Based on spatially and temporally resolved numerical solutions to the relativistic quantum field equations, we provide a resolution to the controversial issue of how an incoming electron scatters off a supercritical potential step and how the electron-positron pair production is affected by this collision. The treatment of the problem as a correlated three-particle problem suggests revealing insight into the process.

We introduce a simple stochastic system able to generate anomalous diffusion for both position and velocity. The model represents a viable description of the Fermi’s acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents ${\nu }_x$ and ${\nu }_v$. The diffusion process is anomalous (non-Gaussian) but with a defined scaling property, i.e., $P(|\mathbf{r}|,t)=1/t^{{\nu }_x}{F}_x(|\mathbf{r}|/t^{{\nu }_x})$ and similarly for velocity.

We create rapidly rotating Bose-Einstein condensates in the lowest Landau level by spinning up the condensates to rotation rates $\Omega >99\%$ of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a consequence, the chemical potential drops below the cyclotron energy $2\hslash \Omega$. While in this mean-field quantum-Hall regime we still observe an ordered vortex lattice, its elastic shear strength is strongly reduced, as evidenced by the observed very low frequency of Tkachenko modes. Furthermore, the gas approaches the quasi-two-dimensional limit. The associated crossover from interacting- to ideal-gas behavior along the rotation axis results in a shift of the axial breathing mode frequency.

A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.

Deformations can induce rotation with zero angular momentum where dissipation is a natural “cost function.” This gives rise to an optimization problem of finding the most effective rotation with zero angular momentum. For certain plastic and viscous media in two dimensions the optimal path is the orbit of a charged particle on a surface of constant negative curvature with a magnetic field whose total flux is half a quantum unit.

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [K. E. Strecker et al., Nature (London) 417, 150 (2002).] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton-soliton interactions, produces bursts of hot atoms at different time scales.

We experimentally investigate and analyze the rich dynamics in $F=2$ spinor Bose-Einstein condensates of ${}^{87}\mathrm{R}\mathrm{b}$. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of ${10}^{-12}{\mathrm{c}\mathrm{m}}^3{\mathrm{s}}^{-1}$ for spin-changing collisions within the $F=2$ manifold and spin-dependent loss rates in the range of ${10}^{-13}{\mathrm{c}\mathrm{m}}^3{\mathrm{s}}^{-1}$ for hyperfine-changing collisions. We observe polar behavior in the $F=2$ ground state of ${}^{87}\mathrm{R}\mathrm{b}$, while we find the $F=1$ ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.

We have observed condensation of fermionic atom pairs in the BCS-BEC crossover regime. A trapped gas of fermionic ${}^{40}\mathrm{K}$ atoms is evaporatively cooled to quantum degeneracy and then a magnetic-field Feshbach resonance is used to control the atom-atom interactions. The location of this resonance is precisely determined from low-density measurements of molecule dissociation. In order to search for condensation on either side of the resonance, we introduce a technique that pairwise projects fermionic atoms onto molecules; this enables us to measure the momentum distribution of fermionic atom pairs. The transition to condensation of fermionic atom pairs is mapped out as a function of the initial atom gas temperature $T$ compared to the Fermi temperature $T_F$ for magnetic-field detunings on both the BCS and BEC sides of the resonance.

Despite great technological relevance, the initial steps of nucleation and crystal growth from solution are still poorly understood. While experimentally difficult to access, simulations in principle may provide insight at the atomic level. However, in most cases the computational demand dramatically exceeds the scope of current hardware. Since crystallization usually occurs on time scales much larger than the few ns of a molecular dynamics simulation, special techniques for the study of rare events are of particular interest. In the present work the nucleation of sodium chloride aggregates from aqueous solution is investigated from path sampling molecular dynamics simulation. The introduced simulation schemes appear to be widely applicable.

We report on measurements of the critical temperature of a harmonically trapped, weakly interacting Bose gas as a function of atom number. Our results exclude ideal-gas behavior by more than two standard deviations, and agree quantitatively with mean-field theory. At our level of sensitivity, we find no additional shift due to critical fluctuations. In the course of this measurement, the onset of hydrodynamic expansion in the thermal component has been observed. Our thermometry method takes this feature into account.

The cross-helicity integral is known in fluid dynamics and plasma physics as a topological invariant which measures the mutual linkage of two divergence-free vector fields, e.g., magnetic fields, on a three-dimensional domain. Generalizing this concept, a new topological invariant is found which measures the mutual linkage of three closed two-forms, e.g., electromagnetic fields, on a four-dimensional domain. The integral is shown to detect a separation of the cross helicity between two of the fields with the help of the third field. It can be related to the triple linking number known in knot theory. Furthermore, it is shown that the well-known three-dimensional cross helicity and the new four-dimensional invariant are the first two examples of a series of topological invariants which are defined by $n-1$ field strengths $F=dA$ on a simply connected $n$-dimensional manifold $M^n$.

The entanglement of multiatom quantum states is considered. In order to cancel noise due to inhomogeneous light-atom coupling, the concept of matched multiatom observables is proposed. As a means to eliminate an important form of decoherence this idea should be of broad relevance for quantum information processing with atomic ensembles. The general approach is illustrated on the example of rotation angle measurement, and it is shown that the multiatom states that were thought to be only weakly entangled can exhibit near-maximum entanglement.

We consider a finite-range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance ${\gamma }^{-1}$. We show that, under mild assumptions on the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit $\gamma \to 0$. This could be a first step toward an expansion around mean-field theory, for spin glass systems.

The quantum Zeno effect—suppression of decay by frequent measurements—was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we show that it can occur even for exactly exponentially decaying systems, for which this condition is never satisfied, by considering a realistic case where the detector has a finite energy band of detection. The conventional theories correspond to the limit of an infinite bandwidth. This implies that the Zeno effect occurs more widely than expected thus far.

Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length $a_{3\mathrm{D}}$. In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative $a_{3\mathrm{D}}$.

Depending on the Hamiltonian parameters, two-component bosons in an optical lattice can form at least three different superfluid phases in which both components participate in the superflow: a (strongly interacting) mixture of two miscible superfluids (2SF), a paired superfluid (PSF) vacuum, and (at a commensurate total filling factor) the super-counter-fluid (SCF) state. We study the universal properties of the 2SF-PSF and 2SF-SCF quantum phase transitions and show that (i) they can be mapped onto each other and (ii) their universality class is identical to the $(d+1)$-dimensional normal-superfluid transition in a single-component liquid. The finite-temperature 2SF-PSF(SCF) transitions and the topological properties of 2SF-PSF(SCF) interfaces are also discussed.

We study many-body quantum dynamics of $\delta$-interacting bosons confined in a one-dimensional ring. Main attention is paid to the transition from the mean-field to the Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wave function and the momentum distribution depend on time for weak and strong interactions. We show that the transition from regular (quasiperiodic) to irregular (“chaotic”) dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime, the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.

Discrete sine-Gordon (SG) chains are studied with path-integral molecular dynamics. Chains commensurate with the substrate show the transition from pinning to quantum creep at bead masses slightly larger than in the continuous SG model. Within the creep regime, a field-driven transition from creep to complete depinning is identified. The effects of disorder on the chain’s dynamics depend on the potential’s roughness exponent $H$. For example, quantum fluctuations are generally too small to depin the chain if $H=1/2$, while an $H=0$ chain can be pinned or unpinned depending on the bead masses. Thermal fluctuations always depin the chain.

Momentum transfer between matter and electromagnetic field is analyzed. The related equations of motion and conservation laws are derived using relativistic formalism. Their correspondence to various, at first sight self-contradicting, experimental data (the so-called Abraham-Minkowski controversy) is demonstrated. A new, Casimir-like, quantum phenomenon is predicted: contribution of vacuum fluctuations to the motion of dielectric liquids in crossed electric and magnetic fields. Velocities of about $50\mathrm{n}\mathrm{m}/\mathrm{s}$ can be expected due to the contribution of high frequency vacuum modes. The proposed phenomenon could be used in the future as an investigating tool for zero fluctuations. Other possible applications lie in fields of microfluidics or precise positioning of micro-objects, e.g., cold atoms or molecules.

The neutral kaon system is shown to be suitable to discuss extensions and tests of Bohr’s complementarity principle through the quantum marking and quantum erasure techniques suggested by Scully and Drühl [Phys. Rev. A 25, 2208 (1982)]. Strangeness oscillations play the role of the traditional interference pattern linked to wavelike behavior, whereas the different propagation in free space of the $K_S$ and $K_L$ components mimics the two possible interferometric paths taken by particlelike objects.