Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Probing the charged Higgs boson at the LHC in the CP-violating type-II 2HDM

We present a phenomenological study of a CP-violating two-Higgs-doublet Model with type-II Yukawa couplings at the Large Hadron Collider (LHC). In the light of recent LHC data, we focus on the parameter space that survives the current and past experimental constraints as well as theoretical bounds on the model. Once the phenomenological scenario is set, we analyse the scope of the LHC in exploring this model through the discovery of a charged Higgs boson produced in association with a W boson, with the former decaying into the lightest neutral Higgs and a second W state, altogether yielding a b\bar b W^+W^- signature, of which we exploit the W^+W^- semileptonic decays.Comment: 37 pages, 16 figures; v2 updated treatment of LHC constraint

The Cognitive Impact of the ANK3 Risk Variant for Bipolar Disorder: Initial Evidence of Selectivity to Signal Detection during Sustained Attention

BACKGROUND: Abnormalities in cognition have been reported in patients with Bipolar Disorder (BD) and their first degree relatives, suggesting that susceptibility genes for BD may impact on cognitive processes. Recent genome-wide genetic studies have reported a strong association with BD in a single nucleotide polymorphism (SNP) (rs10994336) within ANK3, which codes for Ankyrin 3. This protein is involved in facilitating the propagation of action potentials by regulating the assembly of sodium gated ion channels. Since ANK3 influences the efficiency of transmission of neuronal impulses, allelic variation in this gene may have widespread cognitive effects. Preclinical data suggest that this may principally apply to sequential signal detection, a core process of sustained attention. METHODOLOGY/PRINCIPAL FINDINGS: One hundred and eighty-nine individuals of white British descent were genotyped for the ANK3 rs10994336 polymorphism and received diagnostic interviews and comprehensive neurocognitive assessment of their general intellectual ability, memory, decision making, response inhibition and sustained attention. Participants comprised euthymic BD patients (n = 47), their unaffected first-degree relatives (n = 75) and healthy controls (n = 67). The risk allele T was associated with reduced sensitivity in target detection (p = 0.0004) and increased errors of commission (p = 0.0018) during sustained attention regardless of diagnosis. We found no effect of the ANK3 genotype on general intellectual ability, memory, decision making and response inhibition. CONCLUSIONS/SIGNIFICANCE: Our results suggest that allelic variation in ANK3 impacts cognitive processes associated with signal detection and this mechanism may relate to risk for BD. However, our results require independent replication and confirmation that ANK3 (rs10994336) is a direct functional variant

Prospects for charged Higgs searches at the LHC

The goal of this report is to summarize the current situation and discuss possible search strategies for charged scalars, in non-supersymmetric extensions of the Standard Model at the LHC. Such scalars appear in Multi-HiggsDoublet models, in particular in the popular Two-HiggsDoublet model, allowing for charged and additional neutral Higgs bosons. These models have the attractive property that electroweak precision observables are automatically in agreement with the Standard Model at the tree level. For the most popular version of this framework, Model II, a discovery of a charged Higgs boson remains challenging, since the parameter space is becoming very constrained, and the QCD background is very high. We also briefly comment on models with dark matter which constrain the corresponding charged scalars that occur in these models. The stakes of a possible discovery of an extended scalar sector are very high, and these searches should be pursued in all conceivable channels, at the LHC and at future colliders.Peer reviewe