Evidence for Bose-Einstein condensation of a gas of spin-polarized ${}^7$Li atoms is reported. Atoms confined to a permanent-magnet trap are laser cooled to 200 μK and are then evaporatively cooled to lower temperatures. Phase-space densities consistent with quantum degeneracy are measured for temperatures in the range of 100 to 400 nK. At these high phase-space densities, diffraction of a probe laser beam is observed. Modeling shows that this diffraction is a sensitive indicator of the presence of a spatially localized condensate. Although measurements of the number of condensate atoms have not been performed, the measured phase-space densities are consistent with a majority of the atoms being in the condensate, for total trap numbers as high as $2\times {10}^5$ atoms. For ${}^7$Li, the spin-triplet $s$-wave scattering length is known to be negative, corresponding to an attractive interatomic interaction. Previously, Bose-Einstein condensation was predicted not to occur in such a system.

We analyze a model that has been shown to undergo a purely noise induced transition, from a monostable regime to a bistable one, when it is submitted to a white or colored noise source. We show, using a consistent interpolating Markovian approximation for the colored noise case, that for large values of the correlation time, the system undergoes a new transition to a monostable state, indicating a reentrancelike phenomenon in its phase diagram. Numerical results support our findings.

By assigning probabilities to the histories of a classical stochastic field, it is possible to construct a Monte Carlo algorithm that evolves an entire space-time configuration, thereby allowing one to compute equilibrium or (in principle) nonequilibrium properties. This new technique is demonstrated on the Glauber kinetic Ising model, and the scaling behavior near the critical temperature is demonstrated.

A particle is assumed to move along a one-dimensional loop such as an ellipse that rotates in a plane. Because of the centrifugal force the particle is subjected to a symmetric double-well potential. Classically, the Coriolis force does not affect the motion of the particle, whereas the corresponding term in the Lagrangian influences the properties of the quantum system: its ground state turns out to be degenerate for a discrete set of angular velocities. The analogy between a constant magnetic field and a uniform rotation is used to propose, in addition, a variant of the Aharonov-Bohm experiment, which can be performed also with neutral particles.

All existing quantum cryptosystems use nonorthogonal states as the carriers of information. Nonorthogonal states cannot be cloned (duplicated) by an eavesdropper. As a result, any eavesdropping attempt must introduce errors in the transmission, and, therefore, can be detected by the legal users of the communication channel. Orthogonal states are not used in quantum cryptography, since they can be faithfully cloned without altering the transmitted data. We present a cryptographic scheme based on orthogonal states, which also assures the detection of any eavesdropper.

Despite the seminal connection between classical multiply periodic motion and Heisenberg matrix mechanics, we show that there are fundamental, previously undisclosed aspects of this quantum-classical correspondence. These include a quantum variational principle that implies the classical variational principle for invariant tori and the connection between commutation relations and quantization of action variables. Possible applications are described briefly.

We show that the asymptotic Bethe ansatz gives the exact zero temperature values of all the integrals of motion for the classical one-dimensional system interacting by an inverse-sinh-squared pair potential, in the thermodynamic limit. It is remarkable that the asymptotic Bethe ansatz, using only the scattering data for finite numbers of particles in an unbounded volume, gives exact results for all density.

An experiment is described which is an analog of Young's double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other.

In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if $\alpha$ or $Z$ is too large. Here we prove that matter is stable if $\alpha <0.06\mathrm{}$ and $Z{\alpha }^2<0.04\mathrm{}$.

We study numerically the one-dimensional quantum evolution of a coherent state when the particle is bound by a nonlinear force. Snapshots of the Husimi function show that there exist times where the initial Gaussian distribution in phase space splits into chains of $2,3,\dots$ distributions of similar form. During their finite lifetime the members of such a string are equally distributed along the classical orbit which passes through the center of the initial distribution, and they move along this curve with the corresponding velocity. This effect, which is generic for integrable bounded motion, is explained in terms of the quantum analogs of action and angle variables.

Monte Carlo calculations of the renormalized coupling constant for the three-dimensional Ising model are reported. Improved estimators both for the second partial of the susceptibility with respect to the magnetic field and for the correlation length are developed. These estimators show greatly improved convergence properties, and allow us to compute for system sizes and temperature rather more relevant to the thermodynamic limit than previously. Our results indicate strongly that hyperscaling holds for this model.

We obtain a lower bound for the mutual information of a quantum transmission channel, which is perfectly analogous with Holevo's upper bound. The Uhlmann inequality for relative entropies is used, in a reverted order, for a completely positive mapping related with the mixed coherent states introduced by us seventeen years ago. Possible applications to quantum cryptography are discussed.

Stability of two-wave solitons supported by resonant parametric interactions in a diffractive (or dispersive) optical quadratic medium is investigated analytically and numerically. It is found that the solitons can become unstable when the phase matching between the fundamental and second harmonics is not exactly satisfied. The analytical criterion for the linear instability is presented, and it is revealed that the instability leads to two possible scenarios of the soliton dynamics, either large-amplitude in-phase oscillations of two harmonics or the soliton decay.

We formulate a method for incorporating quantum fluctuations into molecular-dynamics simulations of many-body systems, such as those employed for energetic nuclear collision processes. Based on Fermi's golden rule, we allow spontaneous transitions to occur between the wave packets which are not energy eigenstates. The ensuing diffusive evolution in the space of the wave packet parameters exhibits appealing physical properties, including relaxation towards quantum statistical equilibrium.

We study theoretically and numerically the dynamical behavior of a two-dimensional sine-Gordon lattice. We show that, via modulational instability, an initial-low-amplitude plane wave can evolve spontaneously into moving localized modes with large amplitude. These nonlinear modes, with dimensions depending on the characteristic wavelengths of the instability, behave like breathing solitary waves and present particlelike properties.

A quantum phase space entropy is defined, which directly reflects the global dynamical properties of the system similar to the synoptic view of several classical trajectories in a Poincaré section. The quantum results allow a direct comparison with a corresponding purely classical entropy. Numerical results for a periodically driven rotor illustrate the usefulness of phase space entropies for systems with mixed chaotic and regular dynamics.

It is pointed out that the generalized statistical mechanics introduced by Tsallis [J. Stat. Phys. 52, 479 (1988)] provides a natural frame for developing a thermodynamical formalism of anomalous diffusion. Within such a frame, we calculate the mean square displacement as a function of time and generalize the Einstein relation of diffusivity and temperature for random walks of the Lévy-flight type.

Breaking of an atomic chain under stress is a collective many-particle tunneling phenomenon. We study classical dynamics in imaginary time by using a conformal mapping technique, and derive an analytic formula for the probability of breaking. The result covers a broad temperature interval and interpolates between two regimes: tunneling and thermal activation. Also, we consider the breaking induced by an ultrasonic wave propagating in the chain, and propose to observe it in a scanning tunneling microscopy experiment.

We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.