An official website of the United States government
Abstract May the triforce be the 3-uniform hypergraph on six vertices with edges {123′, 12′3, 1′23}. We show that the minimum triforce density in a 3-uniform hypergraph of edge density δ is δ 4– o (1) but not O ( δ 4 ). Let M ( δ ) be the maximum number such that the following holds: for every ∊ > 0 and $$G = {\mathbb{F}}_2^n$$ with n sufficiently large, if A ⊆ G × G with A ≥ δ | G | 2 , then there exists a nonzero “popular difference” d ∈ G such that the number of “corners” ( x , y ), ( x + d , y ), ( x , y + d ) ∈ A is at least ( M ( δ )–∊)| G | 2 . As a corollary via a recent result of Mandache, we conclude that M ( δ ) = δ 4– o (1) and M ( δ ) = ω ( δ 4 ). On the other hand, for 0 < δ < 1/2 and sufficiently large N , there exists A ⊆ [ N ] 3 with | A | ≥ δN 3 such that for every d ≠ 0, the number of corners ( x , y , z ), ( x + d , y , z ), ( x , y + d , z ), ( x , y , z + d ) ∈ A is at most δ c log(1/ δ ) N 3 . A similar bound holds in higher dimensions, or for any configuration with at least 5 points or affine dimension at least 3.
more »
« less
Direct mapping of curve-crossing dynamics in IBr by attosecond transient absorption spectroscopy
The electronic character of photoexcited molecules can abruptly change at avoided crossings and conical intersections. Here, we report direct mapping of the coupled interplay between electrons and nuclei in a prototype molecule, iodine monobromide (IBr), by using attosecond transient absorption spectroscopy. A few-femtosecond visible pulse resonantly excites the B ( Π 3 0 + ) , Y(0 + ), and Z(0 + ) states of IBr, and the photodissociation dynamics are tracked with an attosecond extreme-ultraviolet pulse that simultaneously probes the I-4 d and Br-3 d core-level absorption edges. Direct comparison with quantum mechanical simulations unambiguously identifies the absorption features associated with adiabatic and diabatic channels at the B/Y avoided crossing and concurrent two-photon dissociation processes that involve the Y/Z avoided crossing. The results show clear evidence for rapid switching of valence-electronic character at the avoided crossing.
more »
« less
- Award ID(s):
- 1660417
- PAR ID:
- 10158292
- Date Published:
- Journal Name:
- Science
- Volume:
- 365
- Issue:
- 6448
- ISSN:
- 0036-8075
- Page Range / eLocation ID:
- 79 to 83
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Lithium‐rich transition metal chalcogenides are witnessing a revival as candidates for Li‐ion cathode materials, spurred by the boost in their capacities from transcending conventional redox processes based on cationic states and tapping into additional chalcogenide states. A particularly striking case is Li2TiS3‐ySey, which features a d0metal. While the end members are expectedly inactive, substantial capacities are measured when both Se and S are present. Using X‐ray absorption spectroscopy, it is shown that the electronic structure of Li2TiS3‐ySeyis not a simple combination of the end members. The data confirm previous hypotheses that, in Li2TiS2.4Se0.6, this behavior is underpinned by concurrent and reversible redox of only S and Se, and identify key electronic states. Moreover, wavelet transforms of the extended X‐ray absorption fine structure provide direct evidence of the formation of short Se–Se units upon charging. The study uncovers the underpinnings of this intriguing reactivity and highlights the richness of redox chemistry in complex solids.more » « less
-
null (Ed.)A bstract The p T -differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity ( | y | < 0 . 5) in proton-proton collisions at $$ \sqrt{s} $$ s = 5 . 02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19 . 3 ± 0 . 4) nb − 1 . D mesons were reconstructed from their decays D 0 → K − π + , D + → K − π + π + , and $$ {\mathrm{D}}_{\mathrm{s}}^{+}\to \upphi {\uppi}^{+}\to {\mathrm{K}}^{-}{\mathrm{K}}^{+}{\uppi}^{+} $$ D s + → ϕ π + → K − K + π + and their charge conjugates. Compared to previous measurements in the same rapidity region, the cross sections of prompt D + and $$ {\mathrm{D}}_{\mathrm{s}}^{+} $$ D s + mesons have an extended p T coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on p T , allowing for a more precise determination of their p T -integrated cross sections. The results are well described by perturbative QCD calculations. The fragmentation fraction of heavy quarks to strange mesons divided by the one to non-strange mesons, f s / ( f u + f d ), is compatible for charm and beauty quarks and with previous measurements at different centre-of-mass energies and collision systems. The $$ \mathrm{b}\overline{\mathrm{b}} $$ b b ¯ production cross section per rapidity unit at midrapidity, estimated from non-prompt D-meson measurements, is $$ \mathrm{d}{\sigma}_{\mathrm{b}\overline{\mathrm{b}}}/\mathrm{d}y\left|{}_{\left|\mathrm{y}\right|<0.5}=34.5\pm 2.4{\left(\mathrm{stat}\right)}_{-2.9}^{+4.7}\left(\mathrm{tot}.\mathrm{syst}\right)\right. $$ d σ b b ¯ / d y y < 0.5 = 34.5 ± 2.4 stat − 2.9 + 4.7 tot . syst μb. It is compatible with previous measurements at the same centre-of-mass energy and with the cross section pre- dicted by perturbative QCD calculations.more » « less
-
We theoretically investigate the role of complex dipole phase in the attosecond probing of charge migration. The iodobromoacetylene ion (ICCBr+) is considered as an example, in which one can probe charge migration by accessing both the iodine and bromine ends of the molecule with different spectral windows of an extreme-ultraviolet (XUV) pulse. The analytical expression for transient absorption shows that the site-specific information of charge migration is encoded in the complex phase of cross dipole products for XUV transitions between the I-4dand Br-3dspectral windows. Ab-initio quantum chemistry calculations on ICCBr+reveal that there is a constantπphase difference between the I-4dand Br-3dtransient-absorption spectral windows, irrespective of the fine-structure energy splittings. Transient absorption spectra are simulated with a multistate model including the complex dipole phase, and the results correctly reconstruct the charge-migration dynamics via the quantum beats in the two element spectral windows, exhibiting out-of-phase oscillations.more » « less
-
Abstract Reduction of the cobalt(II) chloride complex, Ph2B(tBuIm)2Co(THF)Cl (1) in the presence oftBuN≡C affords the diamagnetic, square planar cobalt(I) complex Ph2B(tBuIm)2Co(C≡NtBu)2(2). This is a rare example of a 16‐electron cobalt(I) complex that is structurally related to square planar noble metal complexes. Accordingly, the electronic structure of2, as calculated by DFT, reveals that the HOMO is largely dz2in character. Complex2is readily oxidized to its cobalt(II) congener [Ph2B(tBuIm)2Co(C=NtBu)2]BPh4(3‐BPh4), whose EPR spectral parameters are characteristic of low‐spin d7with an unpaired electron in an orbital of dz2parentage. This is also consistent with the results of DFT calculations. Despite its 16‐electron configuration and the dz2parentage of the HOMO, the only tractable reactions of2involve one electron oxidation to afford3.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1126/science.aax0076
