The Bose-Einstein condensates of alkali atomic gases are spinor fields with local “spin-gauge” symmetry. This symmetry is manifested by a superfluid velocity ${\mathbf{u}}_s$ (or gauge field) generated by the Berry phase of the spin field. In “static” traps, ${\mathbf{u}}_s$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\Omega }}_{c1\mathrm{}}$, and can lead to vortex ground states.

Using the independent oscillator model with an arbitrary system potential, we derive a quantum Brownian equation assuming a correlated total initial state. Although not of Lindblad form, the equation preserves positivity of the density operator on a restricted set of initial states.

Critical phenomena in the two-dimensional Ising model with a defect line are studied using boundary conformal field theory on the $c=1\mathrm{}$ orbifold. Novel features of the boundary states arising from the orbifold structure, including continuously varying boundary critical exponents, are elucidated. New features of the Ising defect problem are obtained including a novel universality class of defect lines and the universal boundary to bulk crossover of the spin correlation function.

We explore a connection of the forced Burgers equation with the Schrödinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions interpreting the dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of the continuity equation ${\partial }_t\rho =-▽\left(\overrightarrow{\upsilon }\rho \right),$ with $\overrightarrow{\upsilon }=\overrightarrow{\upsilon }(\overrightarrow{x},t)$ the Burgers field and ρ the density of transported matter, is at variance with the explicit diffusion scenario. We give a complete characterization of diffusive matter transport governed by Burgers velocity fields. This extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium.

The asymptotic integrability of the idealized water waves is formally established. Namely, it is shown that in the small amplitude, long wave limit there exists an explicit transformation which maps these equations to a system of two integrable equations. It is also shown that the concepts of master symmetries and of bi-Hamiltonian structures can be used to obtain similar results for other physical systems.

By analyzing a single-photon interference experiment together with a quantum nondemolition measurement scheme for the which-path information, we prove that given the total mean number $〈n〉$ of available photons, the fundamental limit in precision measurement of a phase shift is the Heisenberg limit, i.e., $1/〈n〉$. The analysis is based on the complementarity principle and is independent of the scheme for the measurement of the phase shift. We also show that to achieve the Heisenberg limit states with photon number fluctuations of the order of or larger than the mean photon number have to be exploited.

We have demonstrated a multiple beam atom interferometer. Atoms in a cesium atomic beam are optically pumped into a spatially separating nonabsorbing superposition state consisting of five partial beams in different Zeeman sublevels separated by a momentum of two photon recoils each. When the partial waves are spatially recombined, we observe an interference signal which shows the sharply peaked Airy pattern characteristic for multiple beam interference.

We investigate the low energy excitations of a dilute atomic Bose gas confined in a harmonic trap of frequency ${\omega }_0$ and interacting with repulsive forces. The dispersion law $\omega ={\omega }_0({2n}^2+2n\ell +3n+\ell {)}^{1/2}$ for the elementary excitations is obtained for large numbers of atoms in the trap, to be compared with the prediction $\omega ={\omega }_0(2n+\ell )$ of the noninteracting harmonic oscillator model. Here $n$ is the number of radial nodes and $\ell$ is the orbital angular momentum. The effects of the kinetic energy pressure are estimated using a sum rule approach. Results are also presented for deformed traps and attractive forces.

The notion of thermal ratchet is extended to the $1+1$ dimensional case of an overdamped soliton-bearing theory coupled to a Gaussian source of spatiotemporal noise with finite correlation time. A stationary noise-induced current of kinks and antikinks in opposite directions is computed as a function of the noise correlation time and the kink (antikink) asymmetry.

A Comment on the Letter by Damian Zanette and Pablo A. Alemany, Phys. Rev. Lett. 75, 366 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by Manuel O. Caceres and Carlos E. Budde.

We study the classical dynamics of a charged particle in two dimensions, under the influence of a perpendicular magnetic and an in-plane electric field. We prove the surprising fact that there is a finite region in phase space that corresponds to the otherwise drifting particle being trapped by a local repulsive potential. Our result is a direct consequence of Kolmogorov-Arnold-Moser theory and, in particular, of Moser's theorem. We illustrate it by numerical phase portraits and by an analytic approximation to invariant curves.

An inequality is derived according to which the fringe visibility in a two-way interferometer sets an absolute upper bound on the amount of which-way information that is potentially stored in a which-way detector. In some sense, this inequality can be regarded as quantifying the notion of wave-particle duality. The derivation of the inequality does not make use of Heisenberg's uncertainty relation in any form.

The macroscopic wave function for atomic samples composed of a few thousand particles is shown to exhibit collapses and revivals on a few seconds time scale, while Bose-Einstein condensation remains in the form of off-diagonal long-range order in the one-particle reduced density matrix. A recently proposed measurement scheme which is sensitive to Bose-broken gauge symmetry, and hence to the macroscopic wave function, could be used to detect the collapses and revivals experimentally.

We study noise-controlled resonant behavior in periodically modulated, overdamped bistable dynamic elements subject to a symmetry-breaking dc signal. The spectral amplitudes of the harmonics of the modulation frequency are found to exhibit multiple maxima whose occurrence depends on matchings of deterministic and stochastic time scales; in turn, these times depend on the noise statistics and the degree of asymmetry. We demonstrate the phenomenological results via analytical and numerical computations on an rf SQUID loop, and propose this technique to detect weak signals using a “frequency hopping” mechanism to circumvent detector noise limitations.

An atomic electron is prepared in a state closely analogous to Schrödinger's coherent superposition of “live cat” and “dead cat.” The electronic state is a coherent superposition of two spatially localized wave packets separated by approximately $0.4\mu \mathrm{m}$ at the opposite extremes of a Kepler orbit. State-selective ionization is used to verify that only every other atomic level is populated in the “cat state,” and a Ramsey fringe measurement is used to verify the coherence of the superposition.

We report on a “postponed compensation” experiment in which the observed two-photon entangled state interference cannot be pictured in terms of the overlap of the two individual photon wave packets of a parametric down-conversion pair on a beam splitter. In the sense of a quantum eraser, the distinguishability of the different two-photon Feynman amplitudes leading to a coincidence detection is removed by delaying the compensation until after the output of an unbalanced two-photon interferometer.

The modified Newton-Sabatier method is extended to the inverse scattering problem of coupled channels at fixed energy. The problem is solved for a system of coupled radial Schrödinger equations with a potential matrix independent of the angular momentum of the relative motion. The new method is applied to the example of two channels coupled by complex-valued square well potentials.

A model of globally coupled bistable continuous systems with two series of cells, modeling competing processes between activators and suppressors, subject to periodic and stochastic forces is investigated. In the large system size limit the exact solution of linear response theory is obtained, which shows typical stochastic resonance (SR) behavior. In particular, we find a resonance, sensitively depending not only on noise intensity and coupling strength, but also on the frequency of the periodic forcing. The SR occurs at a noise-induced Hopf bifurcation point, and is associated with the divergence of linear response.

It is shown that the deflection of an atom de Broglie wave at a nonresonant weak cavity field mode can yield a pure entangled quantum state in which discernable atomic beams are entangled to photon number states of the field and to internal states of the atom. The proposed experimental scheme is shown to be applicable for quantum nondemolition measurement of the photon statistics, and for quantum state engineering and reconstruction experiments.