Long-range magnetic fields in the ground state of the Standard Model plasma

In thermal equilibrium the ground state of the plasma of Standard Model particles is determined by temperature and exactly conserved combinations of baryon and lepton numbers. We show that at non-zero values of the global charges a translation invariant and homogeneous state of the plasma becomes unstable and the system transits into a new state, containing a large-scale magnetic field. The origin of this effect is the parity-breaking character of weak interactions and chiral anomaly. This situation can occur in the early Universe and may play an important role in its subsequent evolution.Comment: 6 pages. Comments are welcom

Polaron Crystallization and Melting: Effects of the Long-Range Coulomb Forces

On examining the stability of a Wigner crystal in an ionic dielectric, two competitive effects due to the polaron formation are found to be important: (i) the screening of the Coulomb force, which destabilizes the crystal, compensated by (ii) the increase of the carrier mass (polaron mass). The competition between the two effects is carefully studied, and the quantum melting of the polaronic Wigner crystal is examined by varying the density at zero temperature. By calculating the quantum fluctuations of both the electron and the polarization, we show that there is a competition between the dissociation of the polarons at the insulator-to-metal transition (IMT), and a melting towards a polaron liquid. We find that at strong coupling, a liquid state of dielectric polarons cannot exist, and the IMT is driven by the polaron dissociation. Next, taking into account the dipolar interactions between localized carriers, we show that these are responsible for an instability of the transverse vibrational modes of the polaronic Wigner crystal as the density increases. This provides a new mechanism for the IMT in doped dielectrics, which yields interesting dielectric properties below and beyond the transition. An optical signature of such a mechanism for the IMT is provided.Comment: 10 pages, 3 figures, to be published in Int.J.Mod.Phys.

Topological Field Theory Interpretation of String Topology

The string bracket introduced by Chas and Sullivan [math.GT/9911159] is reinterpreted from the point of view of topological field theories in the Batalin-Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields (generalizing Chern-Simons and BF theories) are considered together with generalized Wilson loops. The latter generate a (Poisson or Gerstenhaber) algebra of functionals with values in the $S^1$-equivariant cohomology of the loop space of the manifold on which the theory is defined. It is proved that, in the case of $GL_n$ with standard representation, the (Poisson or BV) bracket of two generalized Wilson loops applied to two cycles is the same as the generalized Wilson loop applied to the string bracket of the cycles. Generalizations to other groups are briefly described.Comment: 27 pages, 2 figure

Modelling DNA Response to THz Radiation

Collective response of DNA to THz electric fields is studied in a simple pair bond model. We confirm, with some caveats, a previous observation of destabilising DNA breather modes and explore the parameter-dependence of these modes. It is shown that breather modes are eliminated under reasonable physical conditions and that thermal effects are significant.Comment: 6 pages, 3 figures. version to appear in Phys. Rev.

Sympathetic cooling of 4^4He+^+ ions in a radiofrequency trap

We have generated Coulomb crystals of ultracold $^4$He$^+$ ions in a linear radiofrequency trap, by sympathetic cooling via laser--cooled $^9$Be$^+$. Stable crystals containing up to 150 localized He$^+$ ions at $\sim$20 mK were obtained. Ensembles or single ultracold He$^+$ ions open up interesting perspectives for performing precision tests of QED and measurements of nuclear radii. The present work also indicates the feasibility of cooling and crystallizing highly charged atomic ions using $^9$Be$^+$ as coolant.Comment: 4 pages, 2 figure

Spin - or, actually: Spin and Quantum Statistics

The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli's theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin

Ellipsoidal Coulomb Crystals in a Linear Radiofrequency Trap

A static quadrupole potential breaks the cylindrical symmetry of the effective potential of a linear rf trap. For a one-component fluid plasma at low temperature, the resulting equilibrium charge distribution is predicted to be an ellipsoid. We have produced laser-cooled Be$^+$ ellipsoidal ion crystals and found good agreement between their shapes and the cold fluid prediction. In two-species mixtures, containing Be$^+$ and sympathetically cooled ions of lower mass, a sufficiently strong static quadrupole potential produces a spatial separation of the species.Comment: 4 pages, 3 figure

Adaiabtic theorems and reversible isothermal processes

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes (''isothermal theorem'') is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined