Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) level k is briefly presented. This mini review is based on invited talks presented by P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin (China), August 1996; ``Selected Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia), September 1996; to be published in the Proceedings.Comment: LaTeX, 16 pages, references adde

Electron spin coherence in semiconductors: Considerations for a spin-based solid state quantum computer architecture

We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence is dominated by spin-spin interactions, through spectral diffusion and dipolar flip-flop mechanisms. These contributions lead to 1-100 $\mu$s calculated spin coherence times for a wide range of parameters, much higher than former estimates based on $T_{2}^{*}$ measurements.Comment: Role of the dipolar interaction clarified; Included discussion on the approximations employed in the spectral diffusion calculation. Final version to appear in Phys. Rev.

Real Forms of Non-abelian Toda Theories and their W-algebras

We consider real forms of Lie algebras and embeddings of sl(2) which are consistent with the construction of integrable models via Hamiltonian reduction. In other words: we examine possible non-standard reality conditions for non-abelian Toda theories. We point out in particular that the usual restriction to the maximally non-compact form of the algebra is unnecessary, and we show how relaxing this condition can lead to new real forms of the resulting W-algebras. Previous results for abelian Toda theories are recovered as special cases. The construction can be extended straightforwardly to deal with osp(1|2) embeddings in Lie superalgebras. Two examples are worked out in detail, one based on a bosonic Lie algebra, the other based on a Lie superalgebra leading to an action which realizes the N=4 superconformal algebra.Comment: 11 pages, LaTex; minor errors corrected, extra references adde

Electron spin as a spectrometer of nuclear spin noise and other fluctuations

This chapter describes the relationship between low frequency noise and coherence decay of localized spins in semiconductors. Section 2 establishes a direct relationship between an arbitrary noise spectral function and spin coherence as measured by a number of pulse spin resonance sequences. Section 3 describes the electron-nuclear spin Hamiltonian, including isotropic and anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the effective Hamiltonian for nuclear-nuclear coupling mediated by the electron spin hyperfine interaction. Section 4 describes a microscopic calculation of the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops with quasiparticle broadening included. Section 5 compares our explicit numerical results to electron spin echo decay experiments for phosphorus doped silicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low dimensional structures", edited by Marco Fanciulli. To be published by Springer-Verlag in the TAP series. 35 pages, 9 figure

A Self Assembled Nanoelectronic Quantum Computer Based on the Rashba Effect in Quantum Dots

Quantum computers promise vastly enhanced computational power and an uncanny ability to solve classically intractable problems. However, few proposals exist for robust, solid state implementation of such computers where the quantum gates are sufficiently miniaturized to have nanometer-scale dimensions. Here I present a new approach whereby a complete computer with nanoscale gates might be self-assembled using chemical synthesis. Specifically, I demonstrate how to self-assemble the fundamental unit of this quantum computer - a 2-qubit universal quantum controlled-NOT gate - based on two exchange coupled multilayered quantum dots. Then I show how these gates can be wired using thiolated conjugated molecules as electrical connectors. A qubit is encoded in the ground state of a quantum dot spin-split by the Rashba interaction. Arbitrary qubit rotations are effected by bringing the spin splitting energy in a target quantum dot in resonance with a global ac magnetic field by applying a potential pulse of appropriate amplitude and duration to the dot. The controlled dynamics of the 2-qubit controlled-NOT operation (XOR) can be realized by exploiting the exchange coupling with the nearest neighboring dot. A complete prescription for initialization of the computer and data input/output operations is presented.Comment: 22 pages, 4 figure

Nonlinear excitations in CsNiF3 in magnetic fields perpendicular to the easy plane

Experimental and numerical studies of the magnetic field dependence of the specific heat and magnetization of single crystals of CsNiF3 have been performed at 2.4 K, 2.9 K, and 4.2 K in magnetic fields up to 9 T oriented perpendicular to the easy plane. The experimental results confirm the presence of the theoretically predicted double peak structure in the specific heat arising from the formation of nonlinear spin modes. The demagnetizing effects are found to be negligible, and the overall agreement between the data and numerical predictions is better than reported for the case when the magnetic field was oriented in the easy plane. Demagnetizing effects might play a role in generating the difference observed between theory and experiment in previous work analyzing the excess specific heat using the sine-Gordon model.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Scaling anomaly in cosmic string background

We show that the classical scale symmetry of a particle moving in cosmic string background is broken upon inequivalent quantization of the classical system, leading to anomaly. The consequence of this anomaly is the formation of single bound state in the coupling interval \gamma\in(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter \omega. It has been conjectured that the formation of loosely bound state in cosmic string background may lead to the so called anomalous scattering cross section for the particles, which is usually seen in molecular physics.Comment: 4 pages,1 figur

Evidence of Color Coherence Effects in W+jets Events from ppbar Collisions at sqrt(s) = 1.8 TeV

We report the results of a study of color coherence effects in ppbar collisions based on data collected by the D0 detector during the 1994-1995 run of the Fermilab Tevatron Collider, at a center of mass energy sqrt(s) = 1.8 TeV. Initial-to-final state color interference effects are studied by examining particle distribution patterns in events with a W boson and at least one jet. The data are compared to Monte Carlo simulations with different color coherence implementations and to an analytic modified-leading-logarithm perturbative calculation based on the local parton-hadron duality hypothesis.Comment: 13 pages, 6 figures. Submitted to Physics Letters