We find the asymptotic representation of the solution of the variable-order fractional diffusion equation, which remains unsolved since it was proposed by Chechkin, Gorenflo, and Sokolov [J. Phys. A, 38, L679 (2005)]. We identify a new advection term that causes ultraslow spatial aggregation of subdiffusive particles due to dominance over the standard advection and diffusion terms in the long-time limit. This uncovers the anomalous mechanism by which nonuniform distributions can occur. We perform Monte Carlo simulations of the underlying anomalous random walk and find excellent agreement with the asymptotic solution.

The fuzzy dark matter (FDM) model treats DM as a bosonic field with an astrophysically large de Broglie wavelength. A striking feature of this model is $\mathcal{O}(1)$ fluctuations in the dark matter density on time scales which are shorter than the gravitational timescale. Including, for the first time, the effect of core oscillations, we demonstrate how such fluctuations lead to heating of star clusters and, thus, an increase in their size over time. From the survival of the old star cluster in Eridanus II, we infer $m_a\gtrsim 0.6\to 1\times {10}^{-19}\mathrm{eV}$ within modeling uncertainty if FDM is to compose all of the DM and derive constraints on the FDM fraction at lower masses. The subhalo mass function in the Milky Way implies $m_a\gtrsim 0.8\times {10}^{-21}\mathrm{eV}$ to successfully form Eridanus II. The region between ${10}^{-21}$ and ${10}^{-20}\mathrm{eV}$ is affected by narrow band resonances. However, the limited applicability of the diffusion approximation means that some of this region may still be consistent with observations of Eridanus II.

The weak gravity conjecture states that quantum gravity theories have to contain a charged state with a charge-to-mass ratio bigger than unity. By studying unitarity and causality constraints on higher derivative corrections to the charge-to-mass ratio of extremal back holes, we demonstrate that heavy extremal black holes can play the role of the required charged state under several assumptions. In particular, our argument is applicable when the higher-spin states Reggeizing graviton exchange are subdominant in the photon scattering. It covers (1) theories with light neutral bosons such as dilaton and moduli, and (2) UV completion where the photon and the graviton are accompanied by different sets of Regge states just like open string theory. Our result provides an existence proof of the weak gravity conjecture in a wide class of theories, including generic string theory setups with the dilaton or other moduli stabilized below the string scale.

Differences between ${\nu }_e$ and ${\nu }_{\mu }$ quasielastic cross sections are essential in neutrino oscillation analyses and $CP$ violation searches for experiments such as DUNE and T2HK. The ratio of these is however poorly known experimentally and for certain kinematic regions theoretical models give contradictory answers. We use two independent mean-field based models to investigate this ratio using ${}^{40}\mathrm{Ar}$ and ${}^{12}\mathrm{C}$ targets. We demonstrate that a proper treatment of the final nucleon’s wave function confirms the dominance of ${\nu }_{\mu }$ over ${\nu }_e$ induced cross sections at forward lepton scattering.

Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, autosolitons, and spot or pulse solutions, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudocontinuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh-Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudocontinuous spectrum develops a modulational instability.

The extreme electromagnetic fields sustained by plasma-based accelerators could drastically reduce the size and cost of future accelerator facilities. However, they are also an inherent source of correlated energy spread in the produced beams, which severely limits the usability of these devices. We propose here to split the acceleration process into two plasma stages joined by a magnetic chicane in which the energy correlation induced in the first stage is inverted such that it can be naturally compensated in the second. Simulations of a particular 1.5-m-long setup show that 5.5 GeV beams with relative energy spreads of $1.2\times {10}^{-3}$ (total) and $2.8\times {10}^{-4}$ (slice) could be achieved while preserving a submicron emittance. This is at least one order of magnitude below the current state of the art and would enable applications such as compact free-electron lasers.

The fluctuating elasticity (FE) model, introduced phenomenologically and developed by Schirmacher [J. Non-Cryst. Solids 357, 518 (2011)], is today the only theoretical framework available to analyze low-temperature elastic acoustic scattering in glasses. Its existing formulations, which neglect the tensorial nature of elasticity and exclude long-range disorder correlations, predict that the acoustic damping coefficients obey the standard Rayleigh scaling law: $\mathrm{\Gamma }\sim k^{d+1}$, with $k$ the acoustic wave vector, in dimension $d$. However, recent numerical data, supported by the analysis of existing experimental results, show that $\mathrm{\Gamma }$ does not obey this scaling law but $\mathrm{\Gamma }\sim -k^{d+1}\ln k$. Here we analyze in detail how a fully tensorial FE model can be constructed as a long wavelength approximation of the elastic response of the discrete, atomistic, problem. We show that, although it incorporates all long-range correlations, it fails to capture the observed damping in two respects: (i) it misses the anomalous scaling, and predicts the standard Rayleigh law; (ii) it grossly underestimates the amplitude of scattering by about 2 orders of magnitude. This brings clear evidence that the small scale nonaffine displacement fields, although not simply reducible to local defects, play a crucial role in acoustic wave scattering and hence cannot be ignored.

A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full analytical solution reveals that for $S>\frac{1}{2}$ the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for $S=\frac{1}{2}$ the Fano factor is bounded between 1 and 2, generalizing earlier studies.

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and, hence, the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric $\pi$-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.

We discover a new type of multiple-$q$ state, a “ripple state,” in a frustrated honeycomb-lattice Heisenberg antiferromagnet under magnetic fields. The ground state has an infinite ringlike degeneracy in the wave vector space, exhibiting a cooperative paramagnetic state, a “ring-liquid” state. We elucidate that the system exhibits the ripple state as a new low-temperature thermodynamic phase via a second-order phase transition from the ring-liquid state, keeping the ringlike spin structure factor. The spin texture in real space looks like a “water ripple” and can induce a giant electric polarization vortex. A possible relationship to the honeycomb-lattice compound, ${\mathrm{Bi}}_3{\mathrm{Mn}}_4{\mathrm{O}}_{12}({\mathrm{NO}}_3)$, is discussed.

We show that crystal-field calculations for $C_1$ point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a $C_1$-symmetry site in ${{}^{167}\mathrm{Er}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. The calculation simultaneously includes site-selective spectroscopic data up to $20000{\mathrm{cm}}^{-1}$, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the $1.5\mu \mathrm{m}$ telecom transition. We achieve an agreement of better than 50 MHz for assigned hyperfine transitions. The success of this analysis opens the possibility of systematically evaluating the coherence properties, as well as transition energies and intensities, of any rare-earth ion doped into ${\mathrm{Y}}_2{\mathrm{SiO}}_5$.

We demonstrate, theoretically and experimentally, that a traveling electric charge passing from one photonic crystal into another generates edge waves—electromagnetic modes with frequencies inside the common photonic band gap localized at the interface—via a process of transition edge-wave radiation (TER). A simple and intuitive expression for the TER spectral density is derived and then applied to a specific structure: two interfacing photonic topological insulators with opposite spin-Chern indices. We show that TER breaks the time-reversal symmetry and enables valley- and spin-polarized generation of topologically protected edge waves propagating in one or both directions along the interface. Experimental measurements at the Argonne Wakefield Accelerator Facility are consistent with the excitation and localization of the edge waves. The concept of TER paves the way for novel particle accelerators and detectors.

We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature’s collapsed shells could be understood from the viewpoint of material orthotropy.

We study the influence of cell-level mechanical heterogeneity in epithelial tissues using a vertex-based model. Heterogeneity is introduced into the cell shape index ($p_0$) that tunes the stiffness at a single-cell level. The addition of heterogeneity can always enhance the mechanical rigidity of the epithelial layer by increasing its shear modulus, hence making it more rigid. There is an excellent scaling collapse of our data as a function of a single scaling variable $f_r$, which accounts for the overall fraction of rigid cells. We identify a universal threshold $f_r^{*}$ that demarcates fluid versus solid tissues. Furthermore, this rigidity onset is far below the contact percolation threshold of rigid cells. These results give rise to a separation of rigidity and contact percolation processes that leads to distinct types of solid states. We also investigate the influence of heterogeneity on tumor invasion dynamics. There is an overall impedance of invasion as the tissue becomes more rigid. Invasion can also occur in an intermediate heterogeneous solid state that is characterized by significant spatial-temporal intermittency.

Superconducting circuits have emerged as a powerful platform of quantum simulation, especially for emulating the dynamics of quantum many-body systems, because of their tunable interaction, long coherence time, and high-precision control. Here in experiments, we construct a Bose-Hubbard ladder with a ladder array of 20 qubits on a 24-qubit superconducting processor. We investigate theoretically and demonstrate experimentally the dynamics of single- and double-excitation states with distinct behaviors, indicating the uniqueness of the Bose-Hubbard ladder. We observe the linear propagation of photons in the single-excitation case, satisfying the Lieb-Robinson bounds. The double-excitation state, initially placed at the edge, localizes; while placed in the bulk, it splits into two single-excitation modes spreading linearly toward two boundaries, respectively. Remarkably, these phenomena, studied both theoretically and numerically as unique properties of the Bose-Hubbard ladder, are represented coherently by pairs of controllable qubits in experiments. Our results show that collective excitations, as a single mode, are not free. This work paves the way to simulation of exotic logic particles by subtly encoding physical qubits and exploration of rich physics by superconducting circuits.

State-of-the-art numerical simulations of core-collapse supernovae reveal that the main source of gravitational waves is the excitation of protoneutron star modes during postbounce evolution. In this work we derive universal relations that relate the frequencies of the most common oscillation modes observed, i.e., $g$ modes, $p$ modes, and the $f$ mode, with fundamental properties of the system, such as the surface gravity of the protoneutron star or the mean density in the region enclosed by the shock. These relations are independent of the equation of state, the neutrino treatment, and the progenitor mass and, hence, can be used to build methods to infer protoneutron star properties from gravitational-wave observations alone. We outline how these measurements could be done and the constraints that could be placed on the protoneutron star properties.

We demonstrate an unusual manifestation of coherent scattering for electron waves in mesoscopic quantum point contacts, in which fast electron dynamics allows the phonon system to serve as a quasistatic source of disorder. The low-temperature conductance of these devices exhibits a giant ($\gg 2e^2/h$) zero bias anomaly (ZBA), the features of which are reproduced in a nonequilibrium model for coherent scattering from the “frozen” phonon disorder. According to this model, the ZBA is understood to result from the in situ electrical manipulation of the phonon disorder, a mechanism that could open up a pathway to the on-demand control of coherent scattering in the solid state.

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence, the emergence of rigidity at colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

We report on the realization and application of nondestructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by a single-shot nondestructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the maximally mixed state. Furthermore, we implement a single-shot version of the Greenberger-Horne-Zeilinger experiment that can generate a quantum versus classical contradiction in each run. Finally, we test a state-independent noncontextuality inequality in eight dimensions. The techniques and insights developed are relevant for fundamental tests as well as for quantum information protocols such as quantum error correction.