Biochemical processes are inherently stochastic, creating molecular fluctuations in otherwise identical cells. Such “noise” is widespread but has proven difficult to analyze because most systems are sparsely characterized at the single cell level and because nonlinear stochastic models are analytically intractable. Here, we exactly relate average abundances, lifetimes, step sizes, and covariances for any pair of components in complex stochastic reaction systems even when the dynamics of other components are left unspecified. Using basic mathematical inequalities, we then establish bounds for whole classes of systems. These bounds highlight fundamental trade-offs that show how efficient assembly processes must invariably exhibit large fluctuations in subunit levels and how eliminating fluctuations in one cellular component requires creating heterogeneity in another.

By systematically varying the mobility of self-propelled particles in a 2D lattice, we experimentally study the influence of particle mobility on system’s collective motion. Our system is intrinsically nonequilibrium due to the lack of energy equipartition. By constructing the covariance matrix of spatial fluctuations and solving for its eigenmodes, we obtain the collective motions of the system with various magnitudes. Interestingly, our structurally ordered nonequilibrium system exhibits properties almost identical to disordered glassy systems under thermal equilibrium: the modes with large overall motions are spatially correlated and quasilocalized while the modes with small collective motions are highly localized, resembling the low- and high-frequency modes in glass. More surprisingly, a peak similar to the boson peak forms in our nonequilibrium system as the number of mobile particles increases, revealing the possible origin of the boson peak from a dynamic aspect. We further illustrate that the spatially correlated large-movement modes can be produced by the cooperation of highly active particles above a threshold fraction, while the localized small-movement modes can be created by adding individual inactive particles. Our study clarifies the role of mobility in collective motions, and further suggests a promising possibility of extending the powerful mode analysis approach to nonequilibrium systems.

Astrophysical observations spanning dwarf galaxies to galaxy clusters indicate that dark matter (DM) halos are less dense in their central regions compared to expectations from collisionless DM $N$-body simulations. Using detailed fits to DM halos of galaxies and clusters, we show that self-interacting DM (SIDM) may provide a consistent solution to the DM deficit problem across all scales, even though individual systems exhibit a wide diversity in halo properties. Since the characteristic velocity of DM particles varies across these systems, we are able to measure the self-interaction cross section as a function of kinetic energy and thereby deduce the SIDM particle physics model parameters. Our results prefer a mildly velocity-dependent cross section, from $\sigma /m\approx 2{\mathrm{cm}}^2/\mathrm{g}$ on galaxy scales to $\sigma /m\approx 0.1{\mathrm{cm}}^2/\mathrm{g}$ on cluster scales, consistent with the upper limits from merging clusters. Our results dramatically improve the constraints on SIDM models and may allow the masses of both DM and dark mediator particles to be measured even if the dark sector is completely hidden from the standard model, which we illustrate for the dark photon model.

We use time-dependent density functional theory to study self-irradiated Si. We calculate the electronic stopping power of Si in Si by evaluating the energy transferred to the electrons per unit path length by an ion of kinetic energy from 1 eV to 100 keV moving through the host. Electronic stopping is found to be significant below the threshold velocity normally identified with transitions across the band gap. A structured crossover at low velocity exists in place of a hard threshold. An analysis of the time dependence of the transition rates using coupled linear rate equations enables one of the excitation mechanisms to be clearly identified: a defect state induced in the gap by the moving ion acts like an elevator and carries electrons across the band gap.

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive $s$-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature with predictions for both fermions and bosons from quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry transformation. We prove that, in the discrete scenario, this permutation symmetry is equivalent to the symmetry group being a unitary 2 design. Such a highly symmetric representation can only appear in odd prime power dimensions besides dimensions 2 and 8. It suffices to single out a unique discrete Wigner function among all possible quasiprobability representations. In the course of our study, we show that this discrete Wigner function is uniquely determined by Clifford covariance, while no Wigner function is Clifford covariant in any even prime power dimension.

We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than ${10}^{12}\text{photons}/\mathrm{s}$ with a 95% efficiency and a 14 kHz bandwidth. With less than ${10}^{-1}\text{photons}·{\mathrm{s}}^{-1}·{\mathrm{Hz}}^{-1}$ of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.

We demonstrate coherent population trapping of a single nuclear spin in a room-temperature solid. To this end, we exploit a three-level system with a $\mathrm{\Lambda }$ configuration in the microwave domain, which consists of nuclear spin states addressed through their hyperfine coupling to the electron spin of a single nitrogen-vacancy defect in diamond. Moreover, the $\mathrm{\Lambda }$-scheme relaxation is externally controlled through incoherent optical pumping and separated in time from consecutive coherent microwave excitations. Such a scheme allows us (i) to monitor the sequential accumulation of population into the dark state and (ii) to reach a novel regime of coherent population trapping dynamics for which periodic arrays of dark resonances can be observed, owing to multiple constructive interferences. This Letter offers new prospects for quantum state preparation, information storage in hybrid quantum systems, and metrology.

We extract the phase coherence of a qubit defined by singlet and triplet electronic states in a gated GaAs triple quantum dot, measuring on time scales much shorter than the decorrelation time of the environmental noise. In this nonergodic regime, we observe that the coherence is boosted and several dephasing times emerge, depending on how the phase stability is extracted. We elucidate their mutual relations, and demonstrate that they reflect the noise short-time dynamics.

We present significant evidence of halo assembly bias for SDSS redMaPPer galaxy clusters in the redshift range [0.1, 0.33]. By dividing the 8,648 clusters into two subsamples based on the average member galaxy separation from the cluster center, we first show that the two subsamples have very similar halo mass of $M_{200\mathit{m}}\simeq 1.9\times {10}^{14}{h}^{-1}{M}_{\odot }$ based on the weak lensing signals at small radii $R\lesssim 10h^{-1}\mathrm{Mpc}$. However, their halo bias inferred from both the large-scale weak lensing and the projected autocorrelation functions differs by a factor of $\sim 1.5$, which is a signature of assembly bias. The same bias hypothesis for the two subsamples is excluded at $2.5\sigma$ in the weak lensing and $4.4\sigma$ in the autocorrelation data, respectively. This result could bring a significant impact on both galaxy evolution and precision cosmology.

We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.

We describe a general scenario, dubbed “inflatable dark matter,” in which the density of dark matter particles can be reduced through a short period of late-time inflation in the early Universe. The overproduction of dark matter that is predicted within many, otherwise, well-motivated models of new physics can be elegantly remedied within this context. Thermal relics that would, otherwise, be disfavored can easily be accommodated within this class of scenarios, including dark matter candidates that are very heavy or very light. Furthermore, the nonthermal abundance of grand unified theory or Planck scale axions can be brought to acceptable levels without invoking anthropic tuning of initial conditions. A period of late-time inflation could have occurred over a wide range of scales from $\sim \mathrm{MeV}$ to the weak scale or above, and could have been triggered by physics within a hidden sector, with small but not necessarily negligible couplings to the standard model.

The properties of the interfacial layer between the polymer matrix and nanoparticles largely determine the macroscopic properties of polymer nanocomposites (PNCs). Although the static thickness of the interfacial layer was found to increase with the molecular weight (MW), the influence of MW on segmental relaxation and the glass transition in this layer remains to be explored. In this Letter, we show an unexpected MW dependence of the interfacial properties in PNC with attractive polymer-nanoparticle interactions: the thickness of the interfacial layer with hindered segmental relaxation decreases as MW increases, in sharp contrast to theoretical predictions. Further analyses reveal a reduction in mass density of the interfacial layer with increasing MW, which can elucidate these unexpected dynamic effects. Our observations call for a significant revision of the current understandings of PNCs and suggest interesting ways to tailor their properties.

We derive a time-domain mean-field equation to model the full temporal and spectral dynamics of light in singly resonant cavity-enhanced second-harmonic generation systems. We show that the temporal walk-off between the fundamental and the second-harmonic fields plays a decisive role under realistic conditions, giving rise to rich, previously unidentified nonlinear behavior. Through linear stability analysis and numerical simulations, we discover a new kind of quadratic modulation instability which leads to the formation of optical frequency combs and associated time-domain dissipative structures. Our numerical simulations show excellent agreement with recent experimental observations of frequency combs in quadratic nonlinear media [Phys. Rev. A 91, 063839 (2015)]. Thus, in addition to unveiling a new, experimentally accessible regime of nonlinear dynamics, our work enables predictive modeling of frequency comb generation in cavity-enhanced second-harmonic generation systems. We expect our findings to have wide impact on the study of temporal and spectral dynamics in a diverse range of dispersive, quadratically nonlinear resonators.

We demonstrate plasmon-assisted energy transfer between fluorophores located at distances up to $7\mu \mathrm{m}$ on the top of a thin silver film. Thanks to the strong confinement and large propagation length of surface plasmon polaritons, the range of the energy transfer is almost 2 orders of magnitude larger than the values reported in the literature so far. The parameters driving the energy transfer range are thoroughly characterized and are in very good agreement with theoretically expected values.

By experimenting on model colloids where depletion forces can be carefully tuned and quantified, we show that attractive interactions consistently “promote” particle settling, so much that the sedimentation velocity of a moderately concentrated dispersion can even exceed its single-particle value. At larger particle volume fraction $\varphi$, however, hydrodynamic hindrance eventually takes over. Hence, $v(\varphi )$ actually displays a nonmonotonic trend that may threaten the stability of the settling front to thermal perturbations. Finally, by discussing a representative case, we show that these results are relevant to the investigation of protein association effects by ultracentrifugation.

We present results from an analysis of all data taken by the BICEP2 and Keck Array cosmic microwave background (CMB) polarization experiments up to and including the 2014 observing season. This includes the first Keck Array observations at 95 GHz. The maps reach a depth of 50 nK deg in Stokes $Q$ and $U$ in the 150 GHz band and 127 nK deg in the 95 GHz band. We take auto- and cross-spectra between these maps and publicly available maps from WMAP and Planck at frequencies from 23 to 353 GHz. An excess over lensed $\mathrm{\Lambda }\mathrm{CDM}$ is detected at modest significance in the $95\times 150$ $BB$ spectrum, and is consistent with the dust contribution expected from our previous work. No significant evidence for synchrotron emission is found in spectra such as $23\times 95$, or for correlation between the dust and synchrotron sky patterns in spectra such as $23\times 353$. We take the likelihood of all the spectra for a multicomponent model including lensed $\mathrm{\Lambda }\mathrm{CDM}$, dust, synchrotron, and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio $r$) using priors on the frequency spectral behaviors of dust and synchrotron emission from previous analyses of WMAP and Planck data in other regions of the sky. This analysis yields an upper limit $r_{0.05}<0.09$ at 95% confidence, which is robust to variations explored in analysis and priors. Combining these $B$-mode results with the (more model-dependent) constraints from Planck analysis of CMB temperature plus baryon acoustic oscillations and other data yields a combined limit $r_{0.05}<0.07$ at 95% confidence. These are the strongest constraints to date on inflationary gravitational waves.

In this work we study the mechanical properties of a frustrated elastic ribbon spring—the non-Euclidean minimal spring. This spring belongs to the family of non-Euclidean plates: it has no spontaneous curvature, but its lateral intrinsic geometry is described by a non-Euclidean reference metric. The reference metric of the minimal spring is hyperbolic, and can be embedded as a minimal surface. We argue that the existence of a continuous set of such isometric minimal surfaces with different extensions leads to a complete degeneracy of the bulk elastic energy of the minimal spring under elongation. This degeneracy is removed only by boundary layer effects. As a result, the mechanical properties of the minimal spring are unusual: the spring is ultrasoft with a rigidity that depends on the thickness $t$ as $t^{7/2}$ and does not explicitly depend on the ribbon’s width. Moreover, we show that as the ribbon is widened, the rigidity may even decrease. These predictions are confirmed by a numerical study of a constrained spring. This work is the first to address the unusual mechanical properties of constrained non-Euclidean elastic objects.

In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius ${\mathrm{A}}^{*}$ (Sgr ${\mathrm{A}}^{*}$) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr ${\mathrm{A}}^{*}$ with an uncertainty of $\sim 1.5\mu \mathrm{as}$ (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained.