Hurricane eyewalls are often observed to be nearly circular structures, but they are occasionally observed to take on distinctly polygonal shapes. The shapes range from triangles to hexagons and, while they are often incomplete, straight line segments can be identified. Other observations implicate the existence of intense mesovortices within or near the eye region. Is there a relation between polygonal eyewalls and hurricane mesovortices? Are these phenomena just curiosities of the hurricane's inner-core circulation, or are they snapshots of an intrinsic mixing process within or near the eye that serves to determine the circulation and thermal structure of the eye? As a first step toward understanding the asymmetric vorticity dynamics of the hurricane's eye and eyewall region, these issues are examined within the framework of an unforced barotropic nondivergent model. Polygonal eyewalls are shown to form as a result of barotropic instability near the radius of maximum winds. After reviewing linear theory, simulations with a high-resolution pseudospectral numerical model are presented to follow the instabilities into their nonlinear regime. When the instabilities grow to finite amplitude, the vorticity of the eyewall region pools into discrete areas, creating the appearance of polygonal eyewalls. The circulations associated with these pools of vorticity suggest a connection to hurricane mesovortices. At later times the vorticity is ultimately rearranged into a nearly monopolar circular vortex. While the evolution of the finescale vorticity field is sensitive to the initial condition, the macroscopic end-states are found to be similar. In fact, the gross characteristics of the numerically simulated end-states are predicted analytically using a generalization of the minimum enstrophy hypothesis. In an effort to remove some of the weaknesses of the minimum enstrophy approach, a maximum entropy argument developed previously for rectilinear shear flows is extended to the vortex problem, and end-state solutions in the limiting case of tertiary mixing are obtained. Implications of these ideas for real hurricanes are discussed.

High-spin paramagnetic manganese defects in polar piezoelectric zinc oxide exhibit a simple, almost axial anisotropy and phase coherence times of the order of a millisecond at low temperatures. The anisotropy energy is tunable using an externally applied electric field. This can be used to control electrically the phase of spin superpositions and to drive spin transitions with resonant microwave electric fields. DOI: 10.1103/PhysRevLett.110.027601 PACS numbers: 76.30.Fc, 76.60.Lz, 77.65.Àj Couplings between magnetic and electric degrees of freedom give rise to such fundamental phenomena in condensed matter as multiferroelectricity [1,2], unconventional superconductivity [3], and spin-density waves [4], and are key to proposed future technologies such as high sensitivity metrology [5] and quantum-dot-based quantum information processing [6]. The control of spin states using electric fields rather than magnetic fields is particularly valuable for quantum information processing [7], because electric fields can be applied on short length scales, and down to the scale of qubit separations in a device [8][9][10]. In this Letter, we identify a class of electrically controllable spin qubits: high-spin magnetic defects in polar semiconductor hosts. In one member of this class, the manganese substitutional defect in a crystalline zinc oxide host, we demonstrate coherent oscillations of the spin state driven by dc electric field pulses and spin transitions driven by resonant microwave electric fields.Electrical control has been considered in various candidate physical systems for spin qubits, both experimentally and theoretically. In lithographically defined GaAs quantum dots, spin-orbit coupling permits coherent control of an electron spin by applying a resonant high frequency voltage to one of the confining gates [11]. Stark shifts in spin splittings, originating from hybridization with excited state orbitals, have been observed in self-assembled quantum dots [12] and in bound donors in semiconductors [13,14] and in defects in diamond [15], while frustrated spin triangles exhibit spin-electric couplings via modulation of exchange interactions [16,17]. Here, our approach is to manipulate the electrostatic environment of a high-spin paramagnetic defect, manganese, in a polar piezoelectric host material, zinc oxide, thereby controlling electrically the spin Hamiltonian of the defect [18].The spin Hamiltonian of manganese defects in zinc oxide (ZnO:Mn) is well known from continuous-wave ESR [19]. The polar environment lifts the spin degeneracy of the S ¼ 5=2 Mn 2þ ions which are substitutional on Zn 2þ sites, while the I ¼ 5=2 nuclear spin of 55 Mn is coupled to the electron spin by the hyperfine interaction.The Hamiltonian, including a magnetic field which lifts the remaining Kramer's degeneracies, iswhere the axial anisotropy, or zero-field splitting (ZFS), termHigher order effects, such as fourth order electron spin anisotropy and nuclear quadrupole terms, have been detected [19], but they are small and not relevant f...

In the first-quantised worldline approach to quantum field theory, a longstanding problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the "N -photon kernel," where offshell this kernel appears also in "subleading" terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.

Abstract:We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which -by adding a suitable Chern-Simons term to the particle action -can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F ) "flavour" symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction -i.e. the lengths of the columns (rows) of the Young tableauare fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

We construct contact interactions for bosonic and spinning strings. In the tensionless limit of the spinning string this reproduces the super-Wilson loop that couples spinor matter to Abelian gauge theory. Adding boundary terms that quantise the motion of charges results in a string model equivalent to spinor QED. The strings represent lines of electric flux connected to the charges. The purely bosonic model is spoilt by divergences that are excluded from the spinning model by world-sheet supersymmetry, indicating a preference for spinor matter.