New improvement to Falconer distance set problem in higher dimensions

We show that if a compact set $E\subset \mathbb{R}^d$ has Hausdorff dimension larger than $\frac{d}{2}+\frac{1}{4}-\frac{1}{8d+4}$, where $d\geq 3$, then there is a point $x\in E$ such that the pinned distance set $\Delta_x(E)$ has positive Lebesgue measure. This improves upon bounds of Du-Zhang and Du-Iosevich-Ou-Wang-Zhang in all dimensions $d \ge 3$. We also prove lower bounds for Hausdorff dimension of pinned distance sets when $\dim_H (E) \in (\frac{d}{2} - \frac{1}{4} - \frac{3}{8d+4}, \frac{d}{2}+\frac{1}{4}-\frac{1}{8d+4})$, which improves upon bounds of Harris and Wang-Zheng in dimensions $d \ge 3$.Comment: 36 page

Weighted refined decoupling estimates and application to Falconer distance set problem

We prove some weighted refined decoupling estimates. As an application, we give an alternative proof of the following result on Falconer's distance set problem by the authors in a companion work: if a compact set $E\subset \mathbb{R}^d$ has Hausdorff dimension larger than $\frac{d}{2}+\frac{1}{4}-\frac{1}{8d+4}$, where $d\geq 4$, then there is a point $x\in E$ such that the pinned distance set $\Delta_x(E)$ has positive Lebesgue measure. Aside from this application, the weighted refined decoupling estimates may be of independent interest.Comment: 28 pages. arXiv admin note: text overlap with arXiv:2309.0410

Ultrafast all-optical switching via coherent modulation of metamaterial absorption

We report on the demonstration of a femtosecond all-optical modulator providing, without nonlinearity and therefore at arbitrarily low intensity, ultrafast light-by-light control. The device engages the coherent interaction of optical waves on a metamaterial nanostructure only 30 nm thick to efficiently control absorption of near-infrared (750-1040 nm) femtosecond pulses, providing switching contrast ratios approaching 3:1 with a modulation bandwidth in excess of 2 THz. The functional paradigm illustrated here opens the path to a family of novel meta-devices for ultra-fast optical data processing in coherent networks.Comment: 5 pages, 4 figure

Intrinsic optical bistability in nanomechanical metamaterials at milliwatt power levels

We report the first demonstration of optical bistability in nanomechanical metamaterials - arrays of plasmonic or dielectric resonators on flexible nano-membranes. Bistability results from the nonlinearity of the near-field forces induced by light

Photonic Metamaterial Analogue of a Continuous Time Crystal

Time crystals are an eagerly sought phase of matter with broken time-translation symmetry. Quantum time crystals with discretely broken time-translation symmetry have been demonstrated in trapped ions, atoms and spins while continuously broken time-translation symmetry has been observed in an atomic condensate inside an optical cavity. Here we report that a classical metamaterial nanostructure, a two-dimensional array of plasmonic metamolecules supported on flexible nanowires, can be driven to a state possessing all of the key features of a continuous time crystal: continuous coherent illumination by light resonant with the metamolecules' plasmonic mode triggers a spontaneous phase transition to a superradiant-like state of transmissivity oscillations, resulting from many-body interactions among the metamolecules, characterized by long-range order in space and time. The phenomenon is of interest to the study of dynamic classical many-body states in the strongly correlated regime and applications in all-optical modulation, frequency conversion and timing.Comment: 10 pages, 6 figure

Puzzling subunits of mitochondrial cytochrome reductase

The ubiquinol-cytochrome c reductase complex, like the other proton-pumping respiratory complexes of mitochondria, is an assembly of many different subunits. However, only a few of these subunits participate directly in the electron transfer and proton translocation. The roles of the other subunits are largely unknown. We discuss here some intriguing features of two of these subunits