Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one

Electromagnetic Fields of Slowly Rotating Magnetized Gravastars

We study the dipolar magnetic field configuration and present solutions of Maxwell equations in the internal background spacetime of a a slowly rotating gravastar. The shell of gravastar where magnetic field penetrated is modeled as sphere consisting of perfect highly magnetized fluid with infinite conductivity. Dipolar magnetic field of the gravastar is produced by a circular current loop symmetrically placed at radius $a$ at the equatorial plane.Comment: 5 pages, 2 figures, accepted for publication to Mod. Phys. Lett.

Towards absolute calibration of optical tweezers

Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of MDSA (Mie-Debye-Spherical Aberration) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass/water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points and `hopping' effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.Comment: 15 pages, 20 figure

Non-collinear coupling between magnetic adatoms in carbon nanotubes

The long range character of the exchange coupling between localized magnetic moments indirectly mediated by the conduction electrons of metallic hosts often plays a significant role in determining the magnetic order of low-dimensional structures. In addition to this indirect coupling, here we show that the direct exchange interaction that arises when the moments are not too far apart may induce a non-collinear magnetic order that cannot be characterized by a Heisenberg-like interaction between the magnetic moments. We argue that this effect can be manipulated to control the magnetization alignment of magnetic dimers adsorbed to the walls of carbon nanotubes.Comment: 13 pages, 5 figures, submitted to PR

Exceptional structure of the dilute A3_3 model: E8_8 and E7_7 Rogers--Ramanujan identities

The dilute A$_3$ lattice model in regime 2 is in the universality class of the Ising model in a magnetic field. Here we establish directly the existence of an E$_8$ structure in the dilute A$_3$ model in this regime by expressing the 1-dimensional configuration sums in terms of fermionic sums which explicitly involve the E$_8$ root system. In the thermodynamic limit, these polynomial identities yield a proof of the E$_8$ Rogers--Ramanujan identity recently conjectured by Kedem {\em et al}. The polynomial identities also apply to regime 3, which is obtained by transforming the modular parameter by $q\to 1/q$. In this case we find an A_1\times\mbox{E}_7 structure and prove a Rogers--Ramanujan identity of A_1\times\mbox{E}_7 type. Finally, in the critical $q\to 1$ limit, we give some intriguing expressions for the number of $L$-step paths on the A$_3$ Dynkin diagram with tadpoles in terms of the E$_8$ Cartan matrix. All our findings confirm the E$_8$ and E$_7$ structure of the dilute A$_3$ model found recently by means of the thermodynamic Bethe Ansatz.Comment: 9 pages, 1 postscript figur

Chemical Evolution of the Galaxy Based on the Oscillatory Star Formation History

We model the star formation history (SFH) and the chemical evolution of the Galactic disk by combining an infall model and a limit-cycle model of the interstellar medium (ISM). Recent observations have shown that the SFH of the Galactic disk violently variates or oscillates. We model the oscillatory SFH based on the limit-cycle behavior of the fractional masses of three components of the ISM. The observed period of the oscillation ($\sim 1$ Gyr) is reproduced within the natural parameter range. This means that we can interpret the oscillatory SFH as the limit-cycle behavior of the ISM. We then test the chemical evolution of stars and gas in the framework of the limit-cycle model, since the oscillatory behavior of the SFH may cause an oscillatory evolution of the metallicity. We find however that the oscillatory behavior of metallicity is not prominent because the metallicity reflects the past integrated SFH. This indicates that the metallicity cannot be used to distinguish an oscillatory SFH from one without oscillations.Comment: 21 pages LaTeX, to appear in Ap

Topological insulator particles as optically induced oscillators: towards dynamical force measurements and optical rheology

We report the first experimental study upon the optical trapping and manipulation of topological insulator (TI) particles. By virtue of the unique TI properties, which have a conducting surface and an insulating bulk, the particles present a peculiar behaviour in the presence of a single laser beam optical tweezers: they oscillate in a plane perpendicular to the direction of the laser propagation, as a result of the competition between radiation pressure and gradient forces. In other words, TI particles behave as optically induced oscillators, allowing dynamical measurements with unprecedented simplicity and purely optical control. Actually, optical rheology of soft matter interfaces and biological membranes, as well as dynamical force measurements in macromolecules and biopolymers, may be quoted as feasible possibilities for the near future.Comment: 6 pages, 5 figures. Correspondence and requests for Supplementary Material should be addressed to [email protected]

Gravitational Collapse of Self-Similar and Shear-free Fluid with Heat Flow

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.Comment: 34 pages, 9 figures, late

Perturbed Self-Similar Massless Scalar Field in the Spacetimes with Circular Symmetry in 2+1 Gravity

We present in this work the study of the linear perturbations of the 2+1-dimensional circularly symmetric solution, obtained in a previous work, with kinematic self-similarity of the second kind. We have obtained an exact solution for the perturbation equations and the possible perturbation modes. We have shown that the background solution is a stable solution.Comment: no figure