We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that, underlying the stochastic resonancelike behavior with the noise correlation time, there is an effect of optimal localization of the system trajectories in the phase space. This phenomenon is observed in systems with different nonlinearities, suggesting a degree of universality.

The Brownian motion in a tilted washboard potential subjected to a low-frequency periodic drive develops large hysteresis loops, which attain their maximum at the locked-to-running transition in the underdamped regime. The dependence of such a critical phenomenon on the drive parameters and on the temperature is investigated numerically. Moreover, this hysteresis mechanism is related to the occurrence of random multiple jumps, whose length and time duration distributions appear to decay according to a universal power law with exponent $\alpha =1.5\mathrm{}$. This model may explain various instances of low-frequency excess damping in material science.

We report the first large scale numerical study of the dynamics of a second order phase transition caused by a gradual decrease of temperature in a U(1) $\lambda {\phi }^4$ theory in three spatial dimensions. We present a detailed account of the dynamics of the fields and focus on vortex string formation as a function of the quench rate. The results are found in good agreement with the theory of defect formation proposed by Kibble and Zurek.

We consider the overdamped motion of a Brownian particle in a potential well and examine the relaxation of its probability distribution. We give a new definition, based on the mean first passage time, for the intrawell relaxation time, which characterizes the relaxation process in the entire well and can be expressed analytically for an arbitrary potential. Further, we show how it can be approximated by other simple quantities in most cases. If the characteristic time scale of some modulation of the potential is much longer than this intrawell relaxation time, the particle's probability distribution can be considered to be adiabatically adjusted to the potential at every instant.

We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. We demonstrate the possibility of filtering out the effects of unwanted (not necessarily known) system-environment interactions and show that the noise-suppression procedure can be combined with the capability of retaining control over the effective dynamical evolution of the open quantum system. Implications for quantum information processing are discussed.

The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, the observed rate of inelastic collisions was strongly enhanced in a sodium Bose-Einstein condensate when the scattering length was tuned to both larger or smaller values than the off-resonant value. These strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates.

A classical dielectric moving in a charged capacitor can create a magnetic field (Röntgen effect). A quantum-dielectric layer, however, will not produce a magnetization, except at vortices. The magnetic field outside the quantum dielectric appears as the field of quantized monopoles.

We study the sets of possible sign changes that can occur when $n$ real quantum states are transported adiabatically around an $n$-fold degeneracy. The allowed sign changes include those predicted by the familiar spin $j=(n-1\mathrm{})/2$ model as a subset, but we also find at least one other possible set of sign changes for each $n>\mathrm{}2\mathrm{}$. Experimentally verifiable quadrilateral billiard examples are presented to illustrate these additional possibilities for 3- and 4-fold degeneracies.

Bose-Einstein condensates have been prepared in long-lived metastable excited states. Two complementary types of metastable states were observed. The first is due to the immiscibility of multiple components in the condensate, and the second to local suppression of spin-relaxation collisions. Relaxation via recondensation of noncondensed atoms, spin relaxation, and quantum tunneling was observed. These experiments were done with $F=1\mathrm{}$ spinor Bose-Einstein condensates of sodium confined in an optical dipole trap.

We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of $m$ directed random walkers with rather general attractive interactions, when suitably continued to $m=0\mathrm{}$. In $1+1$ dimensions, this is dual to a model of interacting steps on a vicinal surface. A similar correspondence with interacting self-avoiding walks is constructed for isotropic percolation.

We propose an experimental scheme for testing nonlocality of a correlated two-mode quantum state of light. We show that the correlation functions violating the Bell inequalities in the proposed experiment are equal to the joint two-mode $Q$ function and the Wigner function. This assigns a novel operational meaning to these two quasidistribution functions in tests of quantum nonlocality and also establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of the phase-space quasidistribution functions.

We demonstrate guiding of cold neutral atoms along a current carrying wire. Atoms either move in Kepler-like orbits around the wire or are guided in a potential tube on the side of the wire which is created by applying an additional homogeneous bias field. These atom guides are very versatile and promising for applications in atom optics.

We demonstrate the absence of off-diagonal elements for the density matrix of a supersonic Na atomic beam, thus showing that there are no coherent wave packets emerging from this source. We used a differentially detuned separated oscillatory field longitudinal interferometer to search for off-diagonal density matrix elements in the longitudinal energy/momentum basis. Our study places a stringent lower bound on their possible size over an off-diagonal energy range from 0 to 100 kHz.

We calculate the quantum motion of a Bose-Einstein condensate in an optical lattice generated by a standing wave of laser light. We show how to boost a stationary condensate into motion or stop a moving condensate by manipulating the optical lattice and how to achieve Bloch oscillations of the condensate in an accelerating optical lattice. We show how atomic interactions affect these processes and discuss conditions for possible experimental realization.

Level dynamics measurements have been performed in a Sinai microwave billiard as a function of a single length, as well as in rectangular billiards with randomly distributed disks as a function of the position of one disk. In the first case the field distribution is changed globally, and velocity distributions and autocorrelation functions are well described by universal functions derived by Simons and Altshuler. In the second case the field distribution is changed locally. Here another type of universal correlation is observed. It can be derived under the assumption that chaotic wave functions may be described by a random superposition of plane waves.

A non-Markovian stochastic Schrödinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. The ensemble average recovers the reduced density matrix without approximation and hence it allows one to determine open system dynamics with strong and non-Markovian environmental effects in a very efficient way. We demonstrate the power of our approach with several illustrative examples. First, we discuss a measurement-type situation, then a two-state system strongly coupled to a non-Markovian environment, exhibiting decays and revivals. Further examples showing the remarkable features of our new approach to non-Markovian open system dynamics are discussed, for instance, the possibility to shift the “Heisenberg cut” between system and environment.

The first measurements of an exit location distribution are reported for an overdamped nonconservative system perturbed by weak white noise, modeled both numerically and by an analog electronic circuit. In the weak-noise limit the distribution is increasingly concentrated near a saddle point of the dynamics and is increasingly well approximated by a Weibull distribution, in agreement with theoretical predictions. A physical explanation for this behavior is given, which should facilitate the computation of corrections to the limiting form.

The phase shift of the hyperfine Larmor precession of an individual ground-state ${}^{171}{\mathrm{Yb}}^{+}$ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an $E2\mathrm{}$ line.

Attractive Bose-Einstein condensates are investigated with numerical continuation methods capturing stationary solutions of the Gross-Pitaevskii equation. The branches of stable (elliptic) and unstable (hyperbolic) solutions are found to meet at a critical particle number through a generic Hamiltonian saddle node bifurcation. The condensate decay rates corresponding to macroscopic quantum tunneling, two and three body inelastic collisions, and thermally induced collapse are computed from the exact numerical solutions. These rates show experimentally significant differences with previously published rates. Universal scaling laws stemming from the bifurcation are derived.

We investigate stochastic resonance in a globally coupled oscillator system with time delay. The system shows multistability of a desynchronized state and two synchronized states with different collective frequencies, which may be interpreted as multistable perception of ambiguous or reversible figures. Under the influence of a weak periodic external signal, the system exhibits a maximum in the signal-to-noise ratio at an optimum noise level—the characteristic signature of stochastic resonance. We also show stochastic resonance between two limit-cycles in the system.