Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Modeling of Ultra Low Capacitance Transient Voltage Suppression Diode for High ESD Protection

To improve key properties such as ultra-low capacitance (ULC) and high-voltage (HV) breakdown, we have performed a simulation work about transient voltage suppression (TVS) diodes. ULC-TVS diode was designed to employ a double deep trench to cut off the various parasitic effects that may degrade the device performance. The electrostatic discharge (ESD) protection is the targeting for the best applications in high-frequency and high-speed ICs. In this work, the device could present excellent performance in terms of very responsive ESD properties, high breakdown voltage, low leakage current, and very low capacitance level. The double trenches are aligned to the top electrode contact to restrict field crowding effects by the strong electric field intensity. The performance would be sufficient for the robust ESD nature up to IEC61000-4-2 (30 kV) and compatible with strong surge protection IEC61000-4-5 (10A). Their electrical properties have been evaluated for structure from simulation and the results are obtained at the device parameters. Several process of device design related effects on the electrical capability and can be optimized. Keywords: ULC-TVS diode, simulation (TCAD), characteristics, capacitance, ESD protection

Topological quantization and degeneracy in Josephson-junction arrays

We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate values for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed.Comment: To appear in Phys. Rev.

A T-odd asymmetry in neutralino production and decay

We study CP-violating effects in neutralino production and subsequent decay within the Minimal Supersymmetric Standard Model with complex parameters M_1 and mu. The observable we propose is a T-odd asymmetry based on a triple product in neutralino production e^+ e^- -> tilde{chi}^0_i tilde{chi}^0_2, i = 1,...,4, with subsequent leptonic three-body decay tilde{chi}^0_2 -> tilde{chi}^0_1 l^+ l^-, l = e, mu, at an e^+ e^- linear collider with sqrt{s} = 500 GeV and polarised beams. We provide compact analytical formulae for the cross section and the T-odd asymmetry taking into account the complete spin correlations between production and decay. We give numerical predictions for the cross section and the T-odd asymmetry. The asymmetry can go up to 10 %.Comment: 28 pages, LaTeX, 10 figures; v2: typos corrected, published versio

The π\pi, K+K^+, and K0K^0 electromagnetic form factors

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte

Could Large CP Violation Be Detected at Colliders?

We argue that CP--violation effects below a few tenths of a percent are probably undetectable at hadron and electron colliders. Thus only operators whose contributions interfere with tree--level Standard Model amplitudes are detectable. We list these operators for Standard Model external particles and some two and three body final state reactions that could show detectable effects. These could test electroweak baryogenesis scenarios.Comment: 11pp, LaTeX, UM--TH--92--27(massaged to make TeX output cleaner), no picture

Implications of Compressed Supersymmetry for Collider and Dark Matter Searches

Martin has proposed a scenario dubbed ``compressed supersymmetry'' (SUSY) where the MSSM is the effective field theory between energy scales M_{\rm weak} and M_{\rm GUT}, but with the GUT scale SU(3) gaugino mass M_3<< M_1 or M_2. As a result, squark and gluino masses are suppressed relative to slepton, chargino and neutralino masses, leading to a compressed sparticle mass spectrum, and where the dark matter relic density in the early universe may be dominantly governed by neutralino annihilation into ttbar pairs via exchange of a light top squark. We explore the dark matter and collider signals expected from compressed SUSY for two distinct model lines with differing assumptions about GUT scale gaugino mass parameters. For dark matter signals, the compressed squark spectrum leads to an enhancement in direct detection rates compared to models with unified gaugino masses. Meanwhile, neutralino halo annihilation rates to gamma rays and anti-matter are also enhanced relative to related scenarios with unified gaugino masses but, depending on the halo dark matter distribution, may yet be below the sensitivity of indirect searches underway. In the case of collider signals, we compare the rates for the potentially dominant decay modes of the stop_1 which may be expected to be produced in cascade decay chains at the LHC: \tst_1\to c\tz_1 and \tst_1\to bW\tz_1. We examine the extent to which multilepton signal rates are reduced when the two-body decay mode dominates. For the model lines that we examine here, the multi-lepton signals, though reduced, still remain observable at the LHC.Comment: 22 pages including 24 eps figure

Collider and Dark Matter Phenomenology of Models with Mirage Unification

We examine supersymmetric models with mixed modulus-anomaly mediated SUSY breaking (MM-AMSB) soft terms which get comparable contributions to SUSY breaking from moduli-mediation and anomaly-mediation. The apparent (mirage) unification of soft SUSY breaking terms at Q=mu_mir not associated with any physical threshold is the hallmark of this scenario. The MM-AMSB structure of soft terms arises in models of string compactification with fluxes, where the addition of an anti-brane leads to an uplifting potential and a de Sitter universe, as first constructed by Kachru {\it et al.}. The phenomenology mainly depends on the relative strength of moduli- and anomaly-mediated SUSY breaking contributions, and on the Higgs and matter field modular weights, which are determined by the location of these fields in the extra dimensions. We delineate the allowed parameter space for a low and high value of tan(beta), for a wide range of modular weight choices. We calculate the neutralino relic density and display the WMAP-allowed regions. We show the reach of the CERN LHC and of the International Linear Collider. We discuss aspects of MM-AMSB models for Tevatron, LHC and ILC searches, muon g-2 and b->s \gamma branching fraction. We also calculate direct and indirect dark matter detection rates, and show that almost all WMAP-allowed models should be accessible to a ton-scale noble gas detector. Finally, we comment on the potential of colliders to measure the mirage unification scale and modular weights in the difficult case where mu_mir>>M_GUT.Comment: 34 pages plus 42 EPS figures; version with high resolution figures is at http://www.hep.fsu.edu/~bae