Quantum Quenches with Random Matrix Hamiltonians and Disordered Potentials

We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching‐on the off‐diagonal elements of the Hamiltonian. In the latter case, it is sudden switching‐on of the hopping between adjacent lattice sites. The quench‐induced ensembles are compared with the so‐called “quantum micro‐canonical” (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.     

Fractional Gaussian estimates and holomorphy of semigroups

Let $$\Omega \subset {\mathbb {R}}^N$$ be an arbitrary open set, $$0<s<1$$ and denote by $$(e^{-t(-\Delta )_{{{\mathbb {R}}}^N}^s})_{t\ge 0}$$ the semigroup on $$L^2({{\mathbb {R}}}^N)$$ generated by the fractional Laplace operator. In the first part of the paper, we show that if T is a self-adjoint semigroup on $$L^2(\Omega )$$ satisfying a fractional Gaussian estimate in the sense that $$|T(t)f|\le Me^{-bt(-\Delta )_{{{\mathbb {R}}}^N}^s}|f|$$, $$0\le t \le 1$$, $$f\in L^2(\Omega )$$, for some constants $$M\ge 1$$ and $$b\ge 0$$, then T defines a bounded holomorphic semigroup of angle $$\frac{\pi }{2}$$ that interpolates on $$L^p(\Omega )$$, $$1\le p<\infty $$. Using a duality argument, we prove that the same result also holds on the space of continuous functions. In the second part, we apply the above results to the realization of fractional order operators with the exterior Dirichlet conditions.     

Preparation of Conductive Gold Nanowires in Confined Environment of Gold‐Filled Polymer Nanotubes

Continuous conductive gold nanofibers are prepared via the “tubes by fiber templates” process. First, poly(l‐lactide) (PLLA)‐stabilized gold nanoparticles (AuNP) with over 60 wt% gold are synthesized and characterized, including gel permeation chromatography coupled with a diode array detector. Subsequent electrospinning of these AuNP with template PLLA results in composite nanofibers featuring a high gold content of 57 wt%. Highly homogeneous gold nanowires are obtained after chemical vapor deposition of 345 nm of poly(p‐xylylene) (PPX) onto the composite fibers followed by pyrolysis of the polymers at 1050 °C. The corresponding heat‐induced transition from continuous gold‐loaded polymer tubes to smooth gold nanofibers is studied by transmission electron microscopy and helium ion microscopy using both secondary electrons and Rutherford backscattered ions.

     

Impact of Membrane Types and Catalyst Layers Composition on Performance of Polymer Electrolyte Membrane Fuel Cells

Performance of a low temperature polymer electrolyte membrane fuel cell (PEMFC) is highly dependent on the kind of catalysts, catalyst supports, ionomer amount on the catalyst layers (CL), membrane types and operating conditions. In this work, we investigated the influence of membrane types and CL compositions on MEA performance. MEA performance increases under all practically relevant load conditions with reduction of the membrane thickness from 50 to 15 μm, however further decrease in membrane thickness from 15 to 10 μm leads to reduction in cell voltage at high current loads. A thick anode CL is found to be beneficial under wet operating conditions assuming more pore space is provided to accommodate liquid water, whereas under dry operating conditions, an intermediate thickness of the anode CL is beneficial. When studying the impact of catalyst layer thickness, too thin a catalyst layer again shows reduced performance due to increased ohmic resistance ruled out the performance of the MEAs which have identical Pt crystallite sizes on the cathode CLs i. e. the thinnest the cathode CL, the highest the voltage were achieved at a defined current load. Adaptation of the operating conditions is highly anticipated to achieve the highest MEA performance.     

Electrocatalytic CO2 Reduction on CuOx Nanocubes: Tracking the Evolution of Chemical State,Geometric Structure,and Catalytic Selectivity using Operando Spectroscopy

The direct electrochemical conversion of carbon dioxide (CO₂) into multi‐carbon (C₂₊) products still faces fundamental and technological challenges. While facet‐controlled and oxide‐derived Cu materials have been touted as promising catalysts, their stability has remained problematic and poorly understood. Herein we uncover changes in the chemical and morphological state of supported and unsupported Cu₂O nanocubes during operation in low‐current H‐Cells and in high‐current gas diffusion electrodes (GDEs) using neutral pH buffer conditions. While unsupported nanocubes achieved a sustained C₂₊ Faradaic efficiency of around 60 % for 40 h, the dispersion on a carbon support sharply shifted the selectivity pattern towards C₁ products. Operando XAS and time‐resolved electron microscopy revealed the degradation of the cubic shape and, in the presence of a carbon support, the formation of small Cu‐seeds during the surprisingly slow reduction of bulk Cu₂O. The initially (100)‐rich facet structure has presumably no controlling role on the catalytic selectivity, whereas the oxide‐derived generation of under‐coordinated lattice defects, can support the high C₂₊ product yields.     

Triplet Energy Transfer from Ruthenium Complexes to Chiral Eniminium Ions: Enantioselective Synthesis of Cyclobutanecarbaldehydes by [2+2] Photocycloaddition

Chiral eniminium salts, prepared from α,β‐unsaturated aldehydes and a chiral proline derived secondary amine, underwent, upon irradiation with visible light, a ruthenium‐catalyzed (2.5 mol %) intermolecular [2+2] photocycloaddition to olefins, which after hydrolysis led to chiral cyclobutanecarbaldehydes (17 examples, 49–74 % yield), with high diastereo‐ and enantioselectivities. Ru(bpz)₃(PF₆)₂ was utilized as the ruthenium catalyst and laser flash photolysis studies show that the catalyst operates exclusively by triplet‐energy transfer (sensitization). A catalytic system was devised with a chiral secondary amine co‐catalyst. In the catalytic reactions, Ru(bpy)₃(PF₆)₂ was employed, and laser flash photolysis experiments suggest it undergoes both electron and energy transfer. However, experimental evidence supports the hypothesis that energy transfer is the only productive quenching mechanism. Control experiments using Ir(ppy)₃ showed no catalysis for the intermolecular [2+2] photocycloaddition of an eniminium ion.     

Amphiphilic Polymeric Nanoparticles for Photoredox Catalysis in Water

Photoredox catalysis has recently emerged as a powerful synthesis tool in organic and polymer chemistry. In contrast to the great achievements realized in organic solvents, performing photocatalytic processes efficiently in aqueous media encounters several challenges. Here, it is presented how amphiphilic single-chain polymeric nanoparticles (SCPNs) can be utilized as small reactors to conduct light-driven chemical reactions in water. By incorporating a phenothiazine (PTH) catalyst into the polymeric scaffold, metal-free reduction and C−C cross-coupling reactions can be carried out upon exposure to UV light under ambient conditions. The versatility of this approach is underlined by a large substrate scope, tolerance towards oxygen, and excellent recyclability. This approach thereby contributes to a sustainable and green way of implementing photoredox catalysis.