With the measurements made by the experiments at the Large Hadron Collider becoming increasingly precise, it is vital that theoretical predictions reach the same level of precision, including for high multiplicity processes. This necessitates calculations to at least next-to-next-to-leading order (NNLO) in perturbative QCD. One of the challenges in computing such corrections is the treatment of infrared singularities, which arise at intermediate stages of the calculation. Although such singularities must cancel for physical observables, making this cancellation manifest while maintaining fully differential results is challenging, especially at NNLO where singularities from different kinematic limits may overlap in a complicated way. I will discuss the development of the nested soft-collinear subtraction scheme to regulate IR singularities and arrive at a finite physical result at NNLO. I will begin by outlining the method for the production of a color-singlet, and then discuss recent efforts to generalize it to arbitrary hadroproduction processes.

Multivalency describes many types of interfacial interactions in Nature. For example, hemagglutinin coat proteins of the influenza virus bind non-covalently to multiple sialyl-terminated carbohydrates (SLNs) of a host cell. This interaction is weakly multivalent in nature, and therefore it responds very sensitively to the density of carbohydrates on the cell surface and to the individual affinity of the interacting molecular partners. This behavior explains the large differences between virus affinities observed for mutations in the receptor binding domain. A key aspect of the multivalent interaction of viruses at cell membranes is its strong, non-linear dependence on the receptor density displayed at the surface. We here show the development of surface gradients of receptor-modified supported lipid bilayers (SLBs) to visualize and quantify the receptor density dependence in one microscopic image. This technique is called “Multivalent Affinity Profiling”. The fitting of the data by a thermodynamic model allows quantification of the threshold density, comparison of binding selectivities for different virus strains, and thus offers a molecular and quantitative understanding of the supramolecular binding energy landscape. This supramolecular and nanoscopic picture links fundamental molecular aspects of binding to biological processes of antigenic drift and zoonosis. At a more general level, chemically modified interfaces can be used to study complex (bio)chemical recognition processes, such as the binding of viruses and DNA. Exquisite receptor or probe density control is achieved through surface receptor gradients and by poly-L-lysine chemistry with control over grafting density. Multivalent recognition events are probed and controlled at surfaces and in solution by molecular engineering of the interfaces of the involved building blocks. These concepts can, amongst others, be used to control the self-assembly of vesicles and other materials building blocks and to develop a method to isolate the cancer biomarker hyper-methylated DNA. (Co-hosted with SFB 1551 Seminar Series)
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Superradiance and subradiance are fundamental aspects of the open system dynamics of dense ensembles of quantum emitters exhibiting spontaneous emission rates well below or well above the rate for a single isolated system. At the purely theoretical level, superradiance has been first discussed by Dicke in 1954, in the context of accelerated decay of an ensemble of identical N initially inverted two-level quantum systems. In practice, such cooperative behavior associated with super- and subradiance at low excitation levels, has been observed in the 1930s by Jelley and Scheibe, in the context of molecular aggregates: unexpectedly large absorption cross-sections have been recorded for dye molecules. This has been later explained by Kasha in the 1960s as stemming from the alignment of the transition dipole moments of the many nanometer-spaced monomers forming the aggregate. We analytically tackle such issues with methods of open quantum system dynamics, in particular quantum Langevin equations and master equations. For the problem of Dicke superradiance we identify an exact analytical solution for the time evolution of the density operator, valid for any time t any number N of emitters. In the direction of quantum optics with molecules, we provide analytical models and solutions for the excitation migration between collective electronic levels in molecular aggregates and for processes involving non-radiative transitions due to non-adiabatic couplings of potential electronic landscapes in single large organic molecules. [1] R. Holzinger and C. Genes, Exact solution for Dicke superradiance, arXiv:2409.19040, (2024). [2] R. Holzinger, N. S. Bassler, H. Ritsch and C. Genes, Scaling law for Kasha's rule in photoexcited molecular aggregates, J. Phys. Chem. A 128, 19, 3910 (2024). [3] N. S. Bassler, M. Reitz, R. Holzinger, A. Vibók, G. J. Halász, B. Gurlek and C. Genes, Generalized energy gap law: An open system dynamics approach to non-adiabatic phenomena in molecules, arXiv:2405.08718 (2024).