Search for: All records

In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of quantum state types. These are certain lax-monoidal functors from the category of finite-dimensional Hilbert spaces to the category of topological spaces. The universal example takes a finite-dimensional Hilbert space [Formula: see text] to the pure state space of the quasi-local algebra of the quantum spin system with Hilbert space [Formula: see text] at each site of a specified lattice. The lax-monoidal structure encodes the tensor product of states, which corresponds to stacking for quantum systems. We then explain how to formally extract parametrized phases of matter from quantum state types, and how they naturally give rise to [Formula: see text]-spaces for an operad we call the “multiplicative” linear isometry operad. We define the notion of invertible quantum state types and explain how the passage to phases for these is related to group completion. We also explain how invertible quantum state types give rise to loop-spectra. Our motivation is to provide a framework for constructing Kitaev’s loop-spectrum of bosonic invertible gapped phases of matter. Finally, as a first step toward understanding the homotopy types of the loop-spectra associated to invertible quantum state types, we prove that the pure state space of any UHF algebra is simply connected. 

This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian, one considers a family of Hamiltonians that depend continuously on some parameters. After discussing the notion of phases of parametrized systems, we formulate a bulk-boundary correspondence for an important bulk quantity, the Kapustin-Spodyneiko higher Berry curvature, first in one spatial dimension and then in arbitrary dimension. This clarifies the physical interpretation of the higher Berry curvature, which in one spatial dimension is a flow of (ordinary) Berry curvature. In 𝑑 dimensions, the higher Berry curvature is a flow of (𝑑−1)-dimensional higher Berry curvature. Based on this, we discuss one-dimensional systems that pump Chern number to/from spatial boundaries, resulting in anomalous boundary modes featuring isolated Weyl points. In higher dimensions, there are pumps of the analogous quantized invariants obtained by integrating the higher Berry curvature. We also discuss the consequences for parametrized systems of Kitaev's proposal that invertible phases are classified by a generalized cohomology theory, and emphasize the role of the suspension isomorphism in generating new examples of parametrized systems from known invertible phases. Finally, we present a pair of general quantum pumping constructions, based on physical pictures introduced by Kitaev, which take as input a 𝑑-dimensional parametrized system, and produce new (𝑑+1)-dimensional parametrized systems. These constructions are useful for generating examples, and we conjecture that one of the constructions realizes the suspension isomorphism in a generalized cohomology theory of invertible phases. 

In the face of rising atmospheric carbon dioxide (CO 2 ) emissions from fossil fuel combustion, the hydrogen evolution reaction (HER) continues to attract attention as a method for generating a carbon-neutral energy source for use in fuel cells. Since some of the best-known catalysts use precious metals like platinum, which have low natural abundance and high cost, developing efficient Earth abundant transition metal catalysts for HER is an important objective. Building off previous work with transition metal catalysts bearing 2,2′-bipyridine-based ligand frameworks, this work reports the electrochemical analysis of a molecular nickel( ii ) complex, which can act as an electrocatalyst for the HER with a faradaic efficiency for H 2 of 94 ± 8% and turnover frequencies of 103 ± 6 s −1 when pentafluorophenol is used as a proton donor. Computational studies of the Ni catalyst suggest that non-covalent interactions between the proton donor and ligand heteroatoms are relevant to the mechanism for electrocatalytic HER. 

We consider how the outputs of the Kadison transitivity theorem and Gelfand–Naimark–Segal (GNS) construction may be obtained in families when the initial data are varied. More precisely, for the Kadison transitivity theorem, we prove that for any nonzero irreducible representation [Formula: see text] of a [Formula: see text]-algebra [Formula: see text] and [Formula: see text], there exists a continuous function [Formula: see text] such that [Formula: see text] for all [Formula: see text], where [Formula: see text] is the set of pairs of [Formula: see text]-tuples [Formula: see text] such that the components of [Formula: see text] are linearly independent. Versions of this result where [Formula: see text] maps into the self-adjoint or unitary elements of [Formula: see text] are also presented. Regarding the GNS construction, we prove that given a topological [Formula: see text]-algebra fiber bundle [Formula: see text], one may construct a topological fiber bundle [Formula: see text] whose fiber over [Formula: see text] is the space of pure states of [Formula: see text] (with the norm topology), as well as bundles [Formula: see text] and [Formula: see text] whose fibers [Formula: see text] and [Formula: see text] over [Formula: see text] are the GNS Hilbert space and closed left ideal, respectively, corresponding to [Formula: see text]. When [Formula: see text] is a smooth fiber bundle, we show that [Formula: see text] and [Formula: see text] are also smooth fiber bundles; this involves proving that the group of ∗-automorphisms of a [Formula: see text]-algebra is a Banach Lie group. In service of these results, we review the topology and geometry of the pure state space. A simple non-interacting quantum spin system is provided as an example illustrating the physical meaning of some of these results. 

Electrocatalytic CO 2 reduction is an attractive strategy to mitigate the continuous rise in atmospheric CO 2 concentrations and generate value-added chemical products. A possible strategy to increase the activity of molecular systems for these reactions is the co-catalytic use of redox mediators (RMs), which direct reducing equivalents from the electrode surface to the active site. Recently, we demonstrated that a sulfone-based RM could trigger co-electrocatalytic CO 2 reduction via an inner-sphere mechanism under aprotic conditions. Here, we provide support for inner-sphere cooperativity under protic conditions by synthetically modulating the mediator to increase activity at lower overpotentials (inverse potential scaling). Furthermore, we show that both the intrinsic and co-catalytic performance of the Cr-centered catalyst can be enhanced by ligand design. By tuning both the Cr-centered catalyst and RM appropriately, an optimized co-electrocatalytic system with quantitative selectivity for CO at an overpotential ( η ) of 280 mV and turnover frequency (TOF) of 194 s −1 is obtained, representing a three-fold increase in co-catalytic activity at 130 mV lower overpotential than our original report. Importantly, this work lays the foundation of a powerful tool for developing co-catalytic systems for homogeneous electrochemical reactions. 

Pentacoordinate Al catalysts comprising bipyridine (bpy) and phenanthroline (phen) backbones were synthesized and their catalytic activity in epoxide/anhydride copolymerization was investigated and compared to ( t-Bu salph)AlCl. Stoichiometric reactions of tricyclic anhydrides with Al alkoxide complexes produced ring-opened products that were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography, revealing key regio- and stereochemical aspects. 

Personalization of gait neuroprosthetics is paramount to ensure their efficacy for users, who experience severe limitations in mobility without an assistive device. Our goal is to develop assistive devices that collaborate with and are tailored to their users, while allowing them to use as much of their existing capabilities as possible. Currently, personalization of devices is challenging, and technological advances are required to achieve this goal. Therefore, this paper presents an overview of challenges and research directions regarding an interface with the peripheral nervous system, an interface with the central nervous system, and the requirements of interface computing architectures. The interface should be modular and adaptable, such that it can provide assistance where it is needed. Novel data processing technology should be developed to allow for real-time processing while accounting for signal variations in the human. Personalized biomechanical models and simulation techniques should be developed to predict assisted walking motions and interactions between the user and the device. Furthermore, the advantages of interfacing with both the brain and the spinal cord or the periphery should be further explored. Technological advances of interface computing architecture should focus on learning on the chip to achieve further personalization. Furthermore, energy consumption should be low to allow for longer use of the neuroprosthesis. In-memory processing combined with resistive random access memory is a promising technology for both. This paper discusses the aforementioned aspects to highlight new directions for future research in gait neuroprosthetics. 

SUMMARY Identification of protein interactors is ideally suited for the functional characterization of small molecules. 3′,5′‐cAMP is an evolutionary ancient signaling metabolite largely uncharacterized in plants. To tap into the physiological roles of 3′,5′‐cAMP, we used a chemo‐proteomics approach, thermal proteome profiling (TPP), for the unbiased identification of 3′,5′‐cAMP protein targets. TPP measures shifts in the protein thermal stability upon ligand binding. Comprehensive proteomics analysis yielded a list of 51 proteins significantly altered in their thermal stability upon incubation with 3′,5′‐cAMP. The list contained metabolic enzymes, ribosomal subunits, translation initiation factors, and proteins associated with the regulation of plant growth such as CELL DIVISION CYCLE 48. To functionally validate obtained results, we focused on the role of 3′,5′‐cAMP in regulating the actin cytoskeleton suggested by the presence of actin among the 51 identified proteins. 3′,5′‐cAMP supplementation affected actin organization by inducing actin‐bundling. Consistent with these results, the increase in 3′,5′‐cAMP levels, obtained either by feeding or by chemical modulation of 3′,5′‐cAMP metabolism, was sufficient to partially rescue the short hypocotyl phenotype of theactin2 actin7mutant, severely compromised in actin level. The observed rescue was specific to 3′,5′‐cAMP, as demonstrated using a positional isomer 2′,3′‐cAMP, and true for the nanomolar 3′,5′‐cAMP concentrations reported for plant cells.In vitrocharacterization of the 3′,5′‐cAMP–actin pairing argues against a direct interaction between actin and 3′,5′‐cAMP. Alternative mechanisms by which 3′,5′‐cAMP would affect actin dynamics, such as by interfering with calcium signaling, are discussed. In summary, our work provides a specific resource, 3′,5′‐cAMP interactome, as well as functional insight into 3′,5′‐cAMP‐mediated regulation in plants.