Conditions for realizing one-point interactions from a multi-layer structure model

A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

ON THE SPECTRUM OF THE TWO-PARTICLE SCHRÖDINGER OPERATOR WITH POINT POTENTIAL: ONE DIMENTIONAL CASE

In the paper a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schr\"{o}\-dinger operator (energy operator) $h_\varepsilon$ depending on $\varepsilon,$ is constructed as a self-adjoint extension of the symmetric Laplace operator. The main results of the work are based to the study of the operator $h_\varepsilon.$ First the essential spectrum is described. The existence of unique negative eigenvalue of the Schr\"{o}dinger operator is proved. Further, this eigenvalue and corresponding eigenfunction are found.

Development and Characterization of Magnetic SARS-CoV-2 Peptide-Imprinted Polymers

The development of new methods for the rapid, sensitive, and selective detection of SARS-CoV-2 is a key factor in overcoming the global pandemic that we have been facing for over a year. In this work, we focused on the preparation of magnetic molecularly imprinted polymers (MMIPs) based on the self-polymerization of dopamine at the surface of magnetic nanoparticles (MNPs). Instead of using the whole SARS-CoV-2 virion as a template, a peptide of the viral spike protein, which is present at the viral surface, was innovatively used for the imprinting step. Thus, problems associated with the infectious nature of the virus along with its potential instability when used as a template and under the polymerization conditions were avoided. Dopamine was selected as a functional monomer following a rational computational screening approach that revealed not only a high binding energy of the dopamine–peptide complex but also multi-point interactions across the entire peptide template surface as opposed to other monomers with similar binding affinity. Moreover, variables affecting the imprinting efficiency including polymerization time and amount of peptide and dopamine were experimentally evaluated. Finally, the selectivity of the prepared MMIPs vs. other peptide sequences (i.e., from Zika virus) was evaluated, demonstrating that the developed MMIPs were only specific for the target SARS-CoV-2 peptide.

Dark confinement-deconfinement phase transition: a roadmap from Polyakov loop models to gravitational waves

We explore the confinement-deconfinement phase transition (PT) of the first order (FO) arising in SU(N) pure Yang-Mills theory, based on Polyakov loop models (PLMs), in light of the induced gravitational wave (GW) spectra. We demonstrate that the PLMs with the Haar measure term, involving models successful in QCD with N = 3, are potentially incompatible with the large N scaling for the thermodynamic quantities and the latent heat at around the criticality of the FOPT reported from the lattice simulations. We then propose a couple of models of polynomial form, which we call the 4-6 PLM (with four- and six-point interactions among the basic PL fields which have center charge 1) and 4-8 PLM (with four- and eight-point interactions), and discuss how such models can naturally arise in the presence of a heavy PL with charge 2. We show that those models give the consistent thermodynamic and large N properties at around the criticality. The predicted GW spectra are shown to have high enough sensitivity to be probed in the future prospected interferometers such as BBO and DECIGO.

Economic impacts of tipping points in the climate system

Climate scientists have long emphasized the importance of climate tipping points like thawing permafrost, ice sheet disintegration, and changes in atmospheric circulation. Yet, save for a few fragmented studies, climate economics has either ignored them or represented them in highly stylized ways. We provide unified estimates of the economic impacts of all eight climate tipping points covered in the economic literature so far using a meta-analytic integrated assessment model (IAM) with a modular structure. The model includes national-level climate damages from rising temperatures and sea levels for 180 countries, calibrated on detailed econometric evidence and simulation modeling. Collectively, climate tipping points increase the social cost of carbon (SCC) by ∼25% in our main specification. The distribution is positively skewed, however. We estimate an ∼10% chance of climate tipping points more than doubling the SCC. Accordingly, climate tipping points increase global economic risk. A spatial analysis shows that they increase economic losses almost everywhere. The tipping points with the largest effects are dissociation of ocean methane hydrates and thawing permafrost. Most of our numbers are probable underestimates, given that some tipping points, tipping point interactions, and impact channels have not been covered in the literature so far; however, our method of structural meta-analysis means that future modeling of climate tipping points can be integrated with relative ease, and we present a reduced-form tipping points damage function that could be incorporated in other IAMs.

Cooperation and competition between pair and multi-player social games in spatial populations

The conflict between individual and collective interests is in the heart of every social dilemmas established by evolutionary game theory. We cannot avoid these conflicts but sometimes we may choose which interaction framework to use as a battlefield. For instance some people like to be part of a larger group while other persons prefer to interact in a more personalized, individual way. Both attitudes can be formulated via appropriately chosen traditional games. In particular, the prisoner’s dilemma game is based on pair interaction while the public goods game represents multi-point interactions of group members. To reveal the possible advantage of a certain attitude we extend these models by allowing players not simply to change their strategies but also let them to vary their attitudes for a higher individual income. We show that both attitudes could be the winner at a specific parameter value. Interestingly, however, the subtle interplay between different states may result in a counterintuitive evolutionary outcome where the increase of the multiplication factor of public goods game drives the population to a fully defector state. We point out that the accompanying pattern formation can only be understood via the multipoint or multi-player interactions of different microscopic states where the vicinity of a particular state may influence the relation of two other competitors.