We have used diode laser absorption spectroscopy of the “A” band of molecular oxygen near 762 nm to provide a sensitive experimental test of the symmetrization postulate of quantum mechanics. We place an upper limit of $(0.8\pm 1.3)\times {10}^{-6\mathrm{}}$ on the probability of finding two identical ${}^{16}$O nuclei in an antisymmetric state. This is one of the first sensitive tests of the symmetrization postulate for spin-0 particles.

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in classical mechanics. Semiclassical quantization then requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this Letter we construct the corresponding diffractive zeta function and apply it to a scattering problem which has only diffractive periodic orbits. We find that the resonances are accurately given by the zeros of the zeta function.

The synchronization and signal processing properties of a linearly coupled chain of N overdamped bistable elements, subject to a deterministic periodic signal and uncorrelated white noise, are addressed in the continuum limit of a ${\phi }^4$ field theory. The scaling relations for the optimum noise and coupling strengths that correspond to the observed spatiotemporal stochastic resonance are derived via the ${\phi }^4$ theory and shown to conform to the results of earlier numerical simulations in the large N limit.

We review the assumptions on which the Monte Carlo renormalization technique is based, in particular, the analyticity of the block-spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the simulation of a $d=3\mathrm{}$ Ising model with reduced corrections to scaling. This is achieved by including interactions with second and third neighbors. As a consequence of the improved transformation, this Monte Carlo renormalization method yields a fast convergence and a high accuracy. The results for the critical exponents are $y_H=2.481\mathrm{}\left(1\right)$ and $y_T=1.585\mathrm{}\left(3\right)$.

The electrons in a conductor surrounding an external magnetic field are acted on by a vector potential that cannot be removed by a gauge transformation. Nevertheless, a macroscopic normal conductor can experience no Aharonov-Bohm (AB) effect. That is proved by assuming only that a normal conductor lacks off-diagonal long-range order (ODLRO), which means that the electrons lack long-range phase coherence. Then by restricting the Hilbert space to density matrices which lack ODLRO, one can introduce a restricted gauge transformation that removes the interaction of the conductor with the vector potential. Consequently, the AB effect on a beam particle is not shielded by the conductor.

A Comment on the Letter by George A. Baker, Jr. and Naoki Kawashima, Phys. Rev. Lett. 75, 994 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by Jae-Kwon Kim.

We show how to infer the quantum state of a wave packet from position probability distributions measured during the packet's motion in an arbitrary potential. We assume a nonrelativistic one-dimensional or radial wave packet. Temporal Fourier transformation and spatial sampling with respect to a newly found set of functions project the density-matrix elements out of the probability distributions. The sampling functions are derivatives of products of regular and irregular wave functions. We note that the ability to infer quantum states in this way depends on the structure of the Schrödinger equation.

A semiclassical approximation is presented which describes the time-independent wave function as an integral over the Lagrangian manifold associated with the state. The function produced is free of caustic singularities and satisfies the Schrödinger equation with an error that vanishes everywhere uniformly in the classical limit. Illustrative calculations are presented for one-dimensional systems.

A Comment on the Letter by Anupam Garg and N. D. Mermin, Phys. Rev. Lett. 49, 1220 (1982). The authors of the Letter offer a Reply.

A Reply to the Comment by P. Horodecki and R. Horodecki.

We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrödinger operators to the behavior of solutions of the corresponding Schrödinger equation. We use this theory to analyze these properties for several examples having the singular-continuous spectrum, including sparse barrier potentials, the almost Mathieu operator and the Fibonacci Hamiltonian.

We examine the quantum energy levels of rectangular billiards with a pointlike scatterer in one and two dimensions. By varying the location and the strength of the scatterer, we systematically find diabolical degeneracies among various levels. The associated Berry phase is illustrated, and the existence of localized wave functions is pointed out. In one dimension, even the ground state is shown to display the sign reversal with a mechanism to circumvent the Sturm-Liouville theorem.

Light scattered off a dilute Bose-Einstein condensed gas of atoms at large detuning, besides a broad background, shows two symmetrically placed peaks whose intensities are related by detailed balance and whose frequencies depend on the product of the number of atoms in the condensate and the scattering length.

A Comment on the Letter by G. M. D'Ariano, C. Macchiavello, and M. G. A. Paris, Phys. Rev. Lett. 73, 3187 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Olle Nilsson, et al.

According to renormalization theory, Ising systems above their upper critical dimensionality $d_u=4\mathrm{}$ have classical critical behavior and the ratio of magnetization moments $Q=〈m^2{〉}^2/〈m^4〉$ has the universal value $0.456947\dots$. However, Monte Carlo simulations of $d=5\mathrm{}$ Ising models have been reported which yield strikingly different results, suggesting that the renormalization scenario is incorrect. We investigate this issue by simulation of a more general model in which $d_u<4\mathrm{}$, and a careful analysis of the corrections to scaling. Our results are in perfect agreement with the renormalization theory and provide an explanation of the discrepancy mentioned.

The temperature dependence of the moment of inertia of a dilute Bose gas confined in a harmonic trap is determined. Deviations from the rigid value, due to the occurrence of Bose-Einstein condensation, reveal the superfluid behavior of the system. In the noninteracting gas these deviations become important at temperatures of the order of $T_c{N}^{-1\mathrm{}/12}$. The role of interactions is also discussed.

We construct explicit anyon fields from unitary representations of the group diffeomorphisms of the plane, realizing braid group elements as paths in the plane transforming naturally under diffeomorphisms. The fields satisfy q-commutation relations, where q is the anyonic phase shift.