Equivalence of domains arising from duality of orbits on flag manifolds II

In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity will be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type. This conjecture was proved for closed S in [WZ1,WZ2,FH,M6] and for open S in [M6]. In this paper, we prove the conjecture for all the other orbits when G_R is of non-Hermitian type.Comment: 6 pages. Simplified the proof of the main theore

LHC Tests of Light Neutralino Dark Matter without Light Sfermions

We address the question how light the lightest MSSM neutralino can be as dark matter candidate in a scenario where all supersymmetric scalar particles are heavy. The hypothesis that the neutralino accounts for the observed dark matter density sets strong requirements on the supersymmetric spectrum, thus providing an handle for collider tests. In particular for a lightest neutralino below 100 GeV the relic density constraint translates into an upper bound on the Higgsino mass parameter $\mu$ in case all supersymmetric scalar particles are heavy. One can define a simplified model that highlights only the necessary features of the spectrum and their observable consequences at the LHC. Reinterpreting recent searches at the LHC we derive limits on the mass of the lightest neutralino that, in many cases, prove to be more constraining than dark matter experiments themselves.Comment: 22 pages, 8 figure

Absorption-Fluctuation Theorem for Nuclear Reactions: Brink-Axel, Incomplete Fusion and All That

We discuss the connection between absorption, averages and fluctuations in nuclear reactions. The fluctuations in the entrance channel result in the compound nucleus, Hauser-Feshbach, cross section, the fluctuations in the intermediate channels, result in modifications of multistep reaction cross sections, while the fluctuations in the final channel result in hybrid cross sections that can be used to describe incomplete fusion reactions. We discuss the latter in details and comment on the validity of the assumptions used in the develpoment of the Surrogate method. We also discuss the theory of multistep reactions with regards to intermediate state fluctuations and the energy dependence and non-locality of the intermediate channels optical potentials.Comment: 9 pages. Contribution to the International Workshop on Compound-Nuclear Reactions and Related Topics (CNR*2007), October 22-26, 2007, Fish Camp, California. To be published in AIP Proceedings (Editor Jutta Escher

Experimental Realization of a Relativistic Harmonic Oscillator

We report the experimental study of a harmonic oscillator in the relativistic regime. The oscillator is composed of Bose-condensed lithium atoms in the third band of an optical lattice, which have an energy-momentum relation nearly identical to that of a massive relativistic particle, with an effective mass reduced below the bare value and a greatly reduced effective speed of light. Imaging the shape of oscillator trajectories at velocities up to 98% of the effective speed of light reveals a crossover from sinusoidal to nearly photon-like propagation. The existence of a maximum velocity causes the measured period of oscillations to increase with energy; our measurements reveal beyond-leading-order contributions to this relativistic anharmonicity. We observe an intrinsic relativistic dephasing of oscillator ensembles, and a monopole oscillation with exactly the opposite phase of that predicted for non-relativistic harmonic motion. All observed dynamics are in quantitative agreement with longstanding but hitherto-untested relativistic predictions.Comment: 10 pages; 4 figure

Entanglement Measures for Intermediate Separability of Quantum States

We present a family of entanglement measures R_m which act as indicators for separability of n-qubit quantum states into m subsystems for arbitrary 2 \leq m \leq n. The measure R_m vanishes if the state is separable into m subsystems, and for m = n it gives the Meyer-Wallach measure while for m = 2 it reduces, in effect, to the one introduced recently by Love et al. The measures R_m are evaluated explicitly for the GHZ state and the W state (and its modifications, the W_k states) to show that these globally entangled states exhibit rather distinct behaviors under the measures, indicating the utility of the measures R_m for characterizing globally entangled states as well.Comment: 8 pages, 8 figure

Observation and uses of position-space Bloch oscillations in an ultracold gas

We report the direct observation and characterization of position-space Bloch oscillations using an ultracold gas in a tilted optical lattice. While Bloch oscillations in momentum space are a common feature of optical lattice experiments, the real-space center-of-mass dynamics are typically too small to resolve. Tuning into the regime of rapid tunneling and weak force, we observe real-space Bloch oscillation amplitudes of hundreds of lattice sites, in both ground and excited bands. We demonstrate two unique capabilities enabled by tracking of Bloch dynamics in position space: measurement of the full position-momentum phase-space evolution during a Bloch cycle, and direct imaging of the lattice band structure. These techniques, along with the ability to exert long-distance coherent control of quantum gases without modulation, may open up new possibilities for quantum control and metrology.Comment: 5 pages, 6 figure