Quantum stochastic calculus and quantum Gaussian processes

In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy [9]. We show how a part of this architecture yields Gaussian fields stationary under a group action. Then we introduce the notion of semigroups of quasifree completely positive maps on the algebra of all bounded operators in the boson Fock space Γ(? ⁿ ) over ? ⁿ . These semigroups are not strongly continuous but their preduals map Gaussian states to Gaussian states. They were first introduced and their generators were shown to be of the Lindblad type by Vanheuverzwijn [19]. They were recently investigated in the context of quantum information theory by Heinosaari et al. [7]. Here we present the exact noisy Schrödinger equation which dilates such a semigroup to a quantum Gaussian Markov process.     

Light-induced antibacterial activity of symmetrical and asymmetrical oligophenylene ethynylenes

The light-induced antibacterial activity of symmetric and asymmetric oligophenylene ethynylenes (OPEs) was investigated against Gram-positive (Staphylococcus aureus and Staphylococcus epidermidis) and Gram-negative (Escherichia coli) bacteria. To understand the light-induced biocidal effect better, the transient absorption and triplet lifetime of OPEs were studied in methanol and water. A higher triplet lifetime was observed for OPE samples in water than in methanol. The magnitudes of the changes in optical density (ΔOD) of the S-OPE-n(H) series of symmetric oligomers are much higher than that of the asymmetric OPE-n series in water and are generally correlated with the singlet oxygen yield. It was found that the antibacterial activity against both Gram-positive and Gram-negative bacteria is size-, concentration-, and time-dependent. The light-induced antibacterial activity may result from the coordinated interactions of membrane disruption and interfacial or intracellular singlet oxygen generation, and the dominant factor is most likely the latter. The results obtained in this study will aid in the design of more efficient biocides in the future.     

On a super-diffusive, nonlinear birth and death process

The explicit and fully analytic transient solution for the transition probability density associated with a nonlinear birth and death process on Z is constructed. The time-dependent variance is proportional to t+Bt² (with B being a constant), thus exhibiting a super-diffusive behavior. The space continuous limit of this process is a well-known diffusion process with nonlinear drift for which the transition probability density is also known explicitly in a very simple way.     

Leveraging Torsional and Steric Strains: A Pre-macrocyclization Strategy Enables Conformation-Specific Fullerene Binding in m-Cyclophanes

Though the chemistry of resorcinarenes is half a century old, the conformationally-locked resorcinarene crowns are generally constructed using hydrogen bonds or covalent tethers. Often, covalent tethering involves extra post-macrocyclization steps involving upper-rim functionalities. We have leveraged the torsional and steric strains through α-substituents of the lower-rim C-alkyl chains and accomplished conformationally-rigid fluorescent m-cyclophane deep-crowns in a predetermined way. The strategy offers a pre-macrocyclization route conserving upper-rim functionalities, an aspect overlooked in resorcinarene chemistry. X-ray structural and computational analyses unveil the cause for conformational rigidity in m-cyclophanes due to α-branching in C-alkyls (linear vs. α-/β-branched). The conformationally-locked fluorescent deep-crown with a preorganized cavity captures hydrophobic spherical guest C₆₀ in both solution and solid states specifically, when compared to conformationally-dynamic boats, enabling conformation-specific binding.