A variation of the prime k-tuples conjecture with applications to quantum limits

Let $$\mathcal {H}^{*}=\{h_1,h_2,\ldots \}$$ H ∗ = { h 1 , h 2 , … } be an ordered set of integers. We give sufficient conditions for the existence of increasing sequences of natural numbers $$a_j$$ a j and $$n_k$$ n k such that $$n_k+h_{a_j}$$ n k + h a j is a sum of two squares for every $$k\ge 1$$ k ≥ 1 and $$1\le j\le k.$$ 1 ≤ j ≤ k . Our method uses a novel modification of the Maynard–Tao sieve together with a second moment estimate. As a special case of our result, we deduce a conjecture due to D. Jakobson which has several implications for quantum limits on flat tori.

Linear and nonlinear low-frequency collisional quantum Buneman Instability in electron-positron-ion Plasmas

The linear and nonlinear low-frequency collisional quantum Buneman instability in electronpositron- ion plasmas have been studied. Buneman instability in low frequency three species quantum plasma has been investigated using the approach of the quantum hydrodynamic model. The one-dimensional low-frequency collisional model is revisited by introducing the Bohm potential term in the momentum equation along with the role of the positron. Low-frequency Buneman instability which arises by one stream of particles drifting over another is investigated in the presence of the positron. Different plasma configurations based on the relative velocities of streaming particles are analyzed and it is observed that positron content enhances the instability in classical limits. Further, we found that in pure quantum limits the instability growth rate is decreased by increasing the positron concentration. The present work is very useful for the nonlinear problems in Quantum Coulomb systems.

Correction: Poljak et al. Metallization-Induced Quantum Limits of Contact Resistance in Graphene Nanoribbons with One-Dimensional Contacts. Materials 2021, 14, 3670

The authors regret that the results presented in Figure 3c,d and Figure 6c,d in our published paper [...]

Metallization-Induced Quantum Limits of Contact Resistance in Graphene Nanoribbons with One-Dimensional Contacts

Graphene has attracted a lot of interest as a potential replacement for silicon in future integrated circuits due to its remarkable electronic and transport properties. In order to meet technology requirements for an acceptable bandgap, graphene needs to be patterned into graphene nanoribbons (GNRs), while one-dimensional (1D) edge metal contacts (MCs) are needed to allow for the encapsulation and preservation of the transport properties. While the properties of GNRs with ideal contacts have been studied extensively, little is known about the electronic and transport properties of GNRs with 1D edge MCs, including contact resistance (RC), which is one of the key device parameters. In this work, we employ atomistic quantum transport simulations of GNRs with MCs modeled with the wide-band limit (WBL) approach to explore their metallization effects and contact resistance. By studying density of states (DOS), transmission and conductance, we find that metallization decreases transmission and conductance, and either enlarges or diminishes the transport gap depending on GNR dimensions. We calculate the intrinsic quantum limit of width-normalized RC and find that the limit depends on GNR dimensions, decreasing with width downscaling to ~3 Ω∙µm in 0.4 nm-wide GNRs, and increasing with length downscaling up to ~30 Ω∙µm in 5 nm-long GNRs. The worst-case total RC is only ~40 Ω∙µm, which demonstrates that there is room for RC improvement in comparison to the published experimental data, and that GNRs present a promising channel material for future extremely-scaled electronic nanodevices.