given of measuring systems that do this job. Such systems might play a crucial role in gravitational-wave detection and elsewhere.

This paper treats the problem of solving the linear equation which arises when a nonlinear evolution equation is linearized around some particular solution. It is shown that if the original equation is of completely integrable Hamiltonian form there are an infinity of explicit solutions of the linearized equation. These are almost always linearly independent.

I examine the new gauge theory of gravitation theory proposed recently by Mansouri and Chang. It appears that the predictions of the theory are indistinguishable from those of general relativity with regard to the usual tests. With the aid of the symbolic manipulation computer system, macsyma, I find that the theory possesses a remarkable similarity to Einstein's theory with respect to vacuum solutions. While the field equations are greatly different, a question arises whether there are any solutions of the new equations which are not Einstein vacuum spaces.

An example is given of a space-time which satisfies the conditions for asymptotic region is not "as large" as that of Minkowski space-time.

We study the steady-state dynamical behavior of a set of torsion-coupled pendula in the presence of damping, fluctuating thermal torques, and constant applied torque. For small applied torque, the average angular velocity of the pendula at low temperature is associated with the motion of thermalized sine-Gordon solitons and as the torque is increased the velocity response becomes strongly nonlinear. These results can be used to describe nonlinear response in Josephson transmission lines and weakly pinned one-dimentional charge-density-wave condensates.

We propose an iterative nonlinear solution to the general potential scattering porblem in quantum mechanics. It is illustrated by the case of $N_I$ localized scatterers of arbitrary strengths $V_j$ located at arbitrary points $R_j$ in an infinite lattice, for which we obtain the complete set of bound and scattering states. The numberical evaluation is estimated to take $O\left(N_I\right)$ steps as opposed to $O\left({N_I}^3\right)$ steps by conventional matrix inversion.

It is rigorously proved that the analog of free energy for the percolation models has a singularity at zero external field as soon as percolation appears. The singularity is an essential one at least for large concentrations. Results on the asymptotic behavior of the cluster-size distribution are also obtained for percolation models and for the Ising model at low temperatures.

The method of synchronizing clocks in accelerating frames through the use of electromagnetic signals can be tested experimentally by considering clocks placed in a set of synchronous satellites about Earth's equator. In synchronizing the clocks in a circuit about the equator, a large measurable time difference (9 μsec) is obtained between the two clocks in the same satellite from which the synchronization process is started and completed. Similarly, Earth's rotation may cause discrepancies in terrestrial time keeping.

The problem of astrophysical sources of detectable gravitational radiation is considered from the stellar-evolution viewpoint. Calculations are presented which indicate that the final stages of evolution may well be dominated by rapidly rotating, collapsing cores which develop nonaxisymmetric configurations. Such events emit large amounts of gravitational radiation which should be detectable in the near future.