Relocalization switch in a triple quantum dot molecule in 2D

A symmetric chain of three quantum dots (i.e., one of the simplest quantum dot molecules) is constructed using a three-parametric non-separable version of an asymptotically separable sextic polynomial potential [Formula: see text]. The probability density [Formula: see text] (admitting either the central or off-central dominance) is assumed measured. A dynamical regime is found with an enhanced sensitivity of the central—off-central transition to the parameters. Quantitatively, the possibility of control of such a switch alias “relocalization catastrophe” is illustrated non-numerically.

On Orthogonal Symmetric Chain Decompositions

The $n$-cube is the poset obtained by ordering all subsets of $\{1,\ldots,n\}$ by inclusion, and it can be partitioned into $\binom{n}{\lfloor n/2\rfloor}$ chains, which is the minimum possible number. Two such decompositions of the $n$-cube are called orthogonal if any two chains of the decompositions share at most a single element. Shearer and Kleitman conjectured in 1979 that the $n$-cube has $\lfloor n/2\rfloor+1$ pairwise orthogonal decompositions into the minimum number of chains, and they constructed two such decompositions. Spink recently improved this by showing that the $n$-cube has three pairwise orthogonal chain decompositions for $n\geq 24$. In this paper, we construct four pairwise orthogonal chain decompositions of the $n$-cube for $n\geq 60$. We also construct five pairwise edge-disjoint symmetric chain decompositions of the $n$-cube for $n\geq 90$, where edge-disjointness is a slightly weaker notion than orthogonality, improving on a recent result by Gregor, Jäger, Mütze, Sawada, and Wille.

α,ω-Epoxide, Oxetane, and Dithiocarbonate Telechelic Copolyolefins: Access by Ring-Opening Metathesis/Cross-Metathesis Polymerization (ROMP/CM) of Cycloolefins in the Presence of Functional Symmetric Chain-Transfer Agents

Epoxide- and oxetane-α,ω-telechelic (co)polyolefins have been successfully synthesized by the tandem ring-opening metathesis polymerization (ROMP)/cross-metathesis (CM) of cyclic olefins using Grubbs’ second-generation catalyst (G2) in the presence of a bifunctional symmetric alkene epoxide- or oxetane-functionalized chain-transfer agent (CTA). From cyclooctene (COE), trans,trans,cis-1,5,9-cyclododecatriene (CDT), norbornene (NB), and methyl 5-norbornene-2-carboxylate (NBCOOMe), with bis(oxiran-2-ylmethyl) maleate (CTA 1), bis(oxetane-2-ylmethyl) maleate (CTA 2), or bis(oxetane-2-ylmethyl) (E)-hex-3-enedioate (CTA 3), well-defined α,ω-di(epoxide or oxetane) telechelic PCOEs, P(COE-co-NB or -NBCOOMe)s, and P(NB-co-CDT)s were isolated under mild operating conditions (40 or 60 °C, 24 h). The oxetane CTA 3 and the epoxide CTA 1 were revealed to be significantly more efficient in the CM step than CTA 2, which apparently inhibits the reaction. Quantitative dithiocarbonatation (CS2/LiBr, 40 °C, THF) of an α,ω-di(epoxide) telechelic P(NB-co-CDT) afforded a convenient approach to the analogous α,ω-bis(dithiocarbonate) telechelic P(NB-co-CDT). The nature of the end-capping function of the epoxide/oxetane/dithiocarbonate telechelic P(NB-co-CDT)s did not impact their thermal signature, as measured by DSC. These copolymers also displayed a low viscosity liquid-like behavior and a shear thinning rheological behavior.

Symmetric Chain Decompositions of Products of Posets with Long Chains

We ask if there exists a symmetric chain decomposition of the cuboid $Q_k \times n$ such that no chain is taut, i.e. no chain has a subchain of the form $(a_1,\ldots, a_k,0)\prec \cdots\prec (a_1,\ldots,a_k,n-1)$. In this paper, we show this is true precisely when $k \ge 5$ and $n\ge 3$. This question arises naturally when considering products of symmetric chain decompositions which induce orthogonal chain decompositions — the existence of the decompositions provided in this paper unexpectedly resolves the most difficult case of previous work by the second author on almost orthogonal symmetric chain decompositions (2017), making progress on a conjecture of Shearer and Kleitman (1979). In general, we show that for a finite graded poset $P$, there exists a canonical bijection between symmetric chain decompositions of $P \times m$ and $P \times n$ for $m, n\ge rk(P) + 1$, that preserves the existence of taut chains. If $P$ has a unique maximal and minimal element, then we also produce a canonical $(rk(P) +1)$ to $1$ surjection from symmetric chain decompositions of $P \times (rk(P) + 1)$ to symmetric chain decompositions of $P \times rk(P)$ which sends decompositions with taut chains to decompositions with taut chains.