We treat the noise-activated escape from a one-dimensional potential well of an overdamped particle, to which a periodic force of fixed frequency is applied. Near the well top, the relevant length scales and the boundary layer structure are determined. We show how behavior near the well top generalizes the behavior determined by Kramers, in the case without forcing. Our analysis includes the case when the forcing does not die away in the weak-noise limit. We discuss the relevance of scaling regimes, defined by the relative strengths of the forcing and the noise, to recent optical trap experiments.

We study the mode-coupling approximation for the Kardar-Parisi-Zhang equation in the strong-coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension $d_c=4\mathrm{}$ and the expansion $z=2-(d-4\mathrm{})/4+O\left(\right(4-d{)}^2)$ around $d_c$. We find the exact $z=3\mathrm{}/2$ value in $d=1\mathrm{}$, and estimate the values $z\simeq 1.62$, $z\simeq 1.78$ in $d=2\mathrm{}$, 3. The result $d_c=4\mathrm{}$ and the expansion around $d_c$ are very robust and can be derived just from a mild assumption on the relative scale on which the response and correlation functions vary as $z$ approaches 2.

We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the Thouless-Anderson-Palmer (TAP) approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings between the random variables is required, our method adapts to the concrete couplings. We demonstrate the validity of our approach, which is so far restricted to models with nonglassy behavior, by replica calculations for a wide class of models as well as by simulations for a real data set.

We show that the probability, $P_0\left(l\right)$, that the height of a fluctuating $(d+1\mathrm{})$-dimensional interface in its steady state stays above its initial value up to a distance $l$, along any linear cut in the $d$-dimensional space, decays as $P_0\left(l\right)\sim l^{-\theta }$. Here $\theta$ is a “spatial” persistence exponent, and takes different values, ${\theta }_s$ or ${\theta }_0$, depending on how the point from which $l$ is measured is specified. These exponents are shown to map onto corresponding temporal persistence exponents for a generalized $d=1\mathrm{}$ random-walk equation. The exponent ${\theta }_0$ is nontrivial even for Gaussian interfaces.

We have observed a Bose-Einstein condensate in a dilute gas of ${}^4\mathrm{He}$ in the ${}_{}{}^3{}_{}{}^{}2S_1^{}{}_{}{}^{}$ metastable state. We find a critical temperature of $(4.7\pm 0.5)\mu \mathrm{K}$ and a typical number of atoms at the threshold of $8\times {10}^6$. The maximum number of atoms in our condensate is about $5\times {10}^5$. An approximate value for the scattering length $a=(16\pm 8)\mathrm{nm}$ is measured. The mean elastic collision rate at threshold is then estimated to be about $2\times {10}^4{\mathrm{s}}^{-1\mathrm{}}$, indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is $2\mathrm{s}$, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.

We study Langevin dynamics describing nonequilibirum steady states. Employing the phenomenological framework of steady-state thermodynamics constructed by Oono and Paniconi [Prog. Theor. Phys. Suppl. 130, 29 (1998)], we find that the extended form of the second law which they proposed holds for transitions between steady states and that the Shannon entropy difference is related to the excess heat produced in an infinitely slow operation. A generalized version of the Jarzynski work relation plays an important role in our theory.

A novel solution to the quantum backreaction problem in a mixed quantum-classical simulation is provided using the Bohmian interpretation of quantum mechanics. The Bohmian backreaction is unique, computationally simple, features reaction channel branching, and easily gives the full classical limit. The Bohmian quantum-classical method is illustrated by application to a model of ${\mathrm{O}}_2$ interacting with a Pt surface.

We show that in certain parameter regimes there is a macroscopic dynamical breakdown of the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive- $P$ representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The full quantum theory includes the spontaneous processes which will become significant when the atomic population is low. The experimental signature of the quantum effects will be the time scale of the revival of the atomic population after a near total conversion to the molecular condensate.

We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\mathrm{sys}}$ of the isolated system. While the golden rule then does not apply we can discard $H_{\mathrm{sys}}$. By allowing for couplings to different reservoirs, we reveal decoherence as a universal short-time phenomenon independent of the character of the system as well as the bath and of the basis the superimposed states are taken from. We discuss consequences for the classical behavior of the macroworld and quantum measurement: For decoherence of superpositions of macroscopically distinct states $H_{\mathrm{sys}}$ is always negligible.

The creation and interaction of dark solitons in a two-component Bose-Einstein condensate is investigated. For a miscible case, the interaction of dark solitons in different components is studied. Various possible scenarios are presented, including the formation of a soliton-soliton bound pair. We also analyze the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when it exceeds a critical velocity. For lower velocities multiple reflections within the domain are observed, where the soliton is evaporated and accelerated after each reflection until it finally escapes from the domain.

A vortex in a condensate in a nonspherical trapping potential will in general experience a torque. The torque will induce tilting of the direction of the vortex axis. We observe this behavior experimentally and show that by applying small distortions to the trapping potential, we can control the tilting behavior. By suppressing vortex tilt, we have been able to hold the vortex axis along the line of sight for up to 15 sec. Alternatively, we can induce a 180° tilt, effectively reversing the charge on the vortex as observed in the lab frame. We characterize the vortex nondestructively with a surface-wave spectroscopic technique.

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.

We study the statistical mechanics of a two-dimensional Bose gas with a repulsive delta-function interaction, using a mean-field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion-statistics gas. We also show that this result is consistent with a full quantum-mechanical treatment of a quasi-two-dimensional system.

Neuronal populations receive signals through temporally inhomogeneous spike trains which can be approximated by an input consisting of a time dependent mean value (additive signal) and noise with a time dependent intensity (noise coded signal). We compare the linear response of an ensemble of model neurons to these signals. Our analytical solution for the mean activity demonstrates the high efficiency of the transmission of a noise coded signal in a broad frequency band. For both kinds of signal we show that the transmission by the ensemble reveals stochastic resonance as well as a nonmonotonous dependence on the driving frequency.

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the “molecular chaos hypothesis.” For $q>\mathrm{}0\mathrm{}$, the $q$-transport equation satisfies an $H$ theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.

The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.

We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing “classical” superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.

On the basis of gauge invariance, it is proven in an elementary and straightforward manner, but without invoking any ad hoc assumption, that the existence of off-diagonal long-range order in one-particle reduced density matrix in Bose liquids implies both the irrotational flow in a simply connected region and the quantization of circulation in a multiply connected region, the two fundamental properties of a Bose superfluid. The origin for both is the phase coherence of condensate wave functions. Some relevant issues are also addressed.

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions $d_1\simeq 26$ and $d_2\simeq 46$. We also give refined measurements of the persistence exponents for low dimensions.

We show that quantum diffusion has well-defined front shape. After an initial transient, the wave packet front (tails) is described by a stretched exponential $P(x,t)=A\left(t\right)\exp (-|x/w{|}^{\gamma })$, with $1<\mathrm{}\gamma <\infty$, where $w\left(t\right)$ is the spreading width which scales as $w\left(t\right)\sim t^{\beta }$, with $0<\mathrm{}\beta \le 1$. The two exponents satisfy the universal relation $\gamma =1/(1-\beta )$. We demonstrate these results through numerical work on one-dimensional quasiperiodic systems and the three-dimensional Anderson model of disorder. We provide an analytical derivation of these relations by using the memory function formalism of quantum dynamics. Furthermore, we present an application to experimental results for the quantum kicked rotor.