Unstable systems such as media with inverted atomic population have been shown to allow the propagation of analytic wave packets with group velocity faster than that of light, without violating causality. We illuminate the important role played by unstable modes in this propagation and show that the quantum fluctuations of these modes and their unitary time evolution impose severe restrictions on the observation of superluminal phenomena.

We present a method of adiabatically changing the local phase-space density of an ultracold gas using a combination of magnetic and optical forces. Applying this method, we observe phase-space density increases in a gas of sodium atoms by as much as 50-fold. The transition to Bose-Einstein condensation was crossed reversibly, attaining condensate fractions of up to $30\%$. Measurements of the condensate fraction reveal its reduction due to interactions.

We present predictions for the frequencies of collective modes of trapped Bose-condensed ${}^{87}\mathrm{Rb}$ atoms at finite temperature. Our treatment includes a self-consistent treatment of the effects upon the mean field from finite- $T$ excitations and the anomalous average. This is the first gapless [A. Griffin, Phys. Rev. B 53, 9341 (1996)] calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2\mathrm{}$ excitation frequencies observed in recent experiments as the critical temperature is approached.

A Comment on the Letter by Kazumoto Iguchi, Phys. Rev. Lett. 78, 3233 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by Wung-Hong Huang.

We investigate the Dirac equation in the semiclassical limit $ħ\to 0$. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.

Using polarized neutrons, we have determined phases as well as interference amplitudes for noncyclic spinor evolutions in static magnetic fields. Both these quantities depend on the angle subtended by the neutron spin with the field. This experiment elucidates the subtle, and widely misunderstood, concepts involved.

Localized oscillating fields are beam splitters that can entangle internal and longitudinal momentum states in an atomic beam. Differentially detuned separated oscillatory fields and an am modulator constitute a “white fringe” longitudinal interferometer which rephases velocity averaging by a process analogous to half a spin echo. Differentially detuned separated oscillatory fields are used to produce a downstream coherence or rephase an upstream coherence in an atomic beam.

The microcanonical transfer matrix is used to study the distribution of Yang-Lee zeros of the $Q$-state Potts model in the complex magnetic field ( ${x=e}^{\beta h}$) plane for the first time. Finite size scaling suggests that at (and below) the critical temperature the zeros lie close to, but not on, the unit circle with the two exceptions of the critical point $x=1\mathrm{}$ ( $h=0\mathrm{}$) itself and the zeros in the limit $T=0\mathrm{}$.

The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of a squeezed state. A class of cyclic states is expressed as a superposition of an infinite number of squeezed states. Then their geometric phases are obtained explicitly and found to be $-(n+1\mathrm{}/2)$ times the classical nonadiabatic Hannay angle. It is shown that the analysis based on the squeezed state approach provides a clear picture of the geometric meaning of the quantal phase.

Using a sum rule approach we calculate the frequency shifts of the quadrupole oscillations of a harmonically trapped Bose gas due to the presence of a quantized vortex. Analytic results are obtained for positive scattering lengths and large $N$ where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as $N^{-2\mathrm{}/5}$. Results are also given for smaller values of $N$ covering the transition between the ideal gas and the Thomas-Fermi limit. The splitting of the collective frequencies in toroidal configurations is also discussed.

We corroborate the idea of a close connection between replica-symmetry breaking and aging in the linear response function for a large class of finite-dimensional systems with short-range interactions. In these systems, which are characterized by a continuity condition with respect to weak random perturbations of the Hamiltonian, the “fluctuation dissipation ratio” in off-equilibrium dynamics should be equal to the static cumulative distribution function of the overlaps. This allows for an experimental measurement of the equilibrium order parameter function.

We report computation of the Kolmogorov-Sinai entropy in a variety of simple liquids studied by molecular dynamics. It is found that this quantity, when expressed in terms of the atomic collision frequency, is uniquely related to the thermodynamic excess entropy by a universal linear scaling law. We also present a simple probabilistic model for relaxation in condensed atomic systems in which the observed scaling relation arises naturally.

A Comment on the Letter by Adrian Kent, Phys. Rev. Lett. 78, 2874 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by Robert B. Griffiths and James B. Hartle.

We describe the first experiments that study in a controlled way the dynamics of distinguishable and interpenetrating bosonic quantum fluids. We work with a two-component system of Bose-Einstein condensates in the $|{F=1,m}_f=-1\mathrm{}〉$ and $|2,1〉$ spin states of ${}^{87}\mathrm{Rb}$. The two condensates are created with complete spatial overlap, and in subsequent evolution they undergo complex relative motions that tend to preserve the total density profile. The motions quickly damp out, leaving the condensates in a steady state with a non-negligible (and adjustable) overlap region.

We have measured the relative phase of two Bose-Einstein condensates using a time-domain, separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double-condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase difference reproduces from realization to realization of the experiment, even after the individual components have separated spatially and their relative center-of-mass motion has damped.

The role of the symmetries in the topology of sets of Lagrangian singularities is studied in a simple physical model: the envelope of the rays emanating from a convex wave front invariant under the action of polyhedral groups. New point singularities are found of integer index and located at the vertices of the polyhedron or of its reciprocal. This remarkable layout results from the interplay between the symmetries of the singularities, the polyhedral symmetries, and the topology of the wave front. An application to fine-particle magnetic systems is given.

A quench in an underdamped one-dimensional ${\phi }^4$ model is studied by analytical methods. The density of kinks just after the transition is proportional to the square root of the rate of the quench for slow quenches. If the quench is shorter than the relaxation time, the density scales like the third root of the rate.

Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to $N=7\mathrm{}$ and verify that they are minimal up to $N=5\mathrm{}$.