Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstr\"om space-time: analytical solutions

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr\"om space-time in terms of the Weierstra{\ss} $\wp$, $\sigma$ and $\zeta$ elliptic functions. Based on the study of the polynomials in the $\vartheta$ and $r$ equations we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstr\"om space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstr\"om space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times

Acoustic Spectroscopy of the DNA in GHz range

We find a parametric resonance in the GHz range of the DNA dynamics, generated by pumping hypersound . There are localized phonon modes caused by the random structure of elastic modulii due to the sequence of base pairs

Symmetry breaking in low-dimensional SU(N) antiferromagnets

Consequences of explicit symmetry breaking in a physically motivated model of SU(N) antiferromagnet in spatial dimensions one and two are studied. It is shown that the case N=3, which can be realized in spin-1 cold atom systems, displays special properties distinctly different from those for N>=4. Qualitative form of the phase diagram depending on the model parameters is given.Comment: 10 pages, 2 figures; added references, corrected fig.2; the final version to appear in PR

Symmetries of Electrostatic Interaction between DNA Molecules

We study a model for pair interaction $U$ of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups, and find noncommutative group of eighth order ${\cal S}$ of symmetries that leave $U$ invariant. We classify the minima using group ${\cal S}$ and employ numerical methods for finding them. The minima may correspond to several cholesteric phases, as well as phases formed by cross-like conformations of molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results depend on the effective charge $Q$ of the phosphate group which can be modified by the polycations or the ions of metals. The snowflake phase could exist for $Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric phases. Close to $Q_C$ the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.Comment: 13 pages, 4 figure

Nahm Transform and Moduli Spaces of CPn Models on the Torus

There is a Nahm transform for two-dimensional gauge fields which establishes a one-to-one correspondence between the orbit space of U(N) gauge fields with topological charge k defined on a torus and that of U(k) gauge fields with charge N on the dual torus. The main result of this paper is to show that a similar duality transform cannot exist for CPn instantons. This fact establishes a significative difference between 4-D gauge theories and CPn models. The result follows from the global analysis of the moduli space of instantons based on a complete and explicit parametrization of all self-dual solutions on the two-dimensional torus. The boundary of the space of regular instantons is shown to coincide with the space of singular instantons. This identification provides a new approach to analyzing the role of overlapping instantons in the infrared sector of CPn sigma models.Comment: 28 pages, 5 eps-figure

Efficient Cluster Algorithm for CP(N-1) Models

Despite several attempts, no efficient cluster algorithm has been constructed for CP(N-1) models in the standard Wilson formulation of lattice field theory. In fact, there is a no-go theorem that prevents the construction of an efficient Wolff-type embedding algorithm. In this paper, we construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems. Such systems provide a regularization for CP(N-1) models in the framework of D-theory. We present detailed studies of the autocorrelations and find a dynamical critical exponent that is consistent with z = 0.Comment: 14 pages, 3 figure

The Topological Susceptibility of the Lattice CP(n-1) Model on the Torus and the Sphere

The topological vacuum structure of the two-dimensional $~CP^{n-1}~$ model for $~n = 3,5,7~$ is studied on the lattice. In particular we investigate the small-volume limit on the torus as well as on the sphere and compare with continuum results. For $~n \ge 5~$ , where lattice artifacts should be suppressed, the topological susceptibility shows unexpectedly strong deviations from asymptotic scaling. On the other hand there is an indication for a convergence to values obtained analytically within the limit $~n \rightarrow \infty~$ .Comment: 20 pages, 14 figures not included, sorry, HU Berlin-IEP-92/2, Nucl. Phys. B in prin