Azimuthal angle for boson-jet production in the back-to-back limit

We show for the first time that the azimuthal angle between a vector boson and a jet, when using the Winner-Take-All recombination scheme, can be predicted at high precision in the back-to-back limit in the transverse plane. Specifically, we present a factorization theorem, and obtain numerical predictions at next-to-next-to-leading logarithmic (NNLL) accuracy. To allow for improved angular resolution, we provide results for track-based jet reconstruction, which only requires minimal changes in the calculation. We also find that linearly-polarized transverse momentum dependent (TMD) beam and jet functions enter at next-to-leading order (NLO) in the factorization theorem, originating from spin superpositions for one gluon, rather than the known case of spin correlations between gluons. We validate the switch from calorimetry to tracks using Pythia, and confirm the presence of linearly-polarized TMD functions using MCFM.Comment: 6 pages, 4 figure

Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure

Separation of endo-polygalacturonase using aqueous two-phase partitioning

The partitioning of endo-polygalacturonase (endo-PG) in polyethylene glycol (PEG)–polyvinyl alcohol (PVA10 000) and PEG–hydroxypropyl starch (Reppal PES100) aqueous two-phase systems was studied, and revealed the possibility of using aqueous two-phase extraction to purify and concentrate endo-PG from its clarified fermentation broth. For the PEG8000– PVA10 000 system, endo-PG presented in the fermentation broth (at concentration that is more than 40% of total protein) mainly dominates in the top phase with a partitioning coefficient of 6, while total protein concentrates in the bottom phase. A separation scheme consisting of two consecutive aqueous two-phase extraction steps was proposed: a first extraction in polyethylene glycol (PEG8000)–polyvinyl alcohol system, followed by a second extraction in PEG8000–(NH4)2SO4 system. This allowed the separation of endo-PG from polymer and the recycling of PEG polymer, since endo-PG was very strongly partitioned into the bottom phase of the PEG8000–(NH4)2SO4 system. Laboratory-scale experiments were performed to test the efficiency of this scheme. It was found that enzyme recovery was up to 91% with a total purification factor of about 1.9 and a concentration factor of more than 5. About 90% of the total PEG added into the systems can be recovered, and no reduction was obtained in the purification factor using recycled PEG.Fundação para a Ciência e a Tecnologia (FCT) – PRAXIS XXI.CEC (INCO-DC) - contract number ERB IC18 CT97 0182

Aqueous two-phase extraction using thermoseparating polymer : a new system for the separation of endo-polygalacturonase

Aqueous two-phase partitioning of endo-polygalacturonase (endo-PG) produced by Kluyveromyces marxianus strains was studied, on systems containing the thermoseparating polymer Ucon 50-HB-5100 (a random copolymer of 50% ethylene oxide (EO) and 50% propylene oxide (PO)) as one of the phase-forming compounds. Ucon 50-HB-5100 (Ucon)–polyvinyl alcohol (PVA 10,000), Ucon 50-HB-5100–hydroxypropyl starch (Reppal PES100) and Ucon 50-HB-5100–(NH4)2SO4 systems were tested. Ucon recycling was also investigated. Ucon–(NH4)2SO4 system proved to be the most efficient system for aqueous two-phase extraction (ATPE) of endo-PG as when compared to total protein partition, the enzyme was strongly partitioned to the salt-rich phase. Using Ucon–(NH4)2SO4 system, a separation scheme consisting of three stages was proposed and tested at laboratory scale. In the first and second stages, operated in series, extractions were performed using the same Ucon–(NH4)2SO4 system. Ucon recycling was done in each stage. In the third stage, removal of the Ucon and salt residues present in the enzyme-rich phase of the second extraction stage was done. The proposed scheme allowed for a 10-fold enzyme concentration and a purification factor close to the expected maximum while maintaining more than 95% of the initial enzyme activity.Fundação para a Ciência e a Tecnologia (FCT) – PRAXIS XXI.INCO DC - ERB IC18 CT97 0182

Dynamical invariants in non-Markovian quantum state diffusion equation

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.Comment: 6 pages, 2 figure