Soluble `Supersymmetric' Quantum XY Model

We present a `supersymmetric' modification of the $d$-dimensional quantum rotor model whose ground state is exactly soluble. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The Hamiltonian contains three-site terms which are relevant: they change the universality class of the transition from that of the ($d+1$)--- to the $d$-dimensional classical XY model. The metallic phase has algebraic ODLRO but the superfluid density is identically zero. Variational wave functions for single-particle and collective excitations are presented.Comment: 12 pages, REVTEX 3.0, IUCM93-00

RHESSI Results -- Time For a Rethink?

Hard X-rays and gamma-rays are the most direct signatures of energetic electrons and ions in the sun's atmosphere which is optically thin at these energies and their radiation involves no coherent processes. Being collisional they are complementary to gyro-radiation in probing atmospheric density as opposed to magnetic field and the electrons are primarily 10--100 keV in energy, complementing the (>100 keV) electrons likely responsible for microwave bursts. The pioneering results of the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are raising the first new major questions concerning solar energetic particles in many years. Some highlights of these results are discussed -- primarily around RHESSI topics on which the authors have had direct research involvement -- particularly when they are raising the need for re-thinking of entrenched ideas. Results and issues are broadly divided into discoveries in the spatial, temporal and spectral domains, with the main emphasis on flare hard X-rays/fast electrons but touching also on gamma-rays/ions, non-flare emissions, and the relationship to radio bursts.Comment: Proceedings CESRA Workshop 2004: "The High Energy Solar Corona: Waves, Eruptions, Particles", Lecture Notes in Physics, 2006 (accepted

Low-temperature nonequilibrium transport in a Luttinger liquid

The temperature-dependent nonlinear conductance for transport of a Luttinger liquid through a barrier is calculated in the nonperturbative regime for $g=1/2-\epsilon$, where $g$ is the dimensionless interaction constant. To describe the low-energy behavior, we perform a leading-log summation of all diagrams contributing to the conductance which is valid for $|\epsilon| << 1$. With increasing external voltage, the asymptotic low-temperature behavior displays a turnover from the $T^{2/g-2}$ to a universal $T^2$ law.Comment: 13 pages RevTeX 3.0, accepted by Physical Review

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

Predicting the Amplitude of a Solar Cycle Using the North-South Asymmetry in the Previous Cycle: II. An Improved Prediction for Solar Cycle~24

Recently, using Greenwich and Solar Optical Observing Network sunspot group data during the period 1874-2006, (Javaraiah, MNRAS, 377, L34, 2007: Paper I), has found that: (1) the sum of the areas of the sunspot groups in 0-10 deg latitude interval of the Sun's northern hemisphere and in the time-interval of -1.35 year to +2.15 year from the time of the preceding minimum of a solar cycle n correlates well (corr. coeff. r=0.947) with the amplitude (maximum of the smoothed monthly sunspot number) of the next cycle n+1. (2) The sum of the areas of the spot groups in 0-10 deg latitude interval of the southern hemisphere and in the time-interval of 1.0 year to 1.75 year just after the time of the maximum of the cycle n correlates very well (r=0.966) with the amplitude of cycle n+1. Using these relations, (1) and (2), the values 112 + or - 13 and 74 + or -10, respectively, were predicted in Paper I for the amplitude of the upcoming cycle 24. Here we found that in case of (1), the north-south asymmetry in the area sum of a cycle n also has a relationship, say (3), with the amplitude of cycle n+1, which is similar to (1) but more statistically significant (r=0.968) like (2). By using (3) it is possible to predict the amplitude of a cycle with a better accuracy by about 13 years in advance, and we get 103 + or -10 for the amplitude of the upcoming cycle 24. However, we found a similar but a more statistically significant (r=0.983) relationship, say (4), by using the sum of the area sum used in (2) and the north-south difference used in (3). By using (4) it is possible to predict the amplitude of a cycle by about 9 years in advance with a high accuracy and we get 87 + or - 7 for the amplitude of cycle 24.Comment: 21 pages, 7 figures, Published in Solar Physics 252, 419-439 (2008

Exact perturbative solution of the Kondo problem

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.Comment: 4 pages in revtex two-colum

Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer

We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double quantum dot artificial molecule, projected to be used as a 2-qubit quantum gate in the proposed quantum dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method which is carried out analytically and the molecular orbital method which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.Comment: 12 pages, 4 figures embedded in tex

Solar-Cycle Characteristics Examined in Separate Hemispheres: Phase, Gnevyshev Gap, and Length of Minimum

Research results from solar-dynamo models show the northern and southern hemispheres may evolve separately throughout the solar cycle. The observed phase lag between the hemispheres provides information regarding the strength of hemispheric coupling. Using hemispheric sunspot-area and sunspot-number data from Cycles 12 - 23, we determine how out of phase the separate hemispheres are during the rising, maximum, and declining period of each solar cycle. Hemispheric phase differences range from 0 - 11, 0 - 14, and 2 - 19 months for the rising, maximum, and declining periods, respectively. The phases appear randomly distributed between zero months (in phase) and half of the rise (or decline) time of the solar cycle. An analysis of the Gnevyshev gap is conducted to determine if the double-peak is caused by the averaging of two hemispheres that are out of phase. We confirm previous findings that the Gnevyshev gap is a phenomenon that occurs in the separate hemispheres and is not due to a superposition of sunspot indices from hemispheres slightly out of phase. Cross hemispheric coupling could be strongest at solar minimum, when there are large quantities of magnetic flux at the Equator. We search for a correlation between the hemispheric phase difference near the end of the solar cycle and the length of solar-cycle minimum, but found none. Because magnetic flux diffusion across the Equator is a mechanism by which the hemispheres couple, we measured the magnetic flux crossing the Equator by examining magnetograms for Solar Cycles 21 - 23. We find, on average, a surplus of northern hemisphere magnetic flux crossing during the mid-declining phase of each solar cycle. However, we find no correlation between magnitude of magnetic flux crossing the Equator, length of solar minima, and phase lag between the hemispheres.Comment: 15 pages, 7 figure

Quantum entanglement and information processing via excitons in optically-driven quantum dots

We show how optically-driven coupled quantum dots can be used to prepare maximally entangled Bell and Greenberger-Horne-Zeilinger states. Manipulation of the strength and duration of the selective light-pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state based quantum information. Theoretical predictions suggest that several hundred single quantum bit rotations and Controlled-Not gates could be performed before decoherence of the excitonic states takes place.Comment: 3 separate PostScript Figures + 7 pages. Typos corrected. Minor changes added. This updated version is to appear in PR

Quantum Chaos Border for Quantum Computing

We study a generic model of quantum computer, composed of many qubits coupled by short-range interaction. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In this regime the noninteracting qubit structure disappears, the eigenstates become complex and the operability of the computer is destroyed. Despite the fact that the spacing between multi-qubit states drops exponentially with the number of qubits $n$, we show that the quantum chaos border decreases only linearly with $n$. This opens a broad parameter region where the efficient operation of a quantum computer remains possible.Comment: revtex, 4 pages, 5 figures, more details and data adde