A Comment on the Letter by Martin Wilkens, Phys. Rev. Lett. 72, 5 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Gianfranco Spavieri.

We have deflected a beam of metastable helium atoms using the inhomogeneous magnetic field above a microfabricated electromagnet mirror. The mirror consisted of a single current-carrying wire in a periodic serpentine pattern on a planar sapphire substrate. A time-dependent current (and magnetic field) synchronized with a pulsed thermal atomic beam was used to compensate for the chromaticity of the deflection. The freedom to fabricate a wide variety of geometries and to employ time-dependent fields make microelectromagnets promising new tools for atom manipulation.

We consider a randomly forced particle moving in a finite, one-dimensional region, which rebounds inelastically with coefficient of restitution $r$ on collision with the boundaries. We show that there is a transition at a critical value of $r$, $r_c\equiv e^{-\pi /\sqrt{3}}$, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of $r_c$ is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.

The phase transitions in Ising thin films with antiferromagnetic interactions are studied as a function of the surface field $h$ for symmetry-preserving surface orientations. It is found that for very large $h$ an $N$-layer system undergoes a separation between its surfaces and the $(N-2\mathrm{})$ inner layers. The system comprised of the surfaces and the inner layers displays a rather unusual phase diagram with a disordered phase lying between the ordered phases down to zero temperature. For large but moderate $h$, both ordered regions merge at high temperatures, isolating a low-temperature disordered region. Cluster variation calculations are used to compute the finite-temperature behavior.

A Comment on the Letter by Masahito Ueda and Anthony J. Leggett, Phys. Rev. Lett. 80, 1576 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by Xiao-Bing Wang, Lee Chang, and Bing-Lin Gu.

A Comment on the Letter by Juha Javanainen and Martin Wilkens, Phys. Rev. Lett. 78, 4675 (1997). The authors of the Letter offer a Reply.

A Reply to the Comment by A. J. Leggett and F. Sols.

Evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by 3-body recombination of Bose-condensed atoms and by feeding of the condensate from the nonequilibrium thermal cloud. The collapse, starting once the number of condensate atoms reaches the critical value, ceases and turns to expansion when the density becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the Bose-condensed atoms.

We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated “cigar”-shaped atomic trap. We show that, in the low-energy scattering regime, the scattering process degenerates to a total reflection, suggesting an experimental realization of a famous model in theoretical physics—a one-dimensional gas of impenetrable bosons (“Tonks” gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.

By charging a thin wire we realize a pure attractive $1/r^2$ potential of variable strength for cold neutral atoms. Scattering experiments are performed where the charged wire is placed inside a confined gas of cold lithium atoms. We observe the “falling” of atoms into the $1/r^2$ singularity which so far has been only theoretically discussed in textbooks.

We show that in an optical trap the ground states of spin-1 bosons such as ${}^{23}\mathrm{Na}$, ${}^{39}\mathrm{K}$, and ${}^{87}\mathrm{Rb}$ can be either ferromagnetic or “polar" states, depending on the scattering lengths in different angular momentum channels. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of ${}^3\mathrm{He}-A$.

We demonstrate a novel type of cesium atom interferometer which uses a combination of a microwave ground state transition and momentum changing adiabatic transfer light pulses as the atom optical components. It is the first atom interferometer where the mechanism which forms the internal superposition plays no part in spatially splitting the atomic wave packets. The coherence length of the atom source is found by measuring the spatial correlation between the two interferometer arms. This allows us to determine the temperature of the atomic ensemble.

Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud analogous to first sound were observed. An out-of-phase dipolar oscillation of the thermal cloud and the condensate was also studied, analogous to second sound. The excitations were observed in situ using nondestructive imaging techniques.

In this paper, we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical regime, we conjecture that the central charge is $c=q-1\mathrm{}$ for $q$ integer $<2\mathrm{}$. Low-lying excitations are examined, supporting a superdiffusive behavior for $q=1\mathrm{}$. We argue that these systems are interesting examples of integrable lattice models realizing $c\le 0$ conformal field theories.

A two-photon transition is used to convert an arbitrary fraction of the ${}^{87}\mathrm{Rb}$ atoms in a $|{F=1,m}_f=-1\mathrm{}〉$ condensate to the $|{F=2,m}_f=1\mathrm{}〉$ state. Transferring the entire population imposes a discontinuous change on the condensate's mean-field repulsion, which leaves a residual ringing in the condensate width. A calculation based on Gross-Pitaevskii theory agrees well with the observed behavior, and from the comparison we obtain the ratio of the intraspecies scattering lengths for the two states, $a_{|1,-1〉}{/a}_{|2,1〉}=1.062\mathrm{}\left(12\right)$.

In this paper the kernel for the spectral correlation functions of invariant chiral random matrix ensembles with real ( $\beta =1\mathrm{}$) and quaternion real ( $\beta =4\mathrm{}$) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitian random matrix ensembles ( $\beta =2\mathrm{}$). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brézin and Neuberger. Universal behavior of the eigenvalues close to zero for all three chiral ensembles then follows from microscopic universality for $\beta =2\mathrm{}$ as shown by Akemann, Damgaard, Magnea, and Nishigaki.

The renormalization group approach is used to study the effects of a “canonical” constraint (e.g., a fixed number of occupied bonds) on critical quenched disordered systems. The constraint is found to be always irrelevant, even near the “random” fixed point. This proves that $\alpha <0\mathrm{}$, or that $\nu >2\mathrm{}/d$. “Canonical” and “grand canonical” averages thus belong to the same universality class. Related predictions concerning the universality of non-self-averaging distributions are tested by Monte Carlo simulations of the site-diluted Ising model on the cubic lattice. In this case, the approach to the asymptotic distribution for “canonical” averaging is slow, resulting in effectively smaller fluctuations.

The theory of quantal revivals is extended to Hamiltonians that are time dependent through the slow noncyclic change of some parameters. It is shown by generalizing the cyclic geometric phase (Berry's phase) to noncyclic Hamiltonians that there is a noncyclic geometric displacement for all quantum revivals. The treatment of the classical mechanical geometric angle is also extended to open paths in parameter space and its semiclassical relation with the noncyclic geometric phase derived. The displacement of the revivals is then shown to be given by the total angle shift on the final torus sum of the dynamical angle and the noncyclic geometric angle.