We consider a two-dimensional electron with an anomalous magnetic moment, <i>g</i>&gt;2, interacting with a nonzero magnetic field <i>B</i> perpendicular to the plane which gives rise to a flux <i>F</i>. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the \mathcal{O}\left( {r^{ - 2 - \delta } } ight) decay at infinity: we show that if \mathcal{O}\left( {r^{ - 2 - \delta } } ight) exceeds an integer <i>N</i>, there is at least \mathcal{O}\left( {r^{ - 2 - \delta } } ight) bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero flux case.

The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -- which we refer to as the PAX and the PAXY model -- are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.

In this paper, we study a class of sphere and torus correlation functions in the W_N minimal model. In particular, we show that a large class of exact sphere three-point functions of W_N primaries, derived using affine Toda theory, exhibit large N factorization. This allows us to identify some fundamental particles and their bound states in the holographic dual, including light states. We also derive the torus two-point function of basic primaries, by directly constructing the relevant conformal blocks. The result can then be analytically continued to give the Lorentzian thermal two-point functions.

In this letter we discuss a new physical effect: we show that the BoseEinstein condensate can be created in quasi-one-dimensional systems in a purely geometrical way, namely by bending or other suitable deformation of a tube. We demonstrate this for the perfect Bose gas as well as for the case of mean-field particle interactions.

Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review offers a survey of such models startingt he classical Friedrichs result and carryingfu rther to recent developments in the theory of quantum graphs. Our attention concentrates on dynamical mechanism underlyingre sonance effects and at time evolution of the related unstable systems.