In turbulent flows, kinetic energy is transferred from the largest scales to progressively smaller scales, until it is ultimately converted into heat. The Navier-Stokes equations are almost universally used to study this process. Here, by comparing with molecular-gas-dynamics simulations, we show that the Navier-Stokes equations do not describe turbulent gas flows in the dissipation range because they neglect thermal fluctuations. We investigate decaying turbulence produced by the Taylor-Green vortex and find that in the dissipation range the molecular-gas-dynamics spectra grow quadratically with wave number due to thermal fluctuations, in agreement with previous predictions, while the Navier-Stokes spectra decay exponentially. Furthermore, the transition to quadratic growth occurs at a length scale much larger than the gas molecular mean free path, namely in a regime that the Navier-Stokes equations are widely believed to describe. In fact, our results suggest that the Navier-Stokes equations are not guaranteed to describe the smallest scales of gas turbulence for any positive Knudsen number.

We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries—termed “Pascal’s triangle symmetries”—which provides a natural U(1) generalization of a spin-($1/2$) system with Sierpinski triangle fractal symmetries introduced in Newman et al., [Phys. Rev. E 60, 5068 (1999).]. The Pascal’s triangle symmetry gives rise to exact degeneracies, as well as a manifold of low-energy states which are absent in the Sierpinski triangle model. Breaking the U(1) symmetry of this model to $Z_p$, with prime integer $p$, yields a lattice model with a unique fractal symmetry which is generated by an operator supported on a fractal subsystem with Hausdorff dimension $d_H=\ln (p(p+1)/2)/\ln p$. The Hausdorff dimension of the fractal can be probed through correlation functions at finite temperature. The phase diagram of these models at zero temperature in the presence of quantum fluctuations, as well as the potential physical construction of the U(1) model, is discussed.

The spatial distributions of antibonding ${\pi }^{*}$ and ${\sigma }^{*}$ states in epitaxial graphene multilayers are mapped using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic channeling simulations validate the interpretation of the spatially resolved signals in terms of electronic orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to resolve the distribution of unoccupied states. This work illustrates the current potential of core-level electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of materials, of huge interest to better understand chemical bonding among many other properties at interfaces and defects in solids.

The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $\nu =n/(2n+1)$ has a striking quantitative correspondence to the localization of a single electron in the ($n+1$)th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation, these results can be extended to situations where a finite density of quasiparticles is present.

We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. In addition to these magnetic phase transitions, we find topological phase transitions within the spin-flop phase. Both types of transitions manifest themselves in prominent and distinguishing features in the thermal conductivity, which changes by several orders of magnitude. The variation of temperature provides a tool to discern experimentally the two types of phase transitions. We include numerical results for the van der Waals magnet ${\mathrm{MnPS}}_3$.

Is a spontaneous perpetual reversal of the arrow of time possible? The out-of-time-ordered correlator (OTOC) is a standard measure of irreversibility, quantum scrambling, and the arrow of time. The question may be thus formulated more precisely and conveniently: can spatially ordered perpetual OTOC oscillations exist in many-body systems? Here we give a rigorous lower bound on the amplitude of OTOC oscillations in terms of a strictly local dynamical algebra allowing for identification of systems that are out-of-time-ordered (OTO) crystals. While OTOC oscillations are possible for few-body systems, due to the spatial order requirement OTO crystals cannot be achieved by effective single or few body dynamics, e.g., a pendulum or a condensate. Rather they signal perpetual motion of quantum scrambling. It is likewise shown that if a Hamiltonian satisfies this novel algebra, it has an exponentially large number of local invariant subspaces, i.e., Hilbert space fragmentation. Crucially, the algebra, and hence the OTO crystal, are stable to local unitary and dissipative perturbations. A Creutz ladder is shown to be an OTO crystal, which thus perpetually reverses its arrow of time.

We present new precision measurements of the elastic electron-proton scattering cross section for momentum transfer ($Q^2$) up to $15.75(\mathrm{GeV}/c{)}^2$. Combined with existing data, these provide an improved extraction of the proton magnetic form factor at high $Q^2$ and double the range over which a longitudinal or transverse separation of the cross section can be performed. The difference between our results and polarization data agrees with that observed at lower $Q^2$ and attributed to hard two-photon exchange (TPE) effects, extending to $8(\mathrm{GeV}/c{)}^2$ the range of $Q^2$ for which a discrepancy is established at $>95\%$ confidence. We use the discrepancy to quantify the size of TPE contributions needed to explain the cross section at high $Q^2$.

Multimode optical cavities can be used to implement interatomic interactions which are highly tunable in strength and range. For bosonic atoms trapped in an optical lattice we show that, for any finite range of the cavity-mediated interaction, quantum self-bound droplets dominate the ground state phase diagram. Their size and in turn density is not externally fixed but rather emerges from the competition between local repulsion and finite-range cavity-mediated attraction. We identify two different regimes of the phase diagram. In the strongly glued regime, the interaction range exceeds the droplet size and the physics resembles the one of the standard Bose-Hubbard model in a (self-consistent) external potential, where in the phase diagram two incompressible droplet phases with different filling are separated by one with a superfluid core. In the opposite weakly glued regime, we find instead direct first order transitions between the two incompressible phases, as well as pronounced metastability. The cavity field leaking out of the mirrors can be measured to distinguish between the various types of droplets.

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of the ground state. We show that, generically within the Hartree-Fock approximation, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides a possible explanation for unreconciled experimental observations on the quantum Hall effect in graphene.

Spin superconductor (SSC) is an exciton condensate state where the spin-triplet exciton superfluidity is charge neutral while spin $2(\hslash /2)$. In analogy to the Majorana zero mode (MZM) in topological superconductors, the interplay between SSC and band topology will also give rise to a specific kind of topological bound state obeying non-Abelian braiding statistics. Remarkably, the non-Abelian geometric phase here originates from the Aharonov-Casher effect of the “half-charge” other than the Aharonov-Bohm effect. Such topological bound state of SSC is bound with the vortex of electric flux gradient and can be experimentally more distinct than the MZM for being electrically charged. This theoretical proposal provides a new avenue investigating the non-Abelian braiding physics without the assistance of MZM and charge superconductor.

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely, charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.

The isothermal crystallization near the glass transition temperature from the melt state of poly(trimethylene terephthalate) has been studied by wide-angle x-ray diffraction (WAXD), small-angle x-ray scattering (SAXS), and optical microscopy. The SAXS and WAXD results show the crystallization mechanism in which the crystalline nodules cover the entire sample with the formation of aggregation regions. The analysis of the SAXS results using Kolmogorov-Johnson-Mehl-Avrami theory indicates that the formation kinetics of the aggregation regions is of three-dimensional homogeneous nucleation type. The analysis of the SAXS profiles using Sekimoto’s theory provides the growth velocity and the nucleation rate of the aggregation region. The temperature dependence of the growth velocity of the aggregation region is a natural extrapolation of that of spherulite to the high supercooling region. The temperature dependence of the nucleation rate of the aggregation region is also represented by the parameters of the spherulitic growth rate. The result of the growth velocities of the aggregation region and the spherulite suggests the existence of precursors at the front of the crystal growth.

When stretched, both DNA and RNA duplexes change their twist angles through twist-stretch coupling. The coupling is negative for DNA but positive for RNA, which is not yet completely understood. Here, our magnetic tweezers experiments show that the coupling of RNA reverses from positive to negative by multivalent cations. Combining with the previously reported tension-induced negative-to-positive coupling reversal of DNA, we propose a unified mechanism of the couplings of both RNA and DNA based on molecular dynamics simulations. Two deformation pathways are competing when stretched: shrinking the radius causes positive couplings but widening the major groove causes negative couplings. For RNA whose major groove is clamped by multivalent cations and canonical DNA, their radii shrink when stretched, thus exhibiting positive couplings. For elongated DNA whose radius already shrinks to the minimum and canonical RNA, their major grooves are widened when stretched, thus exhibiting negative couplings.

Gravitational-wave measurements of the tidal deformability in neutron-star binary coalescences can be used to infer the still unknown equation of state (EOS) of dense matter above the nuclear saturation density. By employing a Bayesian-ranking test, we quantify the ability of current and future gravitational-wave observations to discriminate among families of nuclear-physics based EOS which differ in particle content and ab initio microscopic calculations. While the constraining power of GW170817 is limited, we show that even twenty coalescences detected by LIGO-Virgo at design sensitivity are not enough to discriminate between EOS with similar softness but distinct microphysics. However, just a single detection with a third-generation detector such as the Einstein Telescope or Cosmic Explorer will rule out several families of EOS with very strong statistical significance and can discriminate among models which feature similar softness, hence, constraining the properties of nuclear matter to unprecedented levels.