It is traditionally assumed that Zipf’s law implies the power-law growth of the number of different elements with the total number of elements in a system—the so-called Heaps’ law. We show that a careful definition of Zipf’s law leads to the violation of Heaps’ law in random systems, with growth curves that have a convex shape in log-log scale. These curves fulfill universal data collapse that only depends on the value of Zipf’s exponent. We observe that real books behave very much in the same way as random systems, despite the presence of burstiness in word occurrence. We advance an explanation for this unexpected correspondence.

The ability to probe energy flow in molecules, following the absorption of ultraviolet light, is crucial to unraveling photophysical phenomena. Here we excite a coherent superposition of vibrational states in the first excited electronic state (${\mathit{S}}_1$) in catechol, resulting in a vibrational wave packet. The observed quantum beats, assigned to superpositions of the low-frequency, and strongly mixed, O–H torsional mode ${\tau }_2$, elegantly demonstrate how changes in geometry upon photoionization from the $S_1$ state to the ground state of the cation ($D_0$) enables one to probe energy flow at the very early stages of photoexcitation in this biological chromophore.

The on-chip generation of nonclassical states of light is a key requirement for future optical quantum hardware. In solid-state cavity quantum electrodynamics, such nonclassical light can be generated from self-assembled quantum dots strongly coupled to photonic crystal cavities. Their anharmonic strong light-matter interaction results in large optical nonlinearities at the single photon level, where the admission of a single photon into the cavity may enhance (photon tunneling) or diminish (photon blockade) the probability for a second photon to enter the cavity. Here, we demonstrate that detuning the cavity and quantum-dot resonances enables the generation of high-purity nonclassical light from strongly coupled systems. For specific detunings we show that not only the purity but also the efficiency of single-photon generation increases significantly, making high-quality single-photon generation by photon blockade possible with current state-of-the-art samples.

We present magnetic susceptibility, resistivity, specific heat, and thermoelectric power measurements on $({\mathrm{Ce}}_{1-x}{\mathrm{La}}_x){\mathrm{Cu}}_2{\mathrm{Ge}}_2$ single crystals ($0\le x\le 1$). With La substitution, the antiferromagnetic temperature $T_N$ is suppressed in an almost linear fashion and moves below 0.36 K, the base temperature of our measurements for $x>0.8$. Surprisingly, in addition to robust antiferromagnetism, the system also shows low temperature coherent scattering below $T_{\mathrm{coh}}$ up to $\sim 0.9$ of La, indicating a small percolation limit $\sim 9\%$ of Ce. $T_{\mathrm{coh}}$ as a function of magnetic field was found to have different behavior for $x<0.9$ and $x>0.9$. Remarkably, $(T_{\mathrm{coh}}{)}^2$ at $H=0$ was found to be linearly proportional to $T_N$. The jump in the magnetic specific heat $\delta C_m$ at $T_N$ as a function of $T_K/T_N$ for $({\mathrm{Ce}}_{1-x}{\mathrm{La}}_x){\mathrm{Cu}}_2{\mathrm{Ge}}_2$ follows the theoretical prediction based on the molecular field calculation for the $S=1/2$ resonant level model.

We find, through first-principles calculations, that hole doping induces a ferromagnetic phase transition in monolayer GaSe. Upon increasing hole density, the average spin magnetic moment per carrier increases and reaches a plateau near $1.0{\mu }_B$ per carrier in a range of $3\times {10}^{13}/{\mathrm{cm}}^2-1\times {10}^{14}/{\mathrm{cm}}^2$, with the system in a half-metal state before the moment starts to descend abruptly. The predicted itinerant magnetism originates from an exchange splitting of electronic states at the top of the valence band, where the density of states exhibits a sharp van Hove singularity in this quasi-two-dimensional system.

We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.

We study the angular broadening of a medium-induced QCD cascade. We derive the equation that governs the evolution of the average transverse momentum squared of the gluons in the cascade as a function of the medium length, and we solve this equation analytically. Two regimes are identified. For a medium of a not too large size, and for not too soft gluons, the transverse momentum grows with the size of the medium according to standard momentum broadening. The other regime, visible for a medium of a sufficiently large size and very soft gluons, is a regime dominated by multiple branchings: there, the average transverse momentum saturates to a value that is independent of the size of the medium. This structure of the in-medium QCD cascade is, at least qualitatively, compatible with the recent LHC data on dijet asymmetry.

We demonstrate the mixing of rotational states in the ground electronic state using microwave radiation to enhance optical cycling in the molecule yttrium (II) monoxide (YO). This mixing technique is used in conjunction with a frequency modulated and chirped continuous wave laser to slow longitudinally a cryogenic buffer-gas beam of YO. We generate a flux of YO below $10\mathrm{m}/\mathrm{s}$, directly loadable into a three-dimensional magneto-optical trap. This technique opens the door for laser cooling of diatomic molecules with more complex loss channels due to intermediate states.

We analyze the low-energy physics of nearly ferromagnetic metals in two spatial dimensions using the functional renormalization group technique. We find a new low-energy fixed point, at which the fermionic (electronlike) excitations are non-Fermi-liquid ($z_f=13/10$) and the magnetic fluctuations exhibit an anomalous Landau damping whose rate vanishes as ${\mathrm{\Gamma }}_{\mathbf{q}}\sim |\mathbf{q}{|}^{3/5}$ in the low-$|\mathbf{q}|$ limit. We discuss this renormalization of the Landau-damping exponent, which is the major novel prediction of our work, and highlight the possible link between that renormalization and neutron-scattering data on ${\mathrm{UGe}}_2$ and related compounds. Implications of our analysis for ${\mathrm{YFe}}_2{\mathrm{Al}}_{10}$ are also discussed.

We report on the observation of macroscopic free exciton photoluminescence (PL) rings that appear in spatially resolved PL images obtained on a high purity GaAs sample. We demonstrate that a spatial temperature gradient in the photocarrier system, which is due to nonresonant optical excitation, locally modifies the population balance between free excitons and the uncorrelated electron-hole plasma described by the Saha equation and accounts for the experimentally observed nontrivial PL profiles. The exciton ring formation is a particularly instructive manifestation of the spatially dependent thermodynamics of a partially ionized exciton gas in a bulk semiconductor.

We report on a quantitative measurement of the spatial coherence of electrons emitted from a sharp metal needle tip. We investigate the coherence in photoemission triggered by a near-ultraviolet laser with a photon energy of 3.1 eV and compare it to dc-field emission. A carbon nanotube is brought into close proximity to the emitter tip to act as an electrostatic biprism. From the resulting electron matter wave interference fringes, we deduce an upper limit of the effective source radius both in laser-triggered and dc-field emission mode, which quantifies the spatial coherence of the emitted electron beam. We obtain $(0.80\pm 0.05)\mathrm{nm}$ in laser-triggered and $(0.55\pm 0.02)\mathrm{nm}$ in dc-field emission mode, revealing that the outstanding coherence properties of electron beams from needle tip field emitters are largely maintained in laser-induced emission. In addition, the relative coherence width of 0.36 of the photoemitted electron beam is the largest observed so far. The preservation of electronic coherence during emission as well as ramifications for time-resolved electron imaging techniques are discussed.

We derive rigorous quantum mechanical bounds for the heat current through a nanojunction connecting two thermal baths at different temperatures. Based on exact sum rules, these bounds compliment the well-known quantum of thermal conductance ${\kappa }_Q\equiv \pi k_B^{2}T/6\hslash$, which provides a bound for low-temperature heat transport in all systems, but is saturated only for noninteracting transport. In contrast, our bounds are saturated at high temperatures—but still in the quantum regime—even when interactions are very strong. We evaluate these bounds for harmonic and strongly anharmonic junction models and compare with numerical approaches.

Quantum $n$-body correlations cannot be explained with ($n-1$)-body nonlocality. However, this genuine $n$-body nonlocality cannot surpass certain bounds. Here we address the problem of identifying the principles responsible for these bounds. We show that, for any $n\ge 2$, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory. This provides a unified explanation of the bounds of single-body contextuality and $n$-body nonlocality, and connects two programs towards understanding quantum theory.

Recently, many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are known. Here it is shown that the lack of irreducible third-order interference (a generalization of the idea that no probabilistic interference remains unaccounted for once we have taken into account interference between pairs of slits in a $n$-sit experiment) implies the principle known as the E principle or consistent exclusivity (that, if each pair of a set of experimental outcomes are exclusive alternatives in some measurement, then their probabilities are consistent with the existence of a further measurement in which they are all exclusive). This is a step towards a more unified understanding of quantum nonlocality and contextuality, which promises to allow derivations of important results from minimal, easily grasped assumptions. As one example, this result implies that lack of third-order interference bounds violation of the Clauser-Horne-Shimony-Holt-Bell inequality to 2.883.

Quantum nonlocality stands as a resource for device independent quantum information processing (DIQIP), such as, for instance, device independent quantum key distribution. We investigate, experimentally, the assumption of limited measurement dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particle and/or by an adversary. Using a recently derived Bell-like inequality [G. Pütz, Phys. Rev. Lett. 113, 190402 (2014)] and a 99% fidelity source of partially entangled polarization photonic qubits, we obtain a clear violation of the inequality, excluding a much larger range of measurement dependent local models than would be possible with an adapted Clauser-Horne-Shimony-Holt (CHSH) inequality. It is therefore shown that the measurement independence assumption can be widely relaxed while still demonstrating quantum nonlocality.

Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraint only holds in limited scenarios, and show how to overcome it using a novel method of iterated gate teleportations. This technique enables drastic reductions in the communication required for distributed quantum protocols, extending beyond the blind computation setting. Applied to blind quantum computation, this technique offers significant efficiency improvements, and in some scenarios offers an exponential reduction in communication requirements.