We study the decoherence of a one-particle system, whose classical correspondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt echo (i.e., the revival of a localized density excitation upon reversal of its time evolution), in the presence of the perturbation. We predict an exponential decay for the Loschmidt echo with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths. Our results are consistent with recent experiments of polarization echoes in nuclear magnetic resonance and numerical simulations.

Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of the Boltzmann equation. The particle density and the rms velocity decay as $c\sim t^{-\alpha }$ and $\overline{v}\sim t^{-\beta }$, with the exponents depending on the initial velocity distribution and the spatial dimension $d$. For instance, in one dimension for the uniform initial velocity distribution $\beta =0.230\mathrm{}472\dots$ . In the opposite extreme $d\to \infty$, the dynamics is universal and $\beta \to \left({1-2}^{-1\mathrm{}/2}\right)d^{-1\mathrm{}}$. We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.

We study the effect of metastability onto boundary induced phase transitions in a driven lattice gas. The phase diagram for open systems, parametrized by the input and output rates, consists of two regions corresponding to the free flow and jammed phase. Both have been entirely characterized. The microscopic states in the high density phase are shown to have an interesting striped structure, which undergoes a coarsening process and survives in the thermodynamic limit.

We measure the decoherence of a spatially separated atomic superposition due to spontaneous photon scattering. We observe a qualitative change in decoherence versus separation as the number of scattered photons increases, and verify quantitatively the decoherence rate constant in the many-photon limit. Our results illustrate an evolution of decoherence consistent with general models developed for a broad class of decoherence phenomena.

We report the first experimental observation of Beliaev coupling between collective excitations of a Bose-Einstein condensed gas. Beliaev coupling is not predicted by the Gross-Pitaevskii equation and so this experiment tests condensate theory beyond the mean field approximation. Measurements of the amplitude of a high frequency scissors mode show that the Beliaev process transfers energy to a lower-lying mode and then back and forth between these modes, unlike Landau processes which lead to a monotonic decrease in amplitude. To enhance the Beliaev process we adjusted the geometry of the magnetic trapping potential to give a frequency ratio of 2 to 1 between the two scissors modes.

We propose a method to investigate the energy eigenvalue problem and corresponding yrast line for harmonically trapped interacting $N$-boson systems. This method is particularly simple and effective to obtain the explicit analytical expressions of low-L energy eigenstates with $L$ denoting systems' total angular momentum but with an arbitrarily large $N$. We have derived the explicit analytical results for $L=0,1,\dots ,9\mathrm{}$ and discussed the yrast line for these low- $L$ energy eigenstates.

We show that elastic collisions between atoms in a Bose-Einstein condensate with attractive interactions can lead to an explosion that ejects a large fraction of the collapsing condensate. We study variationally the dynamics of this explosion and find excellent agreement with recent experiments on magnetically trapped ${}^{85}\mathrm{Rb}$. We also determine the energy and angular distribution of the ejected atoms during the collapse.

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.

A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of “nonlocality without inequalities.” However, it works for $100\%$ of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger–like proof involving only two spacelike separated regions.

We show that pair correlations may play an important role in the dynamical properties of a Bose-Einstein condensed gas composed of an atomic field resonantly coupled with a condensed field of molecular dimers. Specifically, pair correlations in this system can dramatically modify the coherent and incoherent transfers between the atomic and molecular fields.

We set a new upper limit of $1.7\times {10}^{-11\mathrm{}}$ to the probability that two spin-0 ${}^{16}\mathrm{O}$ nuclei are in forbidden exchange-antisymmetric states, testing the validity of fundamental principles of quantum mechanics. A newly designed difference-frequency spectrometer is used to look for the existence of these states. The experimental test was performed by tuning the spectrometer across a molecular transition of ${}^{12}\mathrm{C}{}^{16}\mathrm{O}{}_2$ belonging to the rovibrational band at $4.25\mu \mathrm{m}$, connecting the forbidden states $({00}^{0}0,J=25)$ and $({00}^{0}1,J=26)$.

As an important example of noisy rotary oscillations, the dynamic magnetization of an assembly of superparamagnetic particles is considered. In the presence of a bias field, there exists a mechanism that causes selective suppression of higher harmonics in the response spectrum of the system. Manifestation of this effect at temperature variation is known as the noise-induced resonance. Its manifestation at the change of excitation intensity, formerly unknown, we term the force-induced resonance.

We reinterpret the microcanonical conditions in the quantum domain as constraints for the interaction of the “gas subsystem” under consideration and its environment (“container”). The time average of a purity measure is found to equal the average over the respective path in Hilbert space. We then show that for typical (degenerate or nondegenerate) thermodynamical systems almost all states within the allowed region of Hilbert space have a local von Neumann entropy $S$ close to the maximum and a purity $P$ close to its minimum, respectively. Typically, thermodynamical systems should obey the second law.

We prove rigorously and demonstrate in simulations that, for a potential system staying initially at the bottom of a well, the escape flux over the barrier grows on times of the order of a period of eigenoscillation in a stepwise manner, provided that friction is small or moderate. If the initial state is not at the bottom of the well, then, typically, some of the steps transform into oscillations. The stepwise/oscillatory evolution at short times appears to be a generic feature of a noise-induced flux.

We analyze the coherent multimode dynamics of a system of coupled atomic and molecular Bose gases. Starting from an atomic Bose-Einstein condensate with a small thermal component, we observe a complete depletion of the atomic and molecular condensate modes on a short time scale due to a significant population of excited states. Giant coherent oscillations between the two condensates for typical parameters are almost completely suppressed. Our results cast serious doubts on the common use of the 2-mode model for the description of coupled ultracold atomic-molecular systems and should be considered when planning future experiments with ultracold molecules.

We present a new family of stationary solutions to the cubic nonlinear Schrödinger equation with an elliptic function potential. In the limit of a sinusoidal potential our solutions model a quasi-one-dimensional dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided that the ratio of the height of the variations of the condensate to its dc offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Recent developments allow for experimental investigation of these predictions.

The collapsing dynamics of a trapped Bose-Einstein condensate with attractive interaction are revealed to exhibit two previously unknown phenomena. During the collapse, the condensate undergoes a series of rapid implosions that occur intermittently within a very small region. When the sign of the interaction is suddenly switched from repulsive to attractive, e.g., by the Feshbach resonance, density fluctuations grow to form various patterns such as a shell structure.

By performing numerical simulations based on the Gross-Pitaevskii equation, we make direct quantitative measurements of the sound energy released due to superfluid vortex reconnections. We show that the energy radiated expressed in terms of the loss of vortex line length is a simple function of the reconnection angle. In addition, we study the temporal and spatial distribution of the radiation and show that energy is emitted in the form of a sound pulse with a wavelength of a few healing lengths.

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values.

A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum nondemolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.