All articles tagged with #topology
Researchers show that light can naturally develop handedness (chirality) as it travels through empty space—even without mirrors or special materials—due to its internal topology when the beam is prepared in a balanced state. The emergent spin and twist of structured light could enable new ways to encode information, improve medical diagnostics and sensing, and boost data capacity in communications and future quantum networks.
A new knot invariant designed to be both strong and fast to compute outputs hexagonal QR-code images for each knot, enabling reliable distinction even for knots with hundreds of crossings and offering potential insights into genus and other topological features, with the work tying to the Kontsevich integral's two-loop approximation.
Researchers built a 13‑carbon ring that hosts two isolated conjugated subsystems; by placing chlorine atoms to separate them, the ring spontaneously twists by 90 degrees and becomes a single, fully delocalized 24‑electron system with a unique electronic/magnetic profile distinct from classic Möbius structures. The molecule exists as two enantiomers, which can be interconverted using a small external voltage, a breakthrough reported in Science by Manchester and IBM Zurich teams and signaling a new topological approach to designing matter.
Researchers at the University of the Witwatersrand and collaborators demonstrated that entangled photons carry a hidden, high-dimensional topology—up to 48 dimensions—with over 17,000 distinct signatures. This topology arises from a single property of light, its orbital angular momentum, enabling a new high-dimensional encoding scheme for quantum information. Because OAM spans many values, the resulting topology can be very rich, and the effect can be observed using standard SPDC lab setups, potentially improving the robustness of future quantum technologies.
Physicists from the University of the Witwatersrand and Huzhou University report that entangled photons produced via spontaneous parametric downconversion harbor a rich, high-dimensional topological structure within their spatial degrees of freedom, specifically in orbital angular momentum. They observed a topology spanning 48 dimensions with over 17,000 distinct signatures, suggesting new ways to encode and protect quantum information against noise. Because OAM is inherently high-dimensional, the topology is also effectively limitless in practice, and these effects can be explored with standard quantum optics lab setups, offering a practical path toward more stable quantum technologies.
Researchers used quantum hardware to validate a novel 'half-Möbius' molecule topology, confirming a four-loop orbital structure and modeling up to 32 electrons; while not proving quantum supremacy, the work shows quantum computers becoming a practical tool for chemistry and materials science.
The article explains that in four dimensions a knot tied on a rope cannot stay knotted, because the extra dimension lets strands slide past each other; by contrast, two-dimensional surfaces such as balloons can still be knotted in higher dimensions. A guiding formula says you can knot an object of dimension d only up to dimension 2d+1; for a rope (1D) that means up to 3D, while a 2D surface can be knotted in up to 5D. The piece uses analogies (ants on a line, a movie-like sequence of 3D frames) to visualize 4D space and notes that knotted surfaces in 4D is a vibrant area of research linking geometry to our understanding of four-dimensional space.
Researchers demonstrated optical, non-thermal control of magnetism in a twisted bilayer MoTe2; a laser pulse reversibly flips the ferromagnetic polarity, with switching dynamics tied to whether electrons reside in a topological insulating or metallic state. This links topology and magnetism in a single platform and suggests future possibilities for light-written topological circuits and tiny interferometers on chips.
Researchers observed a novel topological semimetal state in CeRu4Sn6 at ultracold temperatures, a phase once deemed impossible, arising from quantum criticality that ties strong electron interactions to topology. The state was signaled by an unusual Hall effect without a magnetic field, indicating robust topological behavior with potential quantum-tech applications. The team plans to explore this state in other materials and refine the topology details. Published in Nature Physics.
Researchers at TU Wien report that the quantum material CeRu4Sn6 enters a quantum-critical regime at ultra-low temperatures where electrons lose their particle-like character, yet the system hosts an emergent topological semimetal state. They observed a spontaneous (anomalous) Hall effect without an external magnetic field, linking quantum fluctuations to topology and suggesting that topological properties can arise even when the conventional particle-picture fails. The work also points to a generalized, emergent view of topology and proposes focusing on quantum-critical materials to discover new topological phases.
A COMPACT collaboration suggests the universe could be finite yet boundary-less, with light looping through space in a 3-torus topology that could create mirrored observations of the same region. While not yet confirmed, the idea expands searches for topological fingerprints in the CMB and broader Euclidean/non-Euclidean models.
The human body has approximately seven or eight topologically distinct holes, including the mouth, anus, nostrils, tear ducts, and possibly the vagina and fallopian tubes, depending on how connections are counted, with the count influenced by the topological perspective that considers how openings connect internally.
In 2002, Russian mathematician Grigori Perelman quietly published a series of papers that proved the long-standing Poincaré conjecture using Ricci flow, solving a major problem in topology. Despite being offered prestigious awards, he declined them and retreated from public life, leaving a lasting impact on mathematics.
Mathematician Richard Schwartz has solved a 50-year-old puzzle about the minimal size of a developable Möbius strip, establishing that its aspect ratio must be greater than √3 (about 1.73) to avoid collapsing, and opening new questions about twisted strips and their properties.
A new study extends the Středa formula to non-equilibrium driven quantum systems, revealing that a 'sum of zeros' mathematically encodes a universal, quantized topological magnetic response, with implications for understanding exotic phases in quantum materials.