N=4 Supersymmetric MICZ-Kepler systems on S3

Proceeding from the superfield action for $N=4, d=1$ nonlinear supermultiplet, equipped with the most general potential term, we find the action describing a charged particle on the sphere $S^3$ in the field of $n$ fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze some particulary interesting potentials corresponding to the N=4 supersymmetric extension of the integrable one- and two-center McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on $S^3$.Comment: 8 pages, PACS: 11.30.Pb, 03.65.-w; corrected a misprint in (3.12), added the last sentence on page 3, added the paragraph after (3.7), added the sentence after (4.5

New insight into WDVV equation

We show that Witten-Dijkgraaf-Verlinde-Verlinde equation underlies the construction of N=4 superconformal multi--particle mechanics in one dimension, including a N=4 superconformal Calogero model.Comment: 16 pages, no figures, LaTeX file, PACS: 04.60.Ds; 11.30.P

Fermionic currents in AdS spacetime with compact dimensions

We derive a closed expression for the vacuum expectation value (VEV) of the fermionic current density in a (D+1)-dimensional locally AdS spacetime with an arbitrary number of toroidally compactified Poincare spatial dimensions and in the presence of a constant gauge field. The latter can be formally interpreted in terms of a magnetic flux treading the compact dimensions. In the compact subspace, the field operator obeys quasiperiodicity conditions with arbitrary phases. The VEV of the charge density is zero and the current density has nonzero components along the compact dimensions only. They are periodic functions of the magnetic flux with the period equal to the flux quantum and tend to zero on the AdS boundary. Near the horizon, the effect of the background gravitational field is small and the leading term in the corresponding asymptotic expansion coincides with the VEV for a massless field in the locally Minkowski bulk. Unlike the Minkowskian case, in the system consisting an equal number of fermionic and scalar degrees of freedom, with same masses, charges and phases in the periodicity conditions, the total current density does not vanish. In these systems, the leading divergences in the scalar and fermionic contributions on the horizon are canceled and, as a consequence of that, the charge flux, integrated over the coordinate perpendicular to the AdS boundary, becomes finite. We show that in odd spacetime dimensions the fermionic fields realizing two inequivalent representations of the Clifford algebra and having equal phases in the periodicity conditions give the same contribution to the VEV of the current density. Combining the contributions from these fields, the current density in odd-dimensional C-,P- and T -symmetric models are obtained. As an application, we consider the ground state current density in curved carbon nanotubes.Comment: 22 pages, 6 figures, PACS numbers: 04.62.+v, 03.70.+k, 98.80.-k, 61.46.F

Channeling of high-energy particles in a multi-wall nanotube

Channeling of high-energy particles in straight and bent multi-wall nanotubes (MWNT) has been studied in computer simulations and compared to the channeling properties of single-wall nanotubes (SWNT) and bent crystal lattices. It is demonstrated that MWNT can efficiently channel positively-charged high-energy particles trapped between the walls of MWNT. Bending dechanneling in MWNT has been computed as a function of the particle momentum to nanotube curvature radius ratio, $pv/R$. It is found that a bent MWNT can steer a particle beam with bending capabilities similar to those of bent silicon crystal lattice and to those of best (i.e. the narrowest) SWNT. In view of channeling applications at particle accelerators, MWNT appear favored as compared to SWNT, because MWNT can be produced quite straight (and in aligned array), while SWNT is typically very curved, thus posing a severe problem for channeling applications. Therefore, we suggest that MWNT provide a better candidate for channeling than SWNT.Comment: 16 pages, 6 figures, to appear in Phys. Lett.

Making the hyper--K\"ahler structure of N=2 quantum string manifest

We show that the Lorentz covariant formulation of N=2 string in a curved space reveals an explicit hyper--K\"ahler structure. Apart from the metric, the superconformal currents couple to a background two--form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.Comment: 8 pages, no figures, PACS: 04.60.Ds; 11.30.Pb, Keywords: N=2 string, hyper-K\"ahler geometry. Presentation improved, references added. The version to appear in PR

Constant magnetic field and 2d non-commutative inverted oscillator

We consider a two-dimensional non-commutative inverted oscillator in the presence of a constant magnetic field, coupled to the system in a ``symplectic'' and ``Poisson'' way. We show that it has a discrete energy spectrum for some value of the magnetic field.Comment: 7 pages, LaTeX file, no figures, PACS number: 03.65.-