Maximal supersymmetry and exceptional groups

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by Pierre Ramond, Sung-Soo Kim and myself where we describe the N = 8 Supergravity in the light-cone formalism. We show how the Cremmer-Julia E7(7) non-linear symmetry is implemented and how the full supermultiplet is a representation of the E7(7) symmetry. I also show how the E7(7) symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.Comment: Proceedings of Conference in Honour of Murray Gell-Mann's 80th Birthda

Supertraces on the algebra of observables of the rational Calogero model based on the classical root system

A complete set of supertraces on the algebras of observables of the rational Calogero models with harmonic interaction based on the classical root systems of B_N, C_N and D_N types is found. These results extend the results known for the case A_N. It is shown that there exist Q independent supertraces where Q(B_N)=Q(C_N) is a number of partitions of N into a sum of positive integers and Q(D_N) is a number of partitions of N into a sum of positive integers with even number of even integers.Comment: 10 pages, LATE

Majorana spin-flip transitions in a magnetic trap

Atoms confined in a magnetic trap can escape by making spin-flip Majorana transitions due to a breakdown of the adiabatic approximation. Several papers have studied this process for atoms with spin $F = 1/2$ or $F= 1$. The present paper calculates the escape rate for atoms with spin $F > 1$. This problem has new features because the perturbation $\Delta T$ which allows atoms to escape satisfies a selection rule $\Delta F_z = 0, \pm 1, \pm 2$ and multi-step processes contribute in leading order. When the adiabatic approximation is satisfied the leading order terms can be summed to yield a simple expression for the escape rate.Comment: 16page

Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure

Local Invariants and Pairwise Entanglement in Symmetric Multi-qubit System

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classifcation scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.Comment: 9 pages, 2 figures, REVTEX, Replaced with a published versio

Electronic Correlations in Oligo-acene and -thiophene Organic Molecular Crystals

From first principles calculations we determine the Coulomb interaction between two holes on oligo-acene and -thiophene molecules in a crystal, as a function of the oligomer length. The relaxation of the molecular geometry in the presence of holes is found to be small. In contrast, the electronic polarization of the molecules that surround the charged oligomer, reduces the bare Coulomb repulsion between the holes by approximately a factor of two. In all cases the effective hole-hole repulsion is much larger than the calculated valence bandwidth, which implies that at high doping levels the properties of these organic semiconductors are determined by electron-electron correlations.Comment: 5 pages, 3 figure

Unraveling Orbital Correlations via Magnetic Resonant Inelastic X-ray Scattering

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on both the symmetry of the orbitals that spins occupy, and on photon polarizations. We show in detail how this effect allows magnetic RIXS to distinguish between alternating orbital ordered and ferro-orbital (or orbital liquid) states.Comment: 7 pages, 4 figures. Supplemental material adde

Electrical Nanoprobing of Semiconducting Carbon Nanotubes using an Atomic Force Microscope

We use an Atomic Force Microscope (AFM) tip to locally probe the electronic properties of semiconducting carbon nanotube transistors. A gold-coated AFM tip serves as a voltage or current probe in three-probe measurement setup. Using the tip as a movable current probe, we investigate the scaling of the device properties with channel length. Using the tip as a voltage probe, we study the properties of the contacts. We find that Au makes an excellent contact in the p-region, with no Schottky barrier. In the n-region large contact resistances were found which dominate the transport properties.Comment: 4 pages, 5 figure

Exploiting entanglement in communication channels with correlated noise

We develop a model for a noisy communication channel in which the noise affecting consecutive transmissions is correlated. This model is motivated by fluctuating birefringence of fiber optic links. We analyze the role of entanglement of the input states in optimizing the classical capacity of such a channel. Assuming a general form of an ensemble for two consecutive transmissions, we derive tight bounds on the classical channel capacity depending on whether the input states used for communication are separable or entangled across different temporal slots. This result demonstrates that by an appropriate choice, the channel capacity may be notably enhanced by exploiting entanglement.Comment: 9 pages, 5 figure