Critical points in edge tunneling between generic FQH states

A general description of weak and strong tunneling fixed points is developed in the chiral-Luttinger-liquid model of quantum Hall edge states. Tunneling fixed points are a subset of `termination' fixed points, which describe boundary conditions on a multicomponent edge. The requirement of unitary time evolution at the boundary gives a nontrivial consistency condition for possible low-energy boundary conditions. The effect of interactions and random hopping on fixed points is studied through a perturbative RG approach which generalizes the Giamarchi-Schulz RG for disordered Luttinger liquids to broken left-right symmetry and multiple modes. The allowed termination points of a multicomponent edge are classified by a B-matrix with rational matrix elements. We apply our approach to a number of examples, such as tunneling between a quantum Hall edge and a superconductor and tunneling between two quantum Hall edges in the presence of interactions. Interactions are shown to induce a continuous renormalization of effective tunneling charge for the integrable case of tunneling between two Laughlin states. The correlation functions of electronlike operators across a junction are found from the B matrix using a simple image-charge description, along with the induced lattice of boundary operators. Many of the results obtained are also relevant to ordinary Luttinger liquids.Comment: 23 pages, 6 figures. Xiao-Gang Wen: http://dao.mit.edu/~we

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

Dynamics of the Tippe Top via Routhian Reduction

We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.Comment: 16 pages, 7 figures, added reference. Typos corrected and a forgotten term in de linearized system is adde

Supersymmetry in carbon nanotubes in a transverse magnetic field

Electron properties of Carbon nanotubes in a transverse magnetic field are studied using a model of a massless Dirac particle on a cylinder. The problem possesses supersymmetry which protects low energy states and ensures stability of the metallic behavior in arbitrarily large fields. In metallic tubes we find suppression of the Fermi velocity at half-filling and enhancement of the density of states. In semiconducting tubes the energy gap is suppressed. These features qualitatively persist (although to a smaller degree) in the presence of electron interactions. The possibilities of experimental observation of these effects are discussed.Comment: A new section on electron interaction effects added and explanation on roles of supersymmetry expanded. Revtex4, 6 EPS figure file

On Quantum Control via Encoded Dynamical Decoupling

I revisit the ideas underlying dynamical decoupling methods within the framework of quantum information processing, and examine their potential for direct implementations in terms of encoded rather than physical degrees of freedom. The usefulness of encoded decoupling schemes as a tool for engineering both closed- and open-system encoded evolutions is investigated based on simple examples.Comment: 12 pages, no figures; REVTeX style. This note collects various theoretical considerations complementing/motivated by the experimental demonstration of encoded control by Fortunato et a

Entanglement of solid-state qubits by measurement

We show that two identical solid-state qubits can be made fully entangled (starting from completely mixed state) with probability 1/4 just measuring them by a detector, equally coupled to the qubits. This happens in the case of repeated strong (projective) measurements as well as in a more realistic case of weak continuous measurement. In the latter case the entangled state can be identified by a flat spectrum of the detector shot noise, while the non-entangled state (probability 3/4) leads to a spectral peak at the Rabi frequency with the maximum peak-to-pedestal ratio of 32/3.Comment: 5 pages, 2 figure

SO(10) unified models and soft leptogenesis

Motivated by the fact that, in some realistic models combining SO(10) GUTs and flavour symmetries, it is not possible to achieve the required baryon asymmetry through the CP asymmetry generated in the decay of right-handed neutrinos, we take a fresh look on how deep this connection is in SO(10). The common characteristics of these models are that they use the see-saw with right-handed neutrinos, predict a normal hierarchy of masses for the neutrinos observed in oscillating experiments and in the basis where the right-handed Majorana mass is diagonal, the charged lepton mixings are tiny. In addition these models link the up-quark Yukawa matrix to the neutrino Yukawa matrix Y^\nu with the special feature of Y^\nu_{11}-> 0 Using this condition, we find that the required baryon asymmetry of the Universe can be explained by the soft leptogenesis using the soft B parameter of the second lightest right-handed neutrino whose mass turns out to be around 10^8 GeV. It is pointed out that a natural way to do so is to use no-scale supergravity where the value of B ~1 GeV is set through gauge-loop corrections.Comment: 26 pages, 2 figures. Added references, new appendix of a relevant fit and improved comment

Measuring the decoherence rate in a semiconductor charge qubit

We describe a method by which the decoherence time of a solid state qubit may be measured. The qubit is coded in the orbital degree of freedom of a single electron bound to a pair of donor impurities in a semiconductor host. The qubit is manipulated by adiabatically varying an external electric field. We show that, by measuring the total probability of a successful qubit rotation as a function of the control field parameters, the decoherence rate may be determined. We estimate various system parameters, including the decoherence rates due to electromagnetic fluctuations and acoustic phonons. We find that, for reasonable physical parameters, the experiment is possible with existing technology. In particular, the use of adiabatic control fields implies that the experiment can be performed with control electronics with a time resolution of tens of nanoseconds.Comment: 9 pages, 6 figures, revtex

Geometric effects on T-breaking in p+ip and d+id superconductors

Superconducting order parameters that change phase around the Fermi surface modify Josephson tunneling behavior, as in the phase-sensitive measurements that confirmed $d$ order in the cuprates. This paper studies Josephson coupling when the individual grains break time-reversal symmetry; the specific cases considered are $p \pm ip$ and $d \pm id$, which may appear in Sr$_2$RuO$_4$ and Na$_x$CoO$_2 \cdot$(H$_2$O)$_y$ respectively. $T$-breaking order parameters lead to frustrating phases when not all grains have the same sign of time-reversal symmetry breaking, and the effects of these frustrating phases depend sensitively on geometry for 2D arrays of coupled grains. These systems can show perfect superconducting order with or without macroscopic $T$-breaking. The honeycomb lattice of superconducting grains has a superconducting phase with no spontaneous breaking of $T$ but instead power-law correlations. The superconducting transition in this case is driven by binding of fractional vortices, and the zero-temperature criticality realizes a generalization of Baxter's three-color model.Comment: 8 page