We study the number of distinct sites $S_N(t)$ and common sites $W_N(t)$ visited by $N$ independent one dimensional random walkers, all starting at the origin, after $t$ time steps. We show that these two random variables can be mapped onto extreme value quantities associated with $N$ independent random walkers. Using this mapping, we compute exactly their probability distributions $P_N^d(S,t)$ and $P_N^c(W,t)$ for any value of $N$ in the limit of large time $t$, where the random walkers can be described by Brownian motions. In the large $N$ limit one finds that $S_N(t)/\sqrt{t}\propto 2\sqrt{\log \hspace{0.17em}N}+\tilde{s}/(2\sqrt{\log \hspace{0.17em}N})$ and $W_N(t)/\sqrt{t}\propto \tilde{w}/N$ where $\tilde{s}$ and $\tilde{w}$ are random variables whose probability density functions are computed exactly and are found to be nontrivial. We verify our results through direct numerical simulations.

An intermediate-mass black hole (IMBH) may have a dark-matter (DM) minihalo around it and develop a spiky structure within less than a parsec from the IMBH. When a stellar mass object is captured by the minihalo, it eventually infalls into such an IMBH due to gravitational wave backreaction which in turn could be observed directly by future space-borne gravitational wave experiments such as eLISA and NGO. In this Letter, we show that the gravitational wave (GW) detectability strongly depends on the radial profile of the DM distribution. So if the GW is detected, the power index, that is, the DM density distribution, would be determined very accurately. The DM density distribution obtained would make it clear how the IMBH has evolved from a seed black hole and whether the IMBH has experienced major mergers in the past. Unlike the $\gamma$-ray observations of DM annihilation, GW is just sensitive to the radial profile of the DM distribution and even to noninteracting DM. Hence, the effect we demonstrate here can be used as a new and powerful probe into DM properties.

The quantum numbers of the $X(3872)$ meson are determined to be $J^{PC}=1^{++}$ based on angular correlations in $B^{+}\to X(3872)K^{+}$ decays, where $X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ and $J/\psi \to {\mu }^{+}{\mu }^{-}$. The data correspond to $1.0{\mathrm{fb}}^{-1}$ of $pp$ collisions collected by the LHCb detector. The only alternative assignment allowed by previous measurements $J^{PC}=2^{-+}$ is rejected with a confidence level equivalent to more than 8 Gaussian standard deviations using a likelihood-ratio test in the full angular phase space. This result favors exotic explanations of the $X(3872)$ state.

Ground-state two-proton ($2p$) radioactivity is a decay mode found in isotopes of elements with even atomic numbers located beyond the two-proton drip line. So far, this exotic process has been experimentally observed in a few light- and medium-mass nuclides with $Z\le 30$. In this study, using state-of-the-art nuclear density functional theory, we globally analyze $2p$ radioactivity and for the first time identify $2p$-decay candidates in elements heavier than strontium. We predict a few cases where the competition between $2p$ emission and $\alpha$ decay may be observed. In nuclei above lead, the $\alpha$-decay mode is found to be dominating and no measurable candidates for the $2p$ radioactivity are expected.

A detailed study of inelastic x-ray scattering from the ground state to the ${}^3\Sigma _g(3{\sigma }_g^{-1}3s_g^1)$ state of the ${\mathrm{O}}_2$ molecule is presented. The observed angular anisotropy shows that the vibrational excitations within this final state are strongly dependent on the polarization of the incident radiation. The analysis demonstrates that this is a manifestation of interference between resonant and direct nonresonant inelastic x-ray scattering. This interference provides a new tool to monitor nuclear dynamics by relative rotation of the polarization vectors of the incident and scattered photons.

We determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. We then show that ultracold molecules trapped in optical lattices can be used as a quantum simulator to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with external electric fields. The parameters of current experiments place them in the region where one of the transitions occurs. We also propose a scheme to measure the polaron dispersion using stimulated Raman spectroscopy.

Vibrational Feshbach resonances are dominant features of positron annihilation for incident positron energies in the range of the molecular vibrations. Studies in relatively small molecules are described that elucidate the role of intramolecular vibrational energy redistribution into near-resonant multimode states, and the subsequent coupling of these modes to the positron continuum, in suppressing or enhancing these resonances. The implications for annihilation in other molecular species, and the necessary ingredients of a more complete theory of resonant positron annihilation, are discussed.

The expectation value of a quantum system observable can be written as a sum over interfering pathway amplitudes. In this Letter, we demonstrate for the fist time adaptive manipulation of quantum pathways using the Hamiltonian encoding-observable decoding (HE-OD) technique. The principles of HE-OD are illustrated for population transfer in atomic rubidium using shaped femtosecond laser pulses. The ability to manipulate multiple pathway amplitudes is of fundamental importance in all quantum control applications.

We provide the first experimental demonstration of defect states in parity-time ($\mathcal{P}\mathcal{T}$) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a $\mathcal{P}\mathcal{T}$-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics.

Systems of nonlocally coupled oscillators can exhibit complex spatiotemporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling typical for phase oscillators. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multichimera states arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models.

In this Letter, we use a nonequilibrium statistical theory, the stochastic structural stability theory (SSST), to show that an extended version of this theory can make predictions for the formation of nonzonal as well as zonal structures (lattice and stripe patterns) in forced homogeneous turbulence on a barotropic $\beta$ plane. Comparison of the theory with nonlinear simulations demonstrates that SSST predicts the parameter values for the emergence of coherent structures and their characteristics (scale, amplitude, phase speed) as they emerge and at finite amplitude. It is shown that nonzonal structures (lattice states or zonons) emerge at lower energy input rates of the stirring compared to zonal flows (stripe states) and their emergence affects the dynamics of jet formation.

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.

We investigate the accuracy of a number of wave function based methods at the heart of quantum chemistry for metallic systems. Using the Hartree-Fock wave function as a reference, perturbative (Møller-Plesset) and coupled cluster theories are used to study the uniform electron gas model. Our findings suggest that nonperturbative coupled cluster theories are acceptable for modeling electronic interactions in metals while perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely used coupled cluster singles and doubles plus perturbative triples method that lifts the divergent behavior and is shown to give very accurate correlation energies for the homogeneous electron gas.

We report measurements of heat transport along the edge conducting channels in monolayer graphene in the integer quantum Hall regime. Hot charge carriers are injected to the edge channels, and the thermoelectric voltage is measured at a distance along the edge from the heat injection point. We confirm that heat transport in graphene in the quantum Hall regime is chiral and the thermoelectric signal is correlated with the charge conductance of ballistic transport, following the Mott relation. The thermoelectric signal decays with distance from the heater, indicating that carriers are partially thermalized during edge transmission.

Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator-superconductor (SC)-quantum spin Hall insulator junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a five-terminal setup or by using the spin selection of the quantum spin Hall effect in an $H$-bar structure.

We solve a long-standing puzzle in statistical mechanics of disordered systems. By performing a high-statistics simulation of the $D=3$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.

Universal sensing of the motion of mechanical resonators with high precision and low backaction is of paramount importance in ultraweak signal detection, which plays a fundamental role in modern physics. Here we present a universal scheme that mechanically transfers the motion of the resonator not directly measurable to the one that can be precisely measured using mechanical frequency conversion. Demonstration of the scheme at room temperature shows that both the motion imprecision and the backaction force are below the intrinsic level of the objective resonator, which agrees well with our theoretical prediction. The scheme developed here provides an effective interface between an arbitrary mechanical resonator and a high quantum efficient displacement sensor, and is expected to find extensive applications in highly demanding mechanical-based force measurements.

We perform polarization-resolved Raman spectroscopy on graphene in magnetic fields up to 45 T. This reveals a filling-factor-dependent, multicomponent anticrossing structure of the Raman $G$ peak, resulting from magnetophonon resonances between magnetoexcitons and $E_{2g}$ phonons. This is explained with a model of Raman scattering taking into account the effects of spatially inhomogeneous carrier densities and strain. Random fluctuations of strain-induced pseudomagnetic fields lead to increased scattering intensity inside the anticrossing gap, consistent with the experiments.

Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, through applied fields, or in quenches to the ordered phase. In equilibrium, pairs of defects coarsen and annihilate as the uniform ground state is approached. Here we show that defects in active liquid crystals exhibit profoundly different behavior, depending on the degree of activity and its contractile or extensile character. While contractile systems enhance the annihilation dynamics of passive systems, extensile systems act to drive defects apart so that they swarm around in the manner of topologically well-characterized self-propelled particles. We develop a simple analytical model for the defect dynamics which reproduces the key features of both the numerical solutions and recent experiments on microtubule-kinesin assemblies.

Taylor dispersion—shear-induced enhancement of translational diffusion—is an important phenomenon with applications ranging from pharmacology to geology. Through experiments and simulations, we show that rotational diffusion is also enhanced for anisotropic particles in oscillatory shear. This enhancement arises from variations in the particle’s rotation (Jeffery orbit) and depends on the strain amplitude, rate, and particle aspect ratio in a manner that is distinct from the translational diffusion. This separate tunability of translational and rotational diffusion opens the door to new techniques for controlling positions and orientations of suspended anisotropic colloids.