Analytically solvable driven time-dependent two-level quantum systems

Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions. Any function satisfying these constraints yields an exact analytical solution. We demonstrate this method by presenting several new exact solutions to the time-dependent Schrodinger equation. Our general method and many of the new solutions we present are particularly relevant to qubit control in quantum computing applications.Comment: 4.5 pages, 4 figures, PRL versio

Photoionisation and Heating of a Supernova Driven, Turbulent, Interstellar Medium

The Diffuse Ionised Gas (DIG) in galaxies traces photoionisation feedback from massive stars. Through three dimensional photoionisation simulations, we study the propagation of ionising photons, photoionisation heating and the resulting distribution of ionised and neutral gas within snapshots of magnetohydrodynamic simulations of a supernova driven turbulent interstellar medium. We also investigate the impact of non-photoionisation heating on observed optical emission line ratios. Inclusion of a heating term which scales less steeply with electron density than photoionisation is required to produce diagnostic emission line ratios similar to those observed with the Wisconsin H{\alpha} Mapper. Once such heating terms have been included, we are also able to produce temperatures similar to those inferred from observations of the DIG, with temperatures increasing to above 15000 K at heights |z| > 1 kpc. We find that ionising photons travel through low density regions close to the midplane of the simulations, while travelling through diffuse low density regions at large heights. The majority of photons travel small distances (< 100pc); however some travel kiloparsecs and ionise the DIG.Comment: 10 pages, 13 figures, accepted to MNRA

Bi-layer splitting in overdoped high TcT_{c} cuprates

Recent angle-resolved photoemission data for overdoped Bi2212 are explained. Of the peak-dip-hump structure, the peak corresponds the $\vec q =0$ component of a hole condensate which appears at $T_c$. The fluctuating part of this same condensate produces the hump. The bilayer splitting is large enough to produce a bonding hole and an electron antibonding quasiparticle Fermi surface. Smaller bilayer splittings observed in some experiments reflect the interaction of the peak structure with quasiparticle states near, but not at, the Fermi surface.Comment: 4 pages with 2 figures - published versio

Intermittency and the passive nature of the magnitude of the magnetic field

It is shown that the statistical properties of the magnitude of the magnetic field in turbulent electrically conducting media resemble, in the inertial range, those of passive scalars in fully developed three-dimensional fluid turbulence. This conclusion, suggested by the data from Advanced Composition Explorer, is supported by a brief analysis of the appropriate magnetohydrodynamic equations

Effective chiral-spin Hamiltonian for odd-numbered coupled Heisenberg chains

An $L \times \infty$ system of odd number of coupled Heisenberg spin chains is studied using a degenerate perturbation theory, where $L$ is the number of coupled chains. An effective chain Hamiltonian is derived explicitly in terms of two spin half degrees of freedom of a closed chain of $L$ sites, valid in the regime the inter-chain coupling is stronger than the intra-chain coupling. The spin gap has been calculated numerically using the effective Hamiltonian for $L=3,5,7,9$ for a finite chain up to ten sites. It is suggested that the ground state of the effective Hamiltonian is correlated, by examining variational states for the effective chiral-spin chain Hamiltonian.Comment: 9 Pages, Latex, report ICTP-94-28

Distinguishing Among Strong Decay Models

Two competing models for strong hadronic decays, the $^3P_0$ and $^3S_1$ models, are currently in use. Attempts to rule out one or the other have been hindered by a poor understanding of final state interactions and by ambiguities in the treatment of relativistic effects. In this article we study meson decays in both models, focussing on certain amplitude ratios for which the relativistic uncertainties largely cancel out (notably the $S/D$ ratios in $b_1\rightarrow\pi\omega$ and $a_1\rightarrow\pi\rho$), and using a Quark Born Formalism to estimate the final state interactions. We find that the $^3P_0$ model is strongly favoured. In addition, we predict a $P/F$ amplitude ratio of $1.6\pm .2$ for the decay $\pi_2\rightarrow\pi\rho$. We also study the parameter-dependence of some individual amplitudes (as opposed to amplitude ratios), in an attempt to identify a ``best'' version of the $^3P_0$ model.Comment: 20 pages, uuencoded postscript file with 7 figures, MIT-CTP-2295; CMU-HEP94-1