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Molecular ions and hybrid platforms that integrate cold trapped ions and neutral particles offer opportunities for many quantum technologies. This Review surveys recent methodological advances and highlights in the study of cold molecular ions.

Ultracold molecules and ion–neutral systems offer unique access to chemistry in a coherent quantum regime. This Review charts the progress of studies of quantum chemistry in such platforms, highlighting the synergy between theory and experiments.

The mechanism by which two-dimensional materials remain stable at a finite temperature is still under debate. Now, numerical calculations suggest that rotational symmetry is crucial in suppressing anharmonic effects that lead to structural instability.

The study of quantum systems in a programmable and controllable fashion is one of the aims of both quantum simulation and computing. This Review covers the prospects and opportunities that ultracold molecules offer in these fields.

Cold and ultracold molecules have emerged in the past two decades as a central topic in quantum gas studies. This Review charts the recent advances in cooling and quantum state control techniques that are shaping this evolving field.

Thousands of Iranians study at German universities every year, but many struggle with the German academic system. Here, we offer some advice.

Active cell contraction drives hole nucleation, fracture and crack propagation in a tissue monolayer through a process reminiscent of dewetting thin films.

Many recent experiments have stored quantum information in bosonic modes, such as photons in resonators or optical fibres. Now an adaptation of the classical spherical codes provides a framework for designing quantum error correcting codes for these platforms.

The properties of quantum matter arise from the combined effects of dimensionality, interactions and quantum statistics. An experiment now studies what happens to ultracold bosons when the dimensionality of the system changes continuously between one and two dimensions.

Spiral waves of cell density can form and propagate through bacterial biofilms. These waves are formed by a self-organization process that coordinates pulling forces between neighbouring cells.

The determination of the order parameter symmetry is a critical issue in the study of unconventional superconductors. Ultrasound measurements on UTe₂, a candidate spin-triplet superconductor, now provide evidence for the single-component nature of its order parameter.

Protein transport across the nuclear membrane is regulated by the nuclear pore complex. Experiments now show that the rates of nuclear transport rely on the presence of locally mechanically soft regions of the transported proteins.

Laser-driven proton acceleration experiments achieve energies of up to 150 MeV with particle yields that are relevant for applications such as radiobiology.

Cells can form a rotating doublet. This rotation is driven by the symmetry breaking of myosin polarization in the cortices of the two cells.

The nuclear pore complex of eukaryotic cells senses the mechanical directionality of translocating proteins, favouring the passage of those that have a leading mechanically labile region. Adding an unstructured, mechanically weak peptide tag to a translocating protein increases its rate of nuclear import and accumulation, suggesting a biotechnological strategy to enhance the delivery of molecular cargos into the cell nucleus.

A Dirac quantum spin liquid phase is predicted to have a continuum of fractionalized spinon excitations with a Dirac cone dispersion. A spin continuum consistent with this picture has now been observed in neutron scattering measurements.

The symmetry of the superconducting order parameter in UTe₂ is still debated. Now ultrasound experiments suggest that the order parameter can only have one component.

Some magnetic phase transitions can be understood as Bose–Einstein condensation of magnons. Close to a quantum critical point, YbCl₃ now provides a realization of a Bose–Einstein condensate that is dominated by two-dimensional physical behaviour.

Rotational symmetry is shown to protect the quadratic dispersion of out-of-plane flexural vibrations in graphene and other two-dimensional materials against phonon–phonon interactions, making the bending rigidity of these materials non-divergent. The quadratic dispersion is then consistent with the propagation of sound in the graphene plane.