A Hamiltonian operator $\widehat{H}$ is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of $\widehat{H}$ is $2xp$, which is consistent with the Berry-Keating conjecture. While $\widehat{H}$ is not Hermitian in the conventional sense, $i\widehat{H}$ is $\mathcal{P}\mathcal{T}$ symmetric with a broken $\mathcal{P}\mathcal{T}$ symmetry, thus allowing for the possibility that all eigenvalues of $\widehat{H}$ are real. A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that $\widehat{H}$ is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true.

We analytically investigate backreaction by a quantum scalar field on two rotating Bañados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we find that quantum effects lead to the formation of a horizon that shields it, thus supporting evidence for the rôle of quantum mechanics as a cosmic censor in nature.

Low-dimensional materials could display anomalous thermal conduction that the thermal conductivity ($\kappa$) diverges with increasing lengths, in ways inconceivable in any bulk materials. However, previous theoretical or experimental investigations were plagued with many finite-size effects, rendering the results either indirect or inconclusive. Indeed, investigations on the anomalous thermal conduction must demand the sample length to be sufficiently long so that the phenomena could emerge from unwanted finite-size effects. Here we report experimental observations that the $\kappa$’s of single-wall carbon nanotubes continuously increase with their lengths over 1 mm, reaching at least $8640\mathrm{W}/\mathrm{mK}$ at room temperature. Remarkably, the anomalous thermal conduction persists even with the presence of defects, isotopic disorders, impurities, and surface absorbates. Thus, we demonstrate that the anomalous thermal conduction in real materials can persist over much longer distances than previously thought. The finding would open new regimes for wave engineering of heat as well as manipulating phonons at macroscopic scales.

For a dilute two-dimensional Bose gas the universal equation of state has a logarithmic dependence on the $s$-wave scattering length. Here we derive nonuniversal corrections to this equation of state, taking account of finite-range effects of the interatomic potential. Our beyond-mean-field analytical results are obtained performing dimensional regularization of divergent zero-point quantum fluctuations within the finite-temperature formalism of functional integration. In particular, we find that in the grand canonical ensemble the pressure has a nonpolynomial dependence on the finite- range parameter and it is a highly nontrivial function of chemical potential and temperature.

The neutralization of a single ${\mathrm{He}}^{2+}$ ion near a Ir surface leads to the emission of an electron pair. Via coincidence spectroscopy we give evidence that a sizable amount of these electron pairs originate from a correlated single step neutralization of the ion involving a total of four electrons from the metal. These correlated electron pairs cannot be explained in the common picture of two consecutive and independent neutralization steps. We infer a characteristic time scale for the correlated electron dynamics in the metal of $40–400\mathrm{as}$.

The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.

We model the superfluid flow of liquid helium over the rough surface of a wire (used to experimentally generate turbulence) profiled by atomic force microscopy. Numerical simulations of the Gross-Pitaevskii equation reveal that the sharpest features in the surface induce vortex nucleation both intrinsically (due to the raised local fluid velocity) and extrinsically (providing pinning sites to vortex lines aligned with the flow). Vortex interactions and reconnections contribute to form a dense turbulent layer of vortices with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk. We characterize this layer for various imposed flows. As boundary layers conventionally arise from viscous forces, this result opens up new insight into the nature of superflows.

We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g., thermal noise) injected into the waveguide. We extend the model and protocol to a cavity QED setup, where atomic ensembles, or single atoms representing quantum memory, are coupled to a cavity mode. We present a detailed study of sensitivity to imperfections, and apply a quantum error correction protocol to account for random losses (or additions) of photons in the waveguide. Our numerical analysis is enabled by matrix product state techniques to simulate the complete quantum circuit, which we generalize to include thermal input fields. Our discussion applies both to photonic and phononic quantum networks.

Correlated valence electrons in Ag and Cu are investigated using double photoemission spectroscopy driven by a high-order harmonic light source. Electron pairs consisting of two $d$ electrons as well as pairs with one $sp$ and one $d$ electron are resolved in the two-dimensional energy spectrum. Surprisingly, the intensity ratio of $sp\text{−}d$ to $d\text{−}d$ pairs from Ag is 3 times higher than in the self-convoluted density of states. Our results directly show the band-resolved configurations of electron pairs in solids and emphasize a band-dependent picture for electron correlation even in these paradigmatic metals.

We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, “shadow” diamonds appear, shifted by $1e$ in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island ($\sim 1\mu \mathrm{s}$) and sets a bound for a weakly coupled island ($>10\mu \mathrm{s}$). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on axis, perpendicular, and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.

Charge-dependent azimuthal particle correlations with respect to the second-order event plane in $p\text{−}\mathrm{Pb}$ and PbPb collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV have been studied with the CMS experiment at the LHC. The measurement is performed with a three-particle correlation technique, using two particles with the same or opposite charge within the pseudorapidity range $|\eta |<2.4$, and a third particle measured in the hadron forward calorimeters ($4.4<|\eta |<5$). The observed differences between the same and opposite sign correlations, as functions of multiplicity and $\eta$ gap between the two charged particles, are of similar magnitude in $p\text{−}\mathrm{Pb}$ and PbPb collisions at the same multiplicities. These results pose a challenge for the interpretation of charge-dependent azimuthal correlations in heavy ion collisions in terms of the chiral magnetic effect.

It is commonly believed that, in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: The gap is nodeless, it has point nodes, or it has line nodes. Here, we show that, for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead, it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by “inflating” point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a ${\mathbb{Z}}_2$ invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these ${\mathbb{Z}}_2$-protected Fermi surfaces to be ubiquitous.

When an ordered spin system of a given dimensionality undergoes a second order phase transition, the dependence of the order parameter, i.e., magnetization on temperature, can be well described by thermal excitations of elementary collective spin excitations (magnons). However, the behavior of magnons themselves, as a function of temperature and across the transition temperature $T_C$, is an unknown issue. Utilizing spin-polarized high resolution electron energy loss spectroscopy, we monitor the high-energy (terahertz) magnons, excited in an ultrathin ferromagnet, as a function of temperature. We show that the magnons’ energy and lifetime decrease with temperature. The temperature-induced renormalization of the magnons’ energy and lifetime depends on the wave vector. We provide quantitative results on the temperature-induced damping and discuss the possible mechanism, e.g., multimagnon scattering. A careful investigation of physical quantities determining the magnons’ propagation indicates that terahertz magnons sustain their propagating character even at temperatures far above $T_C$.

We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.

A scanning tunneling microscope is used to generate the electroluminescence of phthalocyanine molecules deposited on $\mathrm{NaCl}/\mathrm{Ag}(111)$. Photon spectra reveal an intense emission line at $\approx 1.9\mathrm{eV}$ that corresponds to the fluorescence of the molecules, and a series of weaker redshifted lines. Based on a comparison with Raman spectra acquired on macroscopic molecular crystals, these spectroscopic features can be associated with the vibrational modes of the molecules and provide a detailed chemical fingerprint of the probed species. Maps of the vibronic features reveal submolecularly resolved structures whose patterns are related to the symmetry of the probed vibrational modes.

Ice bridges are static structures composed of tightly packed sea ice that can form during the course of its flow through a narrow strait. Despite their important role in local ecology and climate, the formation and breakup of ice bridges is not well understood and has proved difficult to predict. Using long-wave approximations and a continuum description of sea ice dynamics, we develop a one-dimensional theory for the wind-driven formation of ice bridges in narrow straits, which is verified against direct numerical simulations. We show that for a given wind stress and minimum and maximum channel widths, a steady-state ice bridge can only form beyond a critical value of the thickness and the compactness of the ice field. The theory also makes quantitative predictions for ice fluxes, which are particularly useful to estimate the ice export associated with the breakup of ice bridges. We note that similar ideas are applicable to dense granular flows in confined geometries.

Photographs of the asteroid Itokawa reveal unexpectedly strong size segregation between lowlands populated almost entirely by small pebbles and highlands consisting of larger boulders. We propose that this segregation may be caused by a simple and unexplored effect: pebbles accreting onto the asteroid rebound from boulders, but sink into pebbly regions. By number, overwhelmingly more particles on Itokawa are pebbles, and collisions involving these pebbles must unavoidably cause pebbly regions to grow. We carry out experiments and simulations that demonstrate that this mechanism of size sorting based on simple counting of grains produces strong lateral segregation that reliably obeys an analytic formula.

Ferrofluid flow along a tube of radius $R$ in a constant axial magnetic field is revisited. Our analytical solution and numerical simulations predict a transition from an initially axial flow to a steady swirling one. The swirl dynamo arises above some critical pressure drop and magnetic field strength. The new flow pattern consists of two phases of different symmetry: The flow in the core resembles Poiseuille flow in a rotating tube of the radius $r_{*}<R$, where each fluid element moves along a screw path, and the annular layer of the thickness $R-r_{*}$, where the flow remains purely axial. These phases are separated by a thin domain wall. The swirl appearance is accompanied with a sharp increase in the flow rate that might serve for the detection of the swirling instability.

Analytic results for (Q)ED processes in external fields are limited to a few special cases, such as plane waves. However, the strong focusing of intense laser fields implies a need to go beyond the plane wave model. By exploiting Poincaré symmetry and superintegrability we show how to construct, and solve without approximation, new models of laser-matter interactions. We illustrate the method with a model of a radially polarized (TM) laser beam, for which we exactly determine the classical orbits and quantum wave functions. Including in this way the effects of transverse field structure should improve predictions and analyses for experiments at intense laser facilities.