Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions

We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the non-interacting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several re-entrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in real space for odd (even) $q$ and suggest experiments to test our theory.Comment: 8 pages, 11 figures, v

Bosonization for disordered and chaotic systems

Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems can be derived from our exact model using a coarse-graining procedure. As an example, we consider a model for a smooth disorder and demonstrate that using our approach does not lead to a 'mode-locking' problem. As a new application, we consider scattering on strong impurities for which the Born approximation cannot be used. Our method provides a new calculational scheme for disordered and chaotic systems.Comment: 4 pages, no figure, REVTeX4; title changed, revision for publicatio

The Singularity in Generic Gravitational Collapse Is Spacelike, Local, and Oscillatory

A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.Comment: 7 pages includes 4 figures. Uses Revtex and psfig. Received "honorable mention" in 1998 Gravity Research Foundation essay contest. Submitted to Mod. Phys. Lett.

Neutral and charged matter in equilibrium with black holes

We study the conditions of a possible static equilibrium between spherically symmetric, electrically charged or neutral black holes and ambient matter. The following kinds of matter are considered: (1) neutral and charged matter with a linear equation of state p_r = w\rho (for neutral matter the results of our previous work are reproduced), (2) neutral and charged matter with p_r \sim \rho^m, m > 1, and (3) the possible presence of a "vacuum fluid" (the cosmological constant or, more generally, anything that satisfies the equality T^0_0 = T^1_1 at least at the horizon). We find a number of new cases of such an equilibrium, including those generalizing the well-known Majumdar-Papapetrou conditions for charged dust. It turns out, in particular, that ultraextremal black holes cannot be in equilibrium with any matter in the absence of a vacuum fluid; meanwhile, matter with w > 0, if it is properly charged, can surround an extremal charged black hole.Comment: 12 pages, no figures, final version published in PR

Parametric Level Correlations in Random-Matrix Models

We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green's functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle--point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications.Comment: 8 page

Supersymmetry for disordered systems with interaction

Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix sigma-model. The method is based on replacing the initial model of interacting electons by a fully supersymmetric model. Although this replacement is not exact, it is a good approximation for a weak short range interaction and arbitrary disorder. The replacement makes the averaging over disorder and further manipulations straightforward and we come to a supermatrix sigma-model containing an interaction term. The structure of the model is rather similar to the replica one, although the interaction term has a different form. We study the model making perturbation theory and renormalization group calculations. We check the renormalizability of the model in the first loop approximation and in the first order in the interaction. In this limit we reproduce the renormalization group equations known from earlier works. We hope that the new supermatrix sigma-model may become a new tool for non-perturbative calculations for disordered systems with interaction.Comment: 18 pages, 8 figures, published version with minor change