We show that the time-dependent nonlinear Schrödinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference between split condensates that are recombined, whereas an exact many-body treatment shows minimal interference.

We analyze the motion of an overdamped classical particle in a multidimensional periodic potential, driven by an external noise. We demonstrate that in the steady state the presence of temporal correlations in the noise and spatial asymmetry within a period of the potential could lead to particle rotation. The rotation is a direct consequence of a change in the sign of the noise-induced drift motion in each dimension. By choosing different potentials, we can generate a variety of flow patterns from laminar drifts to rotations.

We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of “superchemistry,” in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases.

We introduce a method of solving initial boundary value problems for linear evolution equations in a time-dependent domain, and we apply it to an equation with dispersion relation $\omega \left(k\right)$, in the domain $l\left(t\right)<x<\mathrm{}\infty$, $0<t<T$. We show that the solution of this problem admits an integral representation in the complex $k$ plane, involving either an integral of $\exp [ikx-i\omega (k\left)t\right]\rho \left(k\right)$ along a time-dependent contour, or an integral of $\exp [ikx-i\omega (k\left)t\right]\rho (k,\overline{k})$ over a fixed two-dimensional domain. The functions $\rho \left(k\right)$ and $\rho (k,\overline{k})$ can be computed through the solution of a system of Volterra linear integral equations. This method can be generalized to nonlinear integrable partial differential equations.

In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between nonlocal and local attributes of the topology, which is reminiscent but different from the usual wave-particle complementarity. This complementarity is not a consequence of noncommutativity, rather it is due to the noncanonical nature of the observables. We suggest that a local/nonlocal complementarity is a general feature of topological effects that are “dual” to the Aharonov-Bohm effect.

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We derive formulas for the positions and the density of the zeros. In particular, we show that, for models without symmetry, the curves on which the zeros lie are generically not circles, and can have topologically nontrivial features, such as bifurcation. Our results are illustrated in three models in a complex field: the low-temperature Ising and Blume-Capel models, and the $q$-state Potts model for large $q$.

A new method is presented to reconstruct the potential of a quantum mechanical many-body system from observational data, combining a nonparametric Bayesian approach with a Hartree-Fock approximation. A priori information is implemented as a stochastic process, defined on the space of potentials. The method is computationally feasible and provides a general framework to treat inverse problems for quantum mechanical many-body systems.

We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a “driven-pendulum” equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.

Recursion relations are presented that allow exact calculation of canonical and microcanonical partition functions of degenerate Fermi systems, assuming no explicit two-body interactions. Calculations of the level density, sorted by angular momentum, are presented for ${}^{56}\mathrm{Ni}$. The issue of treating unbound states is also addressed.

It is commonly believed that distillation of entanglement can be, in general, irreversible. Perhaps the strongest evidence is constituted by the existence of the bound entangled states. However, even a single example of state exhibiting this irreversibility has not been found so far. We show that for a family of states the process of distillation of entanglement is truly irreversible. These states have a nonzero amount of bound entanglement and, at most, a very small amount of free entanglement.

We study the stability and dynamics of vortices in two-species condensates as prepared in the recent JILA experiment [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)]. We find that of the two possible configurations, in which one species has vorticity $m=1\mathrm{}$ and the other one has $m=0\mathrm{}$, only one is linearly stable, which agrees with the experimental results. However, it is found that in the unstable case the vortex is not destroyed by the instability, but may be transferred from one species to the other or display complex spatiotemporal dynamics.

We present a novel approach for constructing nonequilibrium steady states. It is based on a deterministic and time-reversible mechanism for dissipating energy from a subsystem into a thermal reservoir. The key idea is to thermalize a moving particle by appropriately modeling its microscopic collision rules with a boundary mimicking a thermal reservoir with arbitrarily many degrees of freedom. We demonstrate our method for the periodic Lorentz gas with an external electric field. By applying our thermostat we do not find an ergodic breakdown with increasing field strength.

A “universal” dependence is predicted of the reduced critical parameters, $\frac{k_B{T}_c}{E_0}\left(\gamma \right)$, $\frac{V_c}{V_0}\left(\gamma \right)$, and $P_c{V}_c/k_B{T}_c{=Z}_c\left(\gamma \right)$, on the crystal anharmonicity $\gamma$ (closely related to the Grüneisen parameter ${\Gamma }_G$). It is based on a simplified embedded-atom type approach which enables one to utilize the universal zero-temperature equation of state in a version of fluid perturbation theory. This model's critical temperature and density agree with the experimental results for both the heavy rare gases ( $\gamma \simeq 2.85$) and heavy alkali metals ( $\gamma \simeq 1.35$). Predicted critical parameters for many other liquid metals are consistent with previous estimates, but the model is not applicable when directional bonding is important.

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator $E\left(t\right)=U\left(t\right){\mathrm{EU}}^{†}\left(t\right)$ is measured continuously from $t=0\mathrm{}$ to $T$, where $E$ is a projector leaving the initial state unchanged and $U\left(t\right)$ a unitary operator obeying $U\left(0\right)=1\mathrm{}$. We prove that the probability of always finding $E\left(t\right)=1\mathrm{}$ from $t=0\mathrm{}$ to $T$ is unity. If $U\left(t\right)\ne 1$, the watched kettle is sure to “boil.”

A coherent atomic beam splitter can be realized using the transient dynamics of a chaotic system. We have experimentally observed such an effect using ultracold rubidium atoms. Our experimental results are in good agreement with numerical simulations of the Schrödinger equation for the system.

Electric-field-controlled atomic holography has been demonstrated. A binary hologram pattern was encoded in the gaps of regularly spaced parallel stripes of platinum electrodes formed on ${\mathrm{SiN}}_4$ thin film. Each electrode was either grounded or connected to a terminal. The electrode connections were arranged so that an electric field appeared in approximately half the 512 gaps when a finite voltage was applied to the terminal. By controlling this voltage, we could shift, erase, or switch holographically reconstructed two-dimensional images of atoms on a screen.

We show that the ground state of a spin-1 Bose gas with an antiferromagnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order $N$) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and method of detecting fragmented states are presented.

We present a quantum theory for the interaction of a quantum target with a time dependent matter beam. When several pulses in the incident beam arrive with a period $\tau$, transitions between levels with an energy difference $h/\tau$ can be enhanced. Unlike all previous studies, we find that transitions in passive targets can distinguish between an incoherent beam and a beam with a coherent wave packet structure. As an example, we calculate the transition probability of Rb Rydberg atoms interacting with a pulsed electron beam.