ALT A snapshot of the Wigner function at a representative time, together with a schematic illustration of the Gaussian decomposition underlying the variational multi-Gaussian ansatz.

ALT Line plot with x-axis λ²t ranging from 0 to 500 and y-axis C₀ₓ(t) ranging from 0 to 0.10. Dozens of curves fan out from near the origin, colored on a gradient from yellow (top) through orange and pink to dark purple (bottom). Yellow curves start near 0.10 and fall steeply; purple curves start near zero and rise gradually. All curves converge and flatten together toward the right side of the plot around 0.01 by λ²t = 500.

ALT An orange diagram on a cream background. Four dots are labeled σ1, σ2, σ3, and σ4 at top-left, bottom-left, top-right, and bottom-right. Diagonal lines connect σ1 to σ2 and σ3 to σ4, meeting at two central points. A horizontal line connects these two center points, labeled 1, ψ.

ALT An illustration of a pyrochlore lattice made of triangular tetrahedra, each with black dots at the corners. The tetrahedra are connected by corners, with one tetrahedron numbered 0, 1, 2, 3 at its corners in the lower right. Each tetrahedron's edges are colored blue (z-chains), red diagonal (y-chains) and orange (x-chains).

ALT A two-part figure. At left: a 3D illustration of a cylindrical test rig with a teal cylindrical sample labeled "Precompressed VACNT" at the base, compressed between metal plates, a dark green arrow pointing downward onto the top plate. At right: a teal dotted-line graph plotting shifted stress labeled σ–σs on the y-axis, from -0.4 to 0.4, against shifted strain labeled ε–εs on the x-axis, from -5 to 5. The curve forms a large outer loop with a smaller loop inside it, with arrows pointing at them labeled "Sub-loops."

ALT A crystal structure diagram. On the left, a tall column shows blue octahedra stacking along a vertical c-axis. Small orange spheres labeled "La" are between the layers. On the right, two larger insets show details of the individual octahedra, with a dark blue center sphere labeled "Ni" surrounded by gray spheres labeled “O.” The lower inset shows a stacked octahedra connected at a 180-degree angle.

ALT A diagram with a stack of four labeled horizontal trajectory plots, f(X₁(t)) through f(Xₙ(t)), each showing a thin blue squiggly line fluctuating around a black horizontal axis, with "t" on the right of each plot. Ellipses sit between f(X3(t)) and f(Xₙ(t)). A vertical magenta band crosses all four plots at the same point, with an arrow pointing up to the label ⟨f⟩. A horizontal green band highlights the second trajectory f(X₂(t)) with an arrow pointing right to the label f̄.

ALT Two side-by-side 3D surface plots shaped like curved valleys, shaded blue in the center and red near the upper edges. Both are labeled with a curved line marked "𝒩" running across the surface. The left is labeled p(x) and shows several black dots scattered across the surface and a black curved line drawn along the “valley” floor. The right is labeled r(x') and shows a red arrow labeled "Blur" pointing from a curved solid line to a curved dashed line with red dots. Curved black arrows show dots moving from open circles to new positions on the dashed line.

ALT Scientific Illustration with four sections: A, B, C, D. Section A is a topographic image of the Co3Sn surface with kagome lattice. A blue rectangle with honeycomb pattern is labeled 'Topography'. It has a small hexagram on top, with 3 balls at 3 points, then 2 balls to its right, 2 balls to its left. The scale bar is labeled 1nm. Section B features six topographic images of the same lattice, each with the same pentagram and balls but the honeycomb patterns are blurred and orange. Starting from the left, each of the six lattices is labeled: -250 meV, -115 meV, -70meV, -25meV, 0meV, and finally 200meV. Lattices 3, 4 and 5 also have label underneath that says 'symmetry broken'. Section C is a graph with amplitude (au) on y axis and E (meV) on x axis. Three lines - red, green and blue display three Bragg peaks. Section D is a graph with phase on y axis, going from 0 at the bottom to 4π at the top and E (meV) on x axis, going from -200 to 200. The bragg peaks are red, green and blue.

ALT A plot of linewidth versus feedback gain. There are three lines going across it. One line connecting orange diamonds shows the intrinsic magnon dissipation rate, which stays nearly constant. One line connecting blue squares shows the effective cavity linewidth, which decreases with feedback. Between them, a line with red circles and green stars shows the lower- and upper-polariton linewidths, respectively. Both decrease as feedback increases, falling below the magnon dissipation rate, showing that feedback can suppress polariton losses beyond the material limit.

ALT A grid of five rows, each showing a filament's shape across one oscillation cycle. Each row has two panels of five frames. Top frames show white fluorescent microscopy images of a glowing actin filament on a black background. Bottom frames show matching black line-tracing on a gray background. Left and right panel groups are separated by a thick vertical line, colored red if the filament is buckled at that point or blue if straight. Across the five rows, the filaments start straight and progressively bend into varied curves and S-shapes.

ALT A graph showing the electronic states at a material’s surface. The x-axis shows momentum along a high-symmetry path on the surface, and the y-axis is labeled E/J. One pair of red and blue lines (with colors depicting spectral weight in the spin-up and down channels, respectively) wiggles across the upper portion near a dashed yellow line that goes straight across at 0.8 E/J, and another pair wiggles across the lower portion roughly centered on -1 E/J, showing surface spin splitting.

ALT Scientific figure. Eight tetrahedra, four on top row, four on bottom row; each with red and blue quadrupolar orbitals at four points. Top left: “A1.” Magenta arrows pointing outward from each orbital. Top middle left: “T2, planar.” Arrows pointing up. Top middle right: “T1.” Top two arrows point up and down. Bottom two arrows point up and down. Top right: “Epsi3.” Top two arrows point left and right. Bottom left arrows point inwards into the shape. Bottom right arrow points leftwards. Bottom left: “T2, ice.” Top two arrows point outwards. Two bottom arrows point inwards. The final three shapes in the bottom row have green arrows. Bottom middle left: “T2, planar.” Four arrows point up. Bottom middle right: “T1.” Top two arrows point up and down. Bottom two arrows point up and down. Bottom right: “Epsi2.” Top two arrows point up. Bottom arrows point down. All shapes are labeled “(t2g),” except for the final 3, labeled “(eg).”

ALT A depiction of a quantum birthmark. The figure displays the long-time average of the probability density for a Gaussian wavepacket initialized along a bowtie quantum scar at the center of a stadium billiard.

ALT A series of sketches illustrating four Kagome lattices (a, b, c, and d), represented as simple, triangular-shaped outlines with various interior lines. Panels (a) and (c) are labelled as geometrically frustrated and contain an internal lattice of grey lines intersecting with pink arrows pointed in various directions. Panels (b) and (d) are labelled as frustration relieved and contain an internal lattice of green and orange lines intersecting with pink arrows pointed in similar directions.

ALT Illustration of spin-polarized electrons passing through an engineered platinum interface, with arrows showing spins being reoriented out-of-plane as they pass through a quantum filtering layer above a crystal lattice structure.

ALT A video showing a binary mixture of starfish embryos moving about under a microscope, with overlaid arrows denoting their two-minute trajectories. E1 embryos are colored blue and E2 embryos are colored red.

ALT A series of three graphs plot the 2D density distributions of |A| and |B|, with |A| on the x-axis and |B| on the y-axis. Each graph contains an oval-like, blue-shaded region, which represents the distribution of |A| and |B| obtained in the new paper. The graphs also contain an array of circular, square, and plus-shaped markers of various colors, which denote theoretical calculations and experimental measurements from previous papers.

ALT A molecular schematic displaying the noncollinear spin-orbit filtering effect in a high-symmetry interface (grey rectangular cuboid). Purple arrows on the surface of the cuboid denote the Rashba-Edelstein field, with one straight arrow pointing in the direction of a smaller set of arrows arranged in a circle. A brown arrow pointing in the x-direction represents the charge current Jc, while grey arrows pointing up and to the left represent the resulting orthogonal spin currents Js1 and Js2. Trios of red spheres with red arrows running through them denote σ, found alongside the orthogonal spin currents. The cuboid also contains a smaller cube at the bottom right, formed by interspersed grey spheres.