The evolution of a two component Bose-Einstein condensate, consisting of atoms in two distinct hyperfine states, is modeled using a generalization of the Gross-Pitaevskii equation. Coherent coupling of the components by a microwave or RF field gives rise to a range of spatiotemporal behaviors, controlled by the strength and detuning of the applied field. From an initial trapped single component state, a second component can be generated which may escape from the trapping region or remain trapped within the first component. The initiating mechanism is identified and characterized.

We exploit the symmetries associated with the stability of the superfluid phase to solve the long-standing problem of interacting bosons in the presence of a condensate at zero temperature. Implementation of these symmetries poses strong conditions on the renormalizations that heal the singularities of perturbation theory. The renormalized theory gives the following: For $d>\mathrm{}3\mathrm{}$ the Bogoliubov quasiparticles as an exact result; for $1<d\le 3$ a nontrivial solution with the exact exponent for the singular longitudinal correlation function, with phonons again as low-lying excitations.

We study nonequilibrium phenomena in a globally coupled oscillator system with a third harmonic pinning force in the presence of an additive noise and a fluctuating interaction. The system shows a subcritical saddle-node bifurcation from an asymmetric state to a symmetric state at a critical noise intensity leading to multistable states. The fluctuating interaction increases the critical noise intensity and thus enhances the multistability drastically. We show phase diagrams and discuss the nature of the phase transition.

Using the energy and canonical momentum conservation, we delineate the acceleration of neutrons in uniform electric and magnetic fields, first enunciated by Anandan. We determine bounds of the velocity change, made cumulative by reversing the electric field periodically in space. We show that the acceleration is observable in an interference experiment, disproving claims to the contrary made by Casella and Werner.

An explicit solution to the Maslov-type semiclassical theory for propagating a wave function, rather than evolving in time the Feynman kernel, is presented. It turns out that the present solution bears distinguished advantages over the semiclassical kernel, one of the most remarkable examples of which is the far less number of classical trajectories required for the propagation, basically proportional to $P^{2N}\sim P^{3N}$ for the kernel while only to $P^N$ in our solution, where N is the dimension in configuration space and P is the number of sampling points in each dimension. As an illustrative example to show the validity of the solution, the theory is applied to the calculation of eigenvalues of the Morse oscillators, giving accurate results in a compact way.

We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding mean-field scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems.

We generalize nonlinear response theory for autonomous systems so that it describes the response of classical many-body systems to large time-dependent external fields. Our formalism represents the first practical application of response theory to such problems. Our expressions for the nonlinear time-dependent response are tested against nonequilibrium molecular dynamics computer simulation. The relation of our results to known special cases (time-dependent linear response and time-independent nonlinear response) is discussed.

A method is introduced to represent many-body systems of arbitrary dimensionality by planar curves. The positions and momenta of the particles are the parameters of a time-dependent nonlinear transformation, which maps the many-body dynamics of the real system to the motion of the curve. The description of the system as a point in a multidimensional phase space is thus replaced by a two-dimensional continuous line. Expressions for the curvature along the curve and the dynamic structure factor are obtained. The formulation holds for Hamiltonian and non-Hamiltonian systems, and two explicit examples are analyzed: harmonic oscillators and a quadratic system.

Discrete breathers are time-periodic, spatially localized solutions of equations of motion for classical degrees of freedom interacting on a lattice. They come in one-parameter families. We report on studies of energy properties of breather families in one-, two-, and three-dimensional lattices. We show that breather energies have a positive lower bound if the lattice dimension of a given nonlinear lattice is greater than or equal to a certain critical value. These findings could be important for the experimental detection of discrete breathers.

Driving a damped, anharmonic oscillator produces stable, steady-state excitations according to the familiar classical description. A quantum mechanical description, however, shows the surprising result that such excitations are intrinsically unstable, and can be much smaller than classical expectations. We illustrate by calculating the motion of one electron in a magnetic field. This physically realizable system is among the simplest of nonlinear systems, being anharmonic because of special relativity and being damped by the spontaneous emission of synchrotron radiation.

We describe here the coalescence and formation of droplets, in a Hamiltonian kinetics of a first order phase transition. In the process of coalescence, the typical linear size of single phase domains grows as a power of time. The density correlation function follows the usual self-similar dynamic scaling. For different initial conditions, we observe the nucleation and dynamics of stable pulses. The stability of such pulses in one dimension is also computed. Both results may be relevant to superfluid H${\mathrm{e}}_4$ cavitation or for filamentation in nonlinear optics and for the recent evidence of Bose-Einstein condensation in L${\mathrm{i}}_7$.

Bose-Einstein condensation of ${}^7\mathrm{Li}$ has been studied in a magnetically trapped gas. Because of the effectively attractive interactions between ${}^7\mathrm{Li}$ atoms, many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms. We observe the condensate number to be limited to a maximum value between 650 and 1300 atoms. The measurements were made using a versatile phase-contrast imaging technique.

We show that the degeneracy parameter of a trapped Bose gas can be changed adiabatically in a reversible way, both in the Boltzmann regime and in the degenerate Bose regime. We have performed measurements on spin-polarized atomic hydrogen in the Boltzmann regime, demonstrating reversible changes of the degeneracy parameter (phase-space density) by more than a factor of 2. This result is in good agreement with theory. By extending our theoretical analysis to the quantum degenerate regime we predict that, starting close enough to the Bose-Einstein phase transition, one can cross the transition by an adiabatic change of the trap shape.

In this Letter we discuss a bistable model driven by two white noise sources, when the correlation time of the correlations between two sources $\tau$ is nonzero. We find that there is a critical value of the correlation time ${\tau }_c$. For $\tau >{\tau }_c$, the system undergoes a succession of two phase transitions (namely, the reentrance phenomenon) as the strength of the correlations between two noise sources $\lambda$ is varied. However, for $\tau <{\tau }_c$, the system undergoes a (single) phase transition as $\lambda$ is varied.

We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of π radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry.

We have measured the phase shift induced by rotation of an atom interferometer at rates of $-2\mathrm{}$ to $+2\mathrm{}$ earth rates and obtained $1\%$ agreement with the predicted Sagnac phase shift for atomic matter waves. The rotational rms noise of our interferometer was $42$ milliearth rates for $1$ sec of integration time, within $9\%$ of shot noise. The high sensitivity and agreement of predicted and measured behavior suggest useful future scientific applications of atom interferometers as inertial sensors.

We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of ${}^{87}\mathrm{Rb}$. Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations.

We present the quantum theory for the nucleation of Bose-Einstein condensation in a dilute atomic Bose gas. This quantum theory has the important advantage that both the kinetic and coherent stages of the nucleation process can be described in a unified way by a single Fokker-Planck equation.

We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical systems in the microcanonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a time average of the functional, $▽̇(▽H/\Vert ▽H{\Vert }^2)$, on the energy surface. Our method not only yields an efficient computational approach for determining the temperature, it also provides an intrinsic link between dynamical systems theory and the statistical mechanics of Hamiltonian systems.

We study the dynamics of the excitable Fitz Hugh–Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon.