Canonical structure of A and B maps

In their seminal 1961 paper, Sudarshan, Mathews and Rau investigated properties of the dynamical A and B maps acting on n-dimensional quantum systems. The nature of dynamical maps in open quantum system evolutions has attracted great deal of attention in the later years. However, the novel paper on the A and B dynamical maps has not received its due attention. In this tutorial article, we review the properties of A and B forms associated with the dynamics of finite dimensional quantum systems. In particular, we investigate a canonical structure associated with the A form and establish its equivalence with the associated B form. We show that the canonical structure of the A form captures the completely positive (not completely positive) nature of the dynamics in a succinct manner. This feature is illustrated through physical examples of qubit channels.Quanta 2021; 10: 34–41.

Koopman wavefunctions and Clebsch variables in Vlasov–Maxwell kinetic theory

Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.

BRST analysis and BFV quantization of the generalized quantum rigid rotor

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We perform the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the [Formula: see text] nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

Heterogeneous non-canonical nucleosomes predominate in yeast cells in situ

Nuclear processes depend heavily on the organization of chromatin, whose subunits are cylinder-shaped complexes called nucleosomes. A subset of mammalian nucleosomes in situ resemble the canonical structure determined in vitro 24 years ago. The structure of nucleosomes in situ is otherwise poorly understood. Here we use cryo-ET and 3-D classification analysis to study the structure of yeast nucleosomes both in vitro and in situ. We show that the class averages of GFP-tagged yeast nucleosomes in vitro resemble canonical nucleosomes, with additional GFP densities. In contrast, none of the class averages of nucleosome-like particles in situ (inside cells) resemble canonical nucleosomes. The heterogeneous nature of the in situ class averages suggests that the intranuclear environment favors multiple conformations. Using the structural observations here and the results of previous genomics and biochemical studies, we propose a model in which the average yeast nucleosome’s DNA is partially detached in situ.

9-[(Z)-2-(4,4,5,5-Tetramethyl-1,3,2-dioxaborolan-2-yl)ethenyl]-9H-carbazole

The title compound, C20H22BNO2, has a polarized π-system due to resonance between N—C(H)=C(H)—B and ionic N+=C(H)—C(H)=B− canonical structures. The dihedral angles between the ethenyl plane (r.m.s. deviation for C2H2 = 0.0333 Å) with the ethenyl-C(NC2-pyrrole) plane (r.m.s. deviation CNC2 0.0423 Å) and the ethenyl-C(BO2-1,3,2-dioxaborolane) plane (r.m.s. deviation BCO2 0.0082 Å) are 45.86 (8) and 37.47 (8)°, respectively, and are greater than those found for the previously reported E-isomer [Hatayama & Okuno (2012) Acta Cryst. E68, o84]. In comparison with the E-isomer, the reduced planarity of Z-isomer results in a decrease of the contribution of the N+=C(H)—C(H)=B− canonical structure.