Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau string vacua, such theta series encode instanton corrections from $k$ Neveu-Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms. This effectively provides a quantum version of these transformations, where the quantization parameter is inversely proportional to the five-brane charge $k$. Consistency with wall-crossing implies a new five-term relation for Faddeev's quantum dilogarithm $\Phi_b$ at $b=1$, which we prove. By allowing the torus to be non-commutative, we obtain a more general five-term relation valid for arbitrary $b$ and $k$, which may be relevant for the physics of five-branes at finite chemical potential for angular momentum.

As the Higgs boson properties settle, the constraints on the Standard Model extensions tighten. We consider all possible new fermions that can couple to the Higgs, inspecting sets of up to four chiral multiplets. We confront them with direct collider searches, electroweak precision tests, and current knowledge of the Higgs couplings. The focus is on scenarios that may depart from the decoupling limit of very large masses and vanishing mixing, as they offer the best prospects for detection. We identify exotic chiral families that may receive a mass from the Higgs only, still in agreement with the $h\gamma\gamma$ signal strength. A mixing $\theta$ between the Standard Model and non-chiral fermions induces order $\theta^2$ deviations in the Higgs couplings. The mixing can be as large as $\theta\sim 0.5$ in case of custodial protection of the $Z$ couplings or accidental cancellation in the oblique parameters. We also notice some intriguing effects for much smaller values of $\theta$, especially in the lepton sector. Our survey includes a number of unconventional pairs of vector-like and Majorana fermions coupled through the Higgs, that may induce order one corrections to the Higgs radiative couplings. We single out the regions of parameters where $h\gamma\gamma$ and $hgg$ are unaffected, while the $h\gamma Z$ signal strength is significantly modified, turning a few times larger than in the Standard Model in two cases. The second run of the LHC will effectively test most of these scenarios.

Due to the existence of open channels, light could theoretically be transmitted through disorderedmedia with 100% efficiency. However, because of the large number of channels to be controlledor measured, this has been never observed experimentally. To avoid this difficulty we considerobservables easier to handle experimentally. By measuring the correlations of the field transmittedthrough a disordered medium, we were able to count the number of channels involved in transmissionand to compare this number with theory. For a sample of transmission 1=25, we get a number ofmodes about 15 times smaller than for free space propagation. This figure is in good agreementwith theoretical prediction.

We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The resulting convergence and scale dependence of optimized thermodynamical quantities, here illustrated up to two-loop order, are drastically improved as compared to standard perturbative expansions, as well as to other related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation, that miss RG invariance (as we explain). Being very general and easy to implement, our method is a potential analytical alternative to dealing with the phase transitions of field theories such as thermal QCD.

The dynamics of the free-exciton capture by boron acceptors and phosphorus donors in diamond is observed in the picosecond range by time-resolved photoluminescence experiments at low temperature. The formation of boron-bound excitons is observed with a delay of 410 ps after the formation of free excitons. For phosphorus, this delay is 120 ps. This is the result of the free-exciton capture by B0 and P0 impurities. The lifetimes of boron- and phosphorus-bound excitons are measured and found to be equal to 270 and 70 ps, respectively. These values are about four orders of magnitude shorter than for the same impurities in silicon. Ei being the ionization energy of dopants, these results scale well with the E4i dependence of the Auger recombination rate expected for bound excitons in indirect band-gap semiconductors.

Thermo-mechanically durable industrial polymer nanocomposites have great demand as structural components. In this work, highly competent filler design is processed via nano-modified of micronic SiO2/Al2O3 particulate ceramics and studied its influence on the rheology, glass transition temperature, composite microstructure, thermal conductivity, mechanical strength, micro hardness, and tribology properties. Composites were fabricated with different proportions of nano-modified micro-composite fillers in epoxy matrix at as much possible filler loadings. Results revealed that nano-modified SiO2/Al2O3 micro-composite fillers enhanced inter-particle network and offer benefits like homogeneous microstructures and increased thermal conductivity. Epoxy composites attained thermal conductivity of 0.8 W/mK at 46% filler loading. Mechanical strength and bulk hardness were reached to higher values on the incorporation of nano-modified fillers. Tribology study revealed an increased specific wear rate and decreased friction coefficient in such fillers. The study is significant in a way that the design of nano-modified mixed-matrix micro-composite fillers are effective where a high loading is much easier, which is critical for achieving desired thermal and mechanical properties for any engineering applications.