Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

Self-Healable Polyelectrolytes with Mechanical Enhancement for Flexible and Durable Supercapacitors

The practical application of advanced personalized electronics is inseparable from flexible, durable, and even self-healable energy storage devices. However, the mechanical and self-healing performance of supercapacitors is still limited at present. Herein, highly transparent, stretchable, and self-healable poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPSA)/poly(vinyl alcohol) (PVA)/LiCl polyelectrolytes were facilely prepared by one-step radical polymerization. The cooperation of PAMPSA and PVA significantly increased the mechanical and self-healing capacity of the polyelectrolyte, which exhibited superior stretchability of 938 %, stress of 112.68 kPa, good electrical performance (ionic conductivity up to 20.6 mS cm⁻¹), and high healing efficiency of 92.68 % after 24 h. After assembly with polypyrrole-coated single-walled carbon nanotubes, the resulting as-prepared supercapacitor had excellent electrochemical properties with high areal capacitance of 297 mF cm⁻² at 0.5 mA cm⁻² and good rate capability (218 mF cm⁻² at 5 mA cm⁻²). Besides, after cutting in two the supercapacitor recovered 99.2 % of its original specific capacitance after healing for 24 h at room temperature. The results also showed negligible change in the interior contact resistance of the supercapacitor after ten cutting/healing cycles. The present work provides a possible solution for the development of smart and durable energy storage devices with low cost for next-generation intelligent electronics.     

Exploring the electro‐optical properties of conjugated polymers based on oligo‐selenophene and oligo(3,4‐ethylenedioxyselenophene)

For seeking high‐efficiency narrow‐band‐gap donor materials to enhance short‐circuit current density for organic solar cells, a series of oligo‐selenophene (OS) and oligo(3,4‐ethylenedioxyselenophene) (OEDOS) with various chain lengths were designed and characterized using density functional theory (DFT) and time‐dependent DFT calculations. Based on the results, it can be seen that with increasing chain length of the oligomers in both syn‐ and anti‐adding manners, the bond length alternation is decreased which indicates that the π‐electron delocalization is increased. Also, when the chain length is increased the electronic energy gap and the optical energy gap are decreased. It can be concluded that the syn‐(OS)_n=10,14,15, anti‐(OS)_n=14 and anti‐(OEDOS)_n=7–12 oligomers can act as low‐band‐gap polymers. Therefore they can absorb more sunlight based on maximum wavelength (higher than 620 nm). Furthermore, a red shift in the simulated absorption spectra of (OS)_n and (OEDOS)_n donors is observed. It is found that (OS)_n=14,15 with syn configuration of the extended oligomers is the most suitable donor for the design of high‐performance organic solar cells possessing a narrow electronic band gap, high exciton lifetime and broad and intense absorption spectra that cover the solar spectrum leading to complete light‐harvesting efficiency.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Enhanced thermal conductivity and mechanical properties of polymeric composites through formation of covalent bonds between boron nitride and rubber chains

Hexagonal boron nitride (BN) platelets, also known as white graphite, are often used to improve the thermal conductivities of polymeric matrices. Due to the poor interfacial compatibility between BN platelets and polymeric matrices, in this study, polyrhodanine (PRd) was used to modify BN platelets and prepared functionalized BN-PRd platelets, thereby enhancing the interfacial interaction between the thermal conductive filler and polymeric matrix. Then, BN-PRd platelets were dispersed into the nitrile butadiene rubber (NBR) matrix to yield high thermally conductive composites. The presence of N? C═S groups in PRd allowed the combination of PRd and NBR chains containing stable covalent bonds via vulcanization reaction. The thermal conductivity of the as-prepared 30 vol% BN-PRd/NBR composite reached 0.40 W/mK, representing an increment of 135% over pure NBR (0.17 W/mK). In addition, the largest tensile strength of NBR composite containing 30 vol% BN-PRd platelets was 880% times of pure NBR. The 30 vol% BN-PRd/NBR composite also displayed a relatively high dielectric constant (9.35 at 100 Hz) and a low dielectric loss tangent value (0.07 at 100 Hz), indicating their usefulness as dielectric flexible materials of microelectronics. In sum, the simplicity and good efficiency of formation of covalent bonds between boron nitride and rubber chains look very promising for large-scale industrial production of high thermally conductive composites.     

Design of Functional Carbon Composite Materials for Energy Conversion and Storage

The carbon composite materials have been a research hotspot in the fields of catalysis, energy conversion and so on, because of their features of large structure and morphology variety, good chemical and electrochemical stability, and high electronic conductivity, large specific surface area and rich active sites. This paper summarizes some research progress of carbon composite materials, including assembly methodologies, their structure regulation, properties, and related applications. Moreover, the current challenges and the prospects of these materials are also discussed.     

The self-assemblies of a newly designed star-shaped molecule end-capped with bromine atoms studied by scanning tunneling microscopy

A new star-shaped molecule StOF-Br_3 containing oligofluorenes and halogen atoms(Bromine) has been synthesized and studied by Scanning Tunneling Microscopy(STM) at the highly oriented pyrolytic graphite(HOPG) surface.We have obtained the high-resolution self-assembled STM images,from which the highly ordered and closely packed non-porous arrangements of the StOF-Br_3 molecular selfassemblies at the heptanoic acid/HOPG surface could be observed.The molecular models and selfassembled StOF-Br_3 architectures have been given in the following text.Besides,we have also figured out the surface free energy by the density functional theory(DFT) calculation,which proved that the halogen...halogen interaction was strong enough to stabilize the ordered molecular self-assemblies.This work verifies the existence of bromine...bromine interactions,and meanwhile provides a kind of effective approach for quickly building ordered molecular nanoarchitectures with large areas and different geometries.