“Beverloo’s law” is considered as the standard expression to estimate the flow rate of particles through apertures. This relation was obtained by simple dimensional analysis and includes empirical parameters whose physical meaning is poorly justified. In this Letter, we study the density and velocity profiles in the flow of particles through an aperture. We find that, for the whole range of apertures studied, both profiles are self-similar. Hence, by means of the functionality obtained for them the mass flow rate is calculated. The comparison of this expression with the Beverloo’s one reveals some differences which are crucial to understanding the mechanism that governs the flow of particles through orifices.

We investigate the possibility that the anomalous acceleration of the Pioneer 10 and 11 spacecraft is due to the recoil force associated with an anisotropic emission of thermal radiation off the vehicles. To this end, relying on the project and spacecraft design documentation, we constructed a comprehensive finite-element thermal model of the two spacecraft. Then, we numerically solve thermal conduction and radiation equations using the actual flight telemetry as boundary conditions. We use the results of this model to evaluate the effect of the thermal recoil force on the Pioneer 10 spacecraft at various heliocentric distances. We found that the magnitude, temporal behavior, and direction of the resulting thermal acceleration are all similar to the properties of the observed anomaly. As a novel element of our investigation, we develop a parametrized model for the thermal recoil force and estimate the coefficients of this model independently from navigational Doppler data. We find no statistically significant difference between the two estimates and conclude that, once the thermal recoil force is properly accounted for, no anomalous acceleration remains.

An equilibrium state can be represented by a pure quantum state, which we call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a simple method of obtaining it. A single realization of the TPQ state suffices for calculating all statistical-mechanical properties, including correlation functions and genuine thermodynamic variables, of a quantum system at finite temperature.

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a ($2J+1$)-dimensional Hilbert space (or, equivalently, of a spin-$J$ system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of $2J$ fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

${}^{77}\mathrm{Se}$ and ${}^{87}\mathrm{Rb}$ nuclear magnetic resonance (NMR) experiments on ${\mathrm{Rb}}_{0.74}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ reveal clearly distinct spectra originating from a majority antiferromagnetic (AF) and a minority metallic-superconducting (SC) phase. The very narrow NMR line of the SC phase evidences the absence of Fe vacancies and any trace of AF order. The Rb content of the SC phase is deduced from intensity measurements identifying ${\mathrm{Rb}}_{0.3(1)}{\mathrm{Fe}}_2{\mathrm{Se}}_2$ as the actual composition of the SC fraction. The resulting estimate of $0.15\mathrm{electrons}/\mathrm{Fe}$ brings this class of superconductors 245 family closer to the other Fe-based superconductor families.

A novel hydrodynamic-driven stability analysis is presented for surface patterns on speleothems, i.e., secondary sedimentary cave deposits, by coupling fluid dynamics to the geochemistry of calcite precipitation or dissolution. Falling film theory provides the solution for the flow-field and depth perturbations, the latter being crucial to triggering patterns known as crenulations. In a wide range of Reynolds numbers, the model provides the dominant wavelengths and pattern celerities, in fair agreement with field data. The analysis of the phase velocity of ridges on speleothems has a potential as a proxy of past film flow rates, thus suggesting a new support for paleoclimate analyses.

We study the quantum electrodynamics vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel’dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis.

We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom’s Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.

Although the precise microscopic knowledge of van der Waals interactions is crucial for understanding bonding in weakly bonded layered compounds, very little quantitative information on the strength of interlayer interaction in these materials is available, either from experiments or simulations. Here, using many-body perturbation and advanced density-functional theory techniques, we calculate the interlayer binding and exfoliation energies for a large number of layered compounds and show that, independent of the electronic structure of the material, the energies for most systems are around $20\mathrm{meV}/{\AA }^2$. This universality explains the successful exfoliation of a wide class of layered materials to produce two-dimensional systems, and furthers our understanding the properties of layered compounds in general.

It is demonstrated that the nearest-neighbor Mn pair on the GaAs (001) surface has a lower energy for the $[\overline{1}10]$ direction compared to the [110] case. According to the group theory and Luttinger’s method of invariants, this specific Mn distribution results in bulk uniaxial in-plane and out-of-plane anisotropies. The sign and magnitude of the corresponding anisotropy energies determined by a perturbation method and ab initio computations are consistent with experimental results.

We report hitherto unnoticed patterns in quasar light curves. We characterize segments of the quasar’s light curves with the slopes of the straight lines fit through them. These slopes appear to be directly related to the quasars’ redshifts. Alternatively, using only global shifts in time and flux, we are able to find significant overlaps between the light curves of different pairs of quasars by fitting the ratio of their redshifts. We are then able to reliably determine the redshift of one quasar from another. This implies that one can use quasars as standard clocks, as we explicitly demonstrate by constructing two independent methods of finding the redshift of a quasar from its light curve.

A search for $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to {\mu }^{+}{\mu }^{-}$ decays is performed using $1.0{\mathrm{fb}}^{-1}$ of $pp$ collision data collected at $\sqrt{s}=7\mathrm{TeV}$ with the LHCb experiment at the Large Hadron Collider. For both decays, the number of observed events is consistent with expectation from background and standard model signal predictions. Upper limits on the branching fractions are determined to be $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})<4.5(3.8)\times {10}^{-9}$ and $\mathcal{B}(B^0\to {\mu }^{+}{\mu }^{-})<1.0(0.81)\times {10}^{-9}$ at 95% (90%) confidence level.

We describe a method for creating a three-dimensional analogue to Rashba spin-orbit coupling in systems of ultracold atoms. This laser induced coupling uses Raman transitions to link four internal atomic states with a tetrahedral geometry, and gives rise to a Dirac point that is robust against environmental perturbations. We present an exact result showing that such a spin-orbit coupling in a fermionic system always gives rise to a molecular bound state.

Single molecular magnets (SMMs) are among the potential systems for quantum memory and quantum information processing. Quantum coherence and oscillation are critical for these applications. The ground-state quantum coherence and Rabi oscillations of the SMM ${\mathrm{V}}_{15}$ ($[{\mathrm{V}}_{15}^{\mathrm{IV}}{\mathrm{As}}_6^{\mathrm{III}}{\mathrm{O}}_{42}({\mathrm{H}}_2\mathrm{O}){]}^{6-}$) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time $T_2$ for the ground states of the ${\mathrm{V}}_{15}$ ion of collective spin $S=1/2$, in addition to confirming the previously reported results for the $S=3/2$ excited states. The oscillations of $S=3/2$ and $S=1/2$ states are of different frequencies, and so can be separately selected for purposive manipulations. $T_2$ of $188\pm 4\mathrm{ns}$ ($S=3/2$) and $149\pm 10\mathrm{ns}$ ($S=1/2$) are much less than $T_1\sim 12\mu \mathrm{s}$ and are further extendible via various approaches for qubit implementations.

We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked $\log (n)$ entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in “$q$-sampling” protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.

Ferroelectric polarization of $6.3\mu \mathrm{C}{\mathrm{cm}}^{-2}$ is induced by the neutral-to-ionic transition, upon which nonpolar molecules of electron donor tetrathiafulvalene (TTF) and acceptor $p$-chloranil (CA) are incompletely ionized to $\pm 0.60e$ and dimerized along the molecular stacking chain. We find that the ferroelectric properties are governed by intermolecular charge transfer rather than simple displacement of static point charge on molecules. The observed polarization and poling effect on the absolute structural configuration can be interpreted in terms of electronic ferroelectricity, which not only exhibits antiparallel polarity to the ionic displacement but also enhances the polarization more than 20 times that of the point-charge model.

Evolving systems rely on the storage and replication of genetic information. Here we present an autonomous, purely thermally driven replication mechanism. A pool of hairpin molecules, derived from transfer RNA replicates the succession of a two-letter code. Energy is first stored thermally in metastable hairpins. Thereafter, energy is released by a highly specific and exponential replication with a duplication time of 30 s, which is much faster than the tendency to produce false positives in the absence of template. Our experiments propose a physical rather than a chemical scenario for the autonomous replication of protein encoding information in a disequilibrium setting.

We present a limiting model for thin non-Euclidean elastic rods. Originating from the three-dimensional (3D) reference metric of the rod, which is determined by its internal material structure, we derive a 1D reduced rod theory. Specifically, we show how the spontaneous twist and curvature of a rod emerge from the reference metric derivatives. Thus, the model allows calculating the unconstrained equilibrium configuration of a thin rod directly from its internal structure. The model is applied to the study of cells from members of the Geraniaceae plant family and their configurational response to dehydration. We show how the geometrical arrangement of cellulose fibrils on the cell walls determines the helical shapes of isolated cells.

We report the first direct observation of collective quantum fluctuations in a continuous field. Shot-to-shot atom number fluctuations in small subvolumes of a weakly interacting, ultracold atomic 1D cloud are studied using in situ absorption imaging and statistical analysis of the density profiles. In the cloud centers, well in the quantum quasicondensate regime, the ratio of chemical potential to thermal energy is $\mu /k_{B}T\simeq 4$, and, owing to high resolution, up to 20% of the microscopically observed fluctuations are quantum phonons. Within a nonlocal analysis at variable observation length, we observe a clear deviation from a classical field prediction, which reveals the emergence of dominant quantum fluctuations at short length scales, as the thermodynamic limit breaks down.

Artificial gauge fields open the possibility to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman shifts resulting from a combination of Raman coupling and radio-frequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.