We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.

In this paper we provide an exhaustive study of the photoemission spectrum of paramagnetic FeO under pressure using a refined version of our recently derived many-body effective energy theory (MEET). We show that, within a nonmagnetic description of the paramagnetic phase, the MEET gives an overall good description of the photoemission spectrum at ambient pressure as well as the changes it undergoes by increasing pressure. In particular at ambient pressure the band gap opens between the mixed Fe $t_{2g}$ and O $2p$ states and the Fe $4s$ states and, moreover, a $d\text{−}d$ gap opens, which is compatible with a high-spin configuration (hence nonzero local magnetic moments as observed in experiment), whereas with decreasing pressure the band gap tends to close, $t_{2g}$ states tend to become fully occupied, and $e_g$ states tend to become fully unoccupied, which is compatible with a low-spin configuration (hence a collapse of the magnetic moments as observed in experiment). This is a remarkable result, since, within a nonmagnetic description of the paramagnetic phase, the MEET is capable to correctly describe the photoemission spectrum and the spin configuration at ambient as well as high pressure. For comparison we report the band-gap values obtained using density-functional theory with a hybrid functional containing screened exchange (HSE06) and a variant of the $GW$ method (self-consistent COHSEX), which are reliable for the description of the antiferromagnetic phase. Both methods open a gap at ambient pressure, although, by construction, they give a low-spin configuration; increasing pressure they correctly describe the band-gap closing. We also report the photoemission spectrum of the metallic phase obtained with one-shot fully dynamical $GW$ on top of the local-density approximation, which gives a spectrum very similar to dynamical mean-field theory results from literature.

The energy landscape of a single electron in a triple quantum dot can be tuned such that the energy separation between ground and excited states becomes a flat function of the relevant gate voltages. These so-called sweet spots are beneficial for charge coherence since the decoherence effects caused by small fluctuations of gate voltages or surrounding charge fluctuators are minimized. We propose a new operation point for a triple quantum dot charge qubit, a so-called $C{Q}_3$-qubit, having a third-order sweet spot. We show strong coupling of the qubit to single photons in a frequency tunable high-impedance SQUID-array resonator. In the dispersive regime, we investigate the qubit linewidth in the vicinity of the proposed operating point. In contrast to the expectation for a higher-order sweet spot, we there find a local maximum of the linewidth. We find that this is due to a non-negligible contribution of noise on the quadrupolar detuning axis not being in a sweet spot at the proposed operating point. While the original motivation to realize a low-decoherence charge qubit was not fulfilled, our analysis provides insights into charge decoherence mechanisms relevant also for other qubits.

Power spectral densities are a common, convenient, and powerful way to analyze signals, so much so that they are now broadly deployed across the sciences and engineering—from quantum physics to cosmology and from crystallography to neuroscience to speech recognition. The features they reveal not only identify prominent signal frequencies but also hint at mechanisms that generate correlation and lead to resonance. Despite their near-centuries-long run of successes in signal analysis, here we show that flat power spectra can be generated by highly complex processes, effectively hiding all inherent structure in complex signals. Historically, this circumstance has been widely misinterpreted, being taken as the renowned signature of “structureless” white noise—the benchmark of randomness. We argue, in contrast, to the extent that most real-world complex systems exhibit correlations beyond pairwise statistics their structures evade power spectra and other pairwise statistical measures. As concrete physical examples, we demonstrate that fraudulent white noise hides the predictable structure of both entangled quantum systems and chaotic crystals. To make these words of warning operational, we present constructive results that explore how this situation comes about and the high toll it takes in understanding complex mechanisms. First, we give the closed-form solution for the power spectrum of a very broad class of structurally complex signal generators. Second, we demonstrate the close relationship between eigenspectra of evolution operators and power spectra. Third, we characterize the minimal generative structure implied by any power spectrum. Fourth, we show how to construct arbitrarily complex processes with flat power spectra. Finally, leveraging this diagnosis of the problem, we point the way to developing more incisive tools for discovering structure in complex signals.

A compound with large anions is known to show large compressibility, whereby a novel response may emerge from the degenerated state by a uniaxial pressure. Neutron scattering study of ${\mathrm{BaCo}}_{0.9}{\mathrm{Ni}}_{0.1}{\mathrm{S}}_{1.9}$ crystal reveals that the tetragonal insulating state has two magnetic domains with in-plane anisotropic antiferromagnetic wave vectors ${\mathbf{Q}}_{\mathbf{1}}=(\pi ,0)$ and ${\mathbf{Q}}_{\mathbf{2}}=(0,\pi )$. The magnetic order with in-plane broken $C_4$ symmetry is realized as a twin of these two domains in the tetragonal state without any strain. One magnetic domain with ${\mathbf{Q}}_{\mathbf{2}}$ becomes dominant under a weak strain without any appreciable structural distortion. Correspondingly, the in-plane broken $C_4$ symmetry is also observed in the in-plane magnetic excitation of the tetragonal state.

Due to the absence of periodic length scale, electronic states and their topological properties in quasicrystals have been barely understood. Here, we focus on one-dimensional quasicrystals and reveal that their electronic critical states are topologically robust. Based on tiling space cohomology, we exemplify the case of one-dimensional aperiodic tilings especially Fibonacci quasicrystals and prove the existence of topological critical states at zero energy. Furthermore, we also show exotic electronic transmittance behavior near such topological critical states. Within the perturbative regime, we discuss the lack of translational symmetries and that the presence of topological critical states lead to an unconventional scaling behavior in transmittance. Considering both analytic analysis and numerics, electronic transmittance is computed in cases where the system is placed in air or is connected by semi-infinite periodic leads. Finally, we also discuss a generalization of our analysis to other quasicrystals. Our findings open a new class of topological quantum states which solely exist in quasicrystals due to exotic tiling patterns in the absence of periodic length scale, and their anomalous electronic transport properties applicable to many experiments.

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. In its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the five-qubit IBMQX2 quantum computer for $2\times 2$ and $3\times 3$ cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This paper is a step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future.

Temporal solitons are optical pulses that arise from the balance of negative group-velocity dispersion and self-phase modulation. For decades, only quadratic dispersion was considered with higher order dispersion often thought of as a nuisance. Following the recent observation of pure-quartic solitons, we here provide experimental and numerical evidence for an infinite hierarchy of solitons that balance self-phase modulation and arbitrary negative pure, even-order dispersion. Specifically, we experimentally demonstrate the existence of solitons with pure-sextic (${\beta }_6$), -octic (${\beta }_8$), and -decic (${\beta }_{10}$) dispersion, limited only by the performance of our components, and we numerically show the existence of solitons involving pure 16th-order dispersion. These results broaden the fundamental understanding of solitons and present avenues to engineer ultrafast pulses in nonlinear optics and its applications.

Nuclear magnetic resonance (NMR) was recently shown to measure the bulk band inversion of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ through changes in the ${}^{209}\mathrm{Bi}$ nuclear quadrupole interaction, and the corresponding tensor of the local electric field gradient was found to follow, surprisingly, the direction of the external magnetic field if the sample is rotated. This manifests a hidden property of the charge carriers in the bulk of this topological insulator, which is explored here with another material, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. It is found that two electric field gradients appear to be present at ${}^{209}\mathrm{Bi}$, one rests with the lattice, as usual, while a second follows the external field if it is rotated with respect to the crystal axes. These electronic degrees of freedom and their lifetime is believed to be responsible for an alternate quadrupolar relaxation that should lead to other special properties including the electronic specific heat.

Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works. In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents, and entropy production rate. We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents. We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics. We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier. For the machines considered here, we also perform an optimization of the system parameters using an algorithm of reinforcement learning.

Low-velocity zones located deep in the subsurface can act as seismic waveguides. Traditionally, their experimental observation has been limited by the practical challenges of in situ recording. We use a measurement technique in which optical fibers are turned into seismic sensors. The fiber is deployed along a horizontal well drilled inside a 15-m-thin shale formation at a depth of about 2 km. Owing to the high-resolution recording of the optical fiber, we can distinctly observe three previously elusive guided wave modes over a wide frequency range. As their propagation is primarily confined to the waveguide and strongly depends on its seismic properties, such guided waves hold tremendous potential for high-resolution imaging of deep low-velocity structures, such as fault zones, saline aquifers, and hydrocarbon reservoirs.

After the blockade that many nations suffered to stop the growth of the incidence curve of COVID-19 during the first half of 2020, they face the challenge of resuming their social and economic activity. The rapid airborne transmissibility of SARS-CoV-2, and the absence of a vaccine, calls for active containment measures to avoid the propagation of transmission chains. The best strategy to date, popularly known as test-track-treat (TTT), consists in testing the population for diagnosis, tracking the contacts of those infected, and treating by quarantine all these cases. The dynamical process that better describes the combined action of the former mechanisms is that of a contagion process that competes with the spread of the pathogen, cutting off potential contagion pathways. Here we propose a compartmental model that couples the dynamics of the infection with the contact tracing and isolation of cases. We develop an analytical expression for the effective case reproduction number $R_c\left(t\right)$ that reveals the role of contact tracing in the mitigation and suppression of the epidemics. We show that there is a trade-off between the infection propagation and the isolation of cases. If the isolation is limited to symptomatic individuals only, the incidence curve can be flattened but not bent. However, if contact tracing is applied to asymptomatic individuals too, the strategy can bend the curve and suppress the epidemics. Quantitative results are dependent on the network topology. We quantify the most important indicator of the effectiveness of contact tracing, namely, its capacity to reverse the increasing tendency of the epidemic curve, causing its bending.

A softening of phonon dispersion has been observed experimentally in underdoped cuprate superconductors at the charge-density-wave (CDW) ordering wave vector. Interestingly, the softening occurs below the superconducting (SC) transition temperature $T_c$, in contrast to the metallic systems, where the softening occurs usually below the CDW onset temperature $T_{\text{CDW}}$. An understanding of the “anomalous” nature of the phonon softening and its connection to the pseudogap phase in underdoped cuprates remain open questions. Employing a perturbative approach, we find that a complex interplay among the ubiquitous CDW order, SC order, and an unusually connected thermal fluctuations of these orders can explain the anomalous phonon softening below $T_c$. Furthermore, our formalism captures different characteristics of the low-temperature phonon softening, depending on material specificity.

We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures of dilute ultracold atomic gases. We use a mean-field Hartree-Fock theory to derive analytical predictions for the miscible-immiscible transition. A nontrivial result of this theory is that a fully miscible phase at $T=0$ may become unstable at $T\ne 0$, as a consequence of a divergent behavior in the spin susceptibility. We test this prediction by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii equation, which includes beyond mean-field effects. We calculate the equilibrium configurations at different temperatures and interaction strengths and we simulate spin oscillations produced by a weak external perturbation. Despite some qualitative agreement, the comparison between the two theories shows that the mean-field approximation is not able to properly describe the behavior of the two-dimensional mixture near the miscible-immiscible transition, as thermal fluctuations smoothen all sharp features both in the phase diagram and in spin dynamics, except for temperature well below the critical temperature for superfluidity.

Material realizations of the bond-dependent Kitaev interactions with $S=1/2$ local moments have vitalized the research in quantum spin liquids. Recently, it has been proposed that higher-spin analogs of the Kitaev interactions may also occur in a number of materials with strong spin-orbit coupling. In contrast to the celebrated $S=1/2$ Kitaev model on the honeycomb lattice, the higher-spin Kitaev models are not exactly solvable. Hence, the existence of quantum spin liquids in these systems remains an outstanding question. In this paper, we use the density matrix renormalization group methods to numerically investigate the $S=1$ Kitaev model with both ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Using results on quasi-one-dimensional finite-size cylindrical geometries with circumferences of up to six legs, we conclude that the ground state of the $S=1$ Kitaev model is a quantum spin liquid with a ${\mathbb{Z}}_2$ gauge structure. We are also able to put an upper bound on the excitation gap. The magnetic field responses for the FM and AFM models are similar to those of the $S=1/2$ counterparts. In particular, in the AFM $S=1$ model, a gapless quantum spin-liquid state emerges in an intermediate window of magnetic field strength, before the system enters a trivial polarized state.

We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity cannot only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light–matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nanogram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.

Geomagnetic field reversals remain as one of the most intriguing problems in geophysics and are regarded as chaotic processes resulting from a dynamo mechanism. In this article we use the polarity scale data of the last 170 Myrs collected from the ocean floor to provide robust evidence for an inverse relationship between the complexity of sequences of consecutive polarity intervals and the respective reversal rate. In particular, the variability of sequences of polarity intervals reaches minimum values in the mid-Jurassic when a maximum reversal rate is found, in the early Cretaceous preceding the Cretaceous Superchron, and twice in the last 20 Myrs. These facts raise the possibility of epochs of high regularity in the geomagnetic field reversals. To shed light on this process, we investigate the transition from regular to chaotic regime in a minimal model for geomagnetic reversals. We show that even in chaotic regimes, the system retains the signature of regular behavior near to transitions. We suggest that geomagnetic reversals have switched between different degrees of irregularity, with a dominant periodicity of $\approx 70$ kyrs that results from the occurrence of “ghost” limit cycles (GLCs) or unstable periodic orbits (UPOs) immersed in a chaotic region of phase space.

We consider a high-Q microresonator with ${\chi }^{\left(2\right)}$ nonlinearity under conditions when the coupling rate between the sidebands around the pump and its second harmonic exceeds the damping rates, implying the strong coupling regime (SC). Using the dressed-resonator approach we demonstrate that this regime leads to the dominance of the Hermitian part of the operator, driving the sideband dynamics over its non-Hermitian part responsible for the parametric gain. This has allowed us to introduce and apply the cross-area concept of the polariton quasiparticles and their effective masses in the context of ${\chi }^{\left(2\right)}$ ring microresonators. We further use polaritons to predict the modified spectral response of the resonator to the weak probe field, and to reveal the splitting of the bare-resonator resonances, avoided crossings, and Rabi dynamics. Polariton basis also allows the deriving of a discrete sequence of the parametric thresholds for generation of sidebands of different orders.

A widely held belief in network epidemiology is that information diffusion makes individuals aware of the epidemic and thus drives them to seek protections from nonpharmaceutical or pharmaceutical resources, which can help suppress its spread. However, as the COVID-19 pandemic has revealed, excessive information diffusion can trigger irrational acquisition and hoarding behaviors, which can lead to shortages of resources even for those in urgent need, consequently, worsening disease spreading. To develop a quantitative understanding of the effect of information diffusion on epidemic spreading, subject to allocations of limited resources, has become an urgently important problem with broad implications. We construct a multiplex network framework to characterize the complex interplay among resource allocation, information diffusion, and epidemic spreading, and develop a microscopic Markov chain theory to analyze their coevolution dynamics. There are two main findings. Firstly, if infected individuals have a large recovery probability, information diffusion plays the expected “normal” role of suppressing the epidemic. However, if the recovery probability is low, information diffusion can anomalously worsen the spread, regardless of the available resources insofar as they are limited. Secondly, different types of resources can lead to distinct phase transitions underlying the epidemic outbreak when the recovery probability is low: with limited cure-focused resources, the phase transition is of the second order, but if resources are of the protection type, the transition becomes first order, and a hysteresis loop emerges. The generality of the findings is established through simulations of synthetic and empirical three-layer networks with results in agreement with the theoretical predictions.

Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to the temperature. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a barrier, particles slide down a sloping potential. We formulate a renormalization group description of this noisy saddle-node transition. We derive the universal scaling behavior and corrections to scaling for the mean escape time in overdamped systems with arbitrary barrier height. We also develop an accurate approximation to the full distribution of barrier escape times by approximating the eigenvalues of the Fokker-Plank operator as equally spaced. This lets us derive a family of distributions that captures the barrier crossing times for arbitrary barrier height. Our critical theory draws links between barrier crossing in chemistry, the renormalization group, and bifurcation theory.