We investigate the electronic structure of the helium atom in a magnetic field between B = 0 and B = 100a.u.. The atom is treated as a nonrelativistic system with two interacting electrons and a fixed nucleus. Scaling laws are provided connecting the fixed-nucleus Hamiltonian to the one for the case of finite nuclear mass. Respecting the symmetries of the electronic Hamiltonian in the presence of a magnetic field, we represent this Hamiltonian as a matrix with respect to a two-particle basis composed of one-particle states of a Gaussian basis set. The corresponding generalized eigenvalue problem is solved numerically, providing in the present paper results for vanishing magnetic quantum number M = 0 and even or odd z-parity, each for both singlet and triplet spin symmetry. Total electronic energies of the ground state and the first few excitations in each subspace as well as their one-electron ionization energies are presented as a function of the magnetic field, and their behaviour is discussed. Energy values for electromagnetic transitions within the M = 0 subspace are shown, and a complete table of wavelengths at all the detected stationary points with respect to their field dependence is given, thereby providing a basis for a comparison with observed absorption spectra of magnetic white dwarfs.

We study the interaction of dark solitons with a localized impurity in Bose-Einstein condensates. We apply the soliton perturbation theory developed earlier in optics for describing the soliton dynamics and solitonimpurity interaction analytically, and then verify the results by direct numerical simulations of the Gross-Pitaevskii equation. We find that a dark soliton can be reflected from or transmitted through a repulsive impurity in a controllable manner, while near the critical point the soliton can be quasitrapped by the impurity. Additionally, we demonstrate that an immobile soliton may be captured and dragged by an adiabatically moving attractive impurity.

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behavior is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.

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The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the ⌺ manifold are studied for ungerade and gerade parity as well as singlet and triplet states covering a broad regime of field strengths from Bϭ0 up to Bϭ100 a.u. A variety of interesting phenomena can be observed. For the 1 ⌺ g state we found a monotonous decrease of the equilibrium distance and a simultaneous increase of the dissociation energy with growing magnetic-field strength. The 3 ⌺ g state is shown to develop an additional minimum which has no counterpart in field-free space. The 1 ⌺ u state shows a monotonous increase in the dissociation energy with a first increasing and then decreasing internuclear distance of the minimum. For this state the dissociation channel is H 2 →H Ϫ ϩH ϩ for magnetic field strengths Bտ20 a.u. due to the existence of strongly bound H Ϫ states in strong magnetic fields. The repulsive 3 ⌺ u state possesses a very shallow van der Waals minimum for magnetic-field strengths smaller than 1.0 a.u. within the numerical accuracy of our calculations. The 1 ⌺ g and 3 ⌺ u states cross as a function of B and the 3 ⌺ u state, which is an unbound state, becomes the ground state of the hydrogen molecule in magnetic fields Bտ0.2 a.u. This is of particular interest for the existence of molecular hydrogen in the vicinity of white dwarfs. In superstrong fields the ground state is again a strongly bound state, the 3 ⌸ u state.