Partially incoherent gap solitons in Bose-Einstein condensates

We construct families of incoherent matter-wave solitons in a repulsive degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and investigate their stability at zero and finite temperature, using the Hartree-Fock-Bogoliubov equations. The gap solitons are composed of a coherent condensate, and normal and anomalous densities of incoherent vapor co-trapped with the condensate. Both intragap and intergap solitons are constructed, with chemical potentials of the components falling in one or different bandgaps in the OL-induced spectrum. Solitons change gradually with temperature. Families of intragap solitons are completely stable (both in direct simulations, and in terms of eigenvalues of perturbation modes), while the intergap family may have a very small unstable eigenvalue (nevertheless, they feature no instability in direct simulations). Stable higher-order (multi-humped) solitons, and bound complexes of fundamental solitons are found too.Comment: 8 pages, 9 figures. Physical Review A, in pres

Power densities for two-step gamma-ray transitions from isomeric states

We have calculated the incident photon power density P_2 for which the two-step induced emission rate from an isomeric nucleus becomes equal to the natural isomeric decay rate. We have analyzed two-step transitions for isomeric nuclei with a half-life greater than 10 min, for which there is an intermediate state of known energy, spin and half-life, for which the intermediate state is connected by a known gamma-ray transition to the isomeric state and to at least another intermediate state, and for which the relative intensities of the transitions to lower states are known. For the isomeric nucleus 166m-Ho, which has a 1200 y isomeric state at 5.98 keV, we have found a value of P_2=6.3 x 10^7 W cm^{-2}, the intermediate state being the 263.8 keV level. We have found power densities P_2 of the order of 10^{10} W cm^{-2} for several other isomeric nuclei.Comment: 9 pages, 1 eps figure, 1 tabl

On the reliability of the theoretical internal conversion coefficients

Possible sources of uncertainties in the calculations of the internal conversion coefficients are studied. The uncertainties induced by them are estimated.Comment: 16 pages (including 3 figures inserted by 'epsfig' macro

Many-body effects on adiabatic passage through Feshbach resonances

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.Comment: 9 pages, 9 figure

Nonlinear adiabatic passage from fermion atoms to boson molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power-law is linear, $\Gamma \propto \alpha$, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and $\Gamma \propto \alpha^{1/3}$ when it is larger. Experimental data agree better with a linear dependence than with an exponential Landau-Zener fit, indicating that many-body effects are significant in the atom-molecule conversion process.Comment: 5 pages, 4 figure

On the terminal velocity of sedimenting particles in a flowing fluid

The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields and, by means of an ordinary perturbation expansion at small Stokes number, leads to closed partial differential equations (PDE) whose solutions contain all relevant information on the sedimentation process. The set of PDE's are solved by means of direct numerical simulations for a class of 2D cellular flows (static and time dependent) and the resulting phenomenology is analysed and discussed.Comment: 13 pages, 2 figures, submitted to JP

Internal conversion coefficients for superheavy elements

The internal conversion coefficients (ICC) were calculated for all atomic subshells of the elements with 104<=Z<=126, the E1...E4, M1...M4 multipolarities and the transition energies between 10 and 1000 keV. The atomic screening was treated in the relativistic Hartree-Fock-Slater model. The Tables comprising almost 90000 subshell and total ICC were recently deposited at LANL preprint server.Comment: 6 pages including 3 figures, needs files myown.sty and epsfig.sty (both included

Thermalization of an impurity cloud in a Bose-Einstein condensate

We study the thermalization dynamics of an impurity cloud inside a Bose-Einstein condensate at finite temperature, introducing a suitable Boltzmann equation. Some values of the temperature and of the initial impurity energy are considered. We find that, below the Landau critical velocity, the macroscopic population of the initial impurity state reduces its depletion rate. For sufficiently high velocities the opposite effect occurs. For appropriate parameters the collisions cool the condensate. The maximum cooling per impurity atom is obtained with multiple collisions.Comment: 4 pages 6 figure

On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions

Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains $\nu_n$ of the $n$-th eigenfunction satisfies $n\ge \nu_n$. Here, we provide a new interpretation for the Courant nodal deficiency $d_n = n-\nu_n$ in the case of quantum graphs. It equals the Morse index --- at a critical point --- of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning --- it is the number of unstable directions in the vicinity of the critical point corresponding to the $n$-th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.Comment: 22 pages, 6 figure

Theory of four-wave mixing of matter waves from a Bose-Einstein condensate

A recent experiment [Deng et al., Nature 398, 218(1999)] demonstrated four-wave mixing of matter wavepackets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this description to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.Comment: 18 pages Revtex preprint form, 13 eps figure