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Discriminating between quantum states is a fundamental task in quantum information theory. Given two quantum states, ρ + and ρ − , the Helstrom measurement distinguishes between them with minimal probability of error. However, finding and experimentally implementing the Helstrom measurement can be challenging for quantum states on many qubits. Due to this difficulty, there is a great interest in identifying local measurement schemes which are close to optimal. In the first part of this work, we generalize previous work by Acin et al. (Phys. Rev. A 71, 032338) and show that a locally greedy (LG) scheme using Bayesian updating can optimally distinguish between any two states that can be written as a tensor product of arbitrary pure states. We then show that the same algorithm cannot distinguish tensor products of mixed states with vanishing error probability (even in a large subsystem limit), and introduce a modified locally-greedy (MLG) scheme with strictly better performance. In the second part of this work, we compare these simple local schemes with a general dynamic programming (DP) approach. The DP approach finds the optimal series of local measurements and optimal order of subsystem measurement to distinguish between the two tensor-product states.1

With analyzing the mass function obtained by solving Dyson-Schwinger Equations, we propose a cut-off independent definition of quark condensate beyond chiral limit. With this well-defined condensate, we then analyze the evolution of the condensate and its susceptibility with the current quark mass. The susceptibility shows a critical mass in the neighborhood of the s-quark current mass, which defines a transition boundary for internal hadron dynamics., 7 pages, 5 figures

We present a numerical study of settling and clustering of small inertial particles in homogeneous and isotropic turbulence. Particles are denser than the fluid, but not in the limit of being much heavier than the displaced fluid. At fixed Reynolds and Stokes numbers we vary the fluid-to-particle mass ratio and the gravitational acceleration. The effect of varying one or the other is similar but not quite the same. We report non-monotonic behavior of the particles' velocity skewness and kurtosis with the second parameter, and an associated anomalous behavior of the settling velocity when compared to the free-fall Stokes velocity, including loitering cases. Clustering increases for increasing gravitational acceleration, and for decreasing fluid-to-particle mass ratio.

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,$\mathbb{C}$) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex., 25 pages, 8 figures

In this paper we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation greatly simplifies the original path-integral-based route to these equations and provides insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a route to the exact dynamical analysis of important related dynamical problems, as well as a means to devise cluster generalizations of the exact solution in infinite dimensions. This latter fact opens the door to the construction of increasingly accurate theories of vitrification in three-dimensional liquids.

The relevance of the generalized/nonlinear Fourier's law in a driven granular gas such as in dust storms is underscored by demonstrating that its linear, isotropic version does not hold even in the continuum limit of zero Knudsen number.

A paradox in neuroscience is the large number of oscillations of small neural networks compared with the few oscillations observed in the conscious brain. It remains unclear what is the maximum number of synchronized oscillations a network can support and whether all or some of these oscillations would survive in noisy heterogenous circuits. Here, we attempt to answer these questions through a comprehensive study of local inhibitory networks of Hodgkin-Huxley neurons. We use a neuromorphic platform combining electronic noise and device-specific heterogeneity with tuneable extrinsic noise, tuneable network connectivity, and controlled initial conditions. As in the brain, stimuli are instantaneously integrated by analog circuits. This gives us the computing power needed to map the network dynamics over the entire phase space and demonstrate the full complement of limit cycles, basins of attraction, and dependence on network parameters. Our main finding is that the maximum number of limit cycles is equal to the combinatorial number of activation pathways through the network, allowing for coincident action potentials, and that all limit cycles are equally robust to noise and mild heterogeneity but highly dependent on inhibition delay and the timing of stimuli. We established the robustness of individual limit cycles by computing the detailed balance of bifurcations between attractors. This accounts for all transitions in a system where Lyapunov exponents are both positive and negative depending on phase space coordinates and noise intensity. Another interesting finding is the unexpected resilience of limit cycles to mild network heterogeneity. This occurs as stochastic processes recruit quiescent neurons whose subthreshold periodic oscillations help maintain the synchronization of limit cycles against heterogeneity.

A paradigm shift in quantum thermometry is proposed. To date, thermometry has relied on local estimation, which is useful to reduce statistical fluctuations once the temperature is very well known. In order to estimate temperatures in cases where few measurement data or no substantial prior knowledge are available, we build instead a theory of global quantum thermometry. Based on scaling arguments, a mean logarithmic error is shown here to be the correct figure of merit for thermometry. Its full minimisation provides an operational and optimal rule to post-process measurements into a temperature reading, and it establishes a global precision limit. We apply these results to the simulated outcomes of measurements on a spin gas, finding that the local approach can lead to biased temperature estimates in cases where the global estimator converges to the true temperature. The global framework thus enables a reliable approach to data analysis in thermometry experiments., 5 + 8 pages, 1 + 1 figures. Accepted in Physical Review Letters

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication or locomotion. Given time series observations of intra-, inter- or multicellular processes, a key challenge is to detect non-equilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and hence can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs and mice., Comment: Improved exposition in main text, expanded supplementary information. 29 pages, 8 figures

Quantum metrology pursues high-precision measurements of physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrological error tends to diverge in the long-encoding-time regime due to the Born-Markovian approximate decoherence, which is called the no-go theorem of noisy quantum metrology. Here we propose a Gaussian quantum metrology scheme using bimodal quantized optical fields as the quantum probe. It achieves the precision of a sub-Heisenberg limit in the ideal case. However, the Markovian decoherence causes the metrological error contributed by the center-of-mass mode of the probe to be divergent. A mechanism to remove this ostensible no-go theorem is found in the non-Markovian dynamics. Our result gives an efficient way to realize high-precision quantum metrology in practical continuous-variable systems., Comment: 7 pages, 2 figures

Understanding the connections between information and thermodynamics has been among the most visible applications of stochastic thermodynamics. While recent theoretical advances have established that the second law of thermodynamics sets limits on information-to-energy conversion, it is currently unclear to what extent real systems can achieve the predicted theoretical limits. Using a simple model of an information engine that has recently been experimentally implemented, we explore the limits of information-to-energy conversion when an information engine's benefit is limited to output energy that can be stored. We find that restricting the engine's output in this way can limit its ability to convert information to energy. Nevertheless, a feedback control that inputs work can allow the engine to store energy at the highest achievable rate. These results sharpen our theoretical understanding of the limits of real systems that convert information to energy., 17 pages, 17 figures

Inequalities are abundant in a society with a number of agents competing for a limited amount of resource. Statistics of such social inequalities are usually represented by the Lorenz function $L(p)$, where $p$ fraction of the population possesses $L(p)$ fraction of the total wealth, when the population is arranged in the ascending order of their wealth. Similarly, in scientometrics, such inequalities can be represented by a plot of the citation count against the respective number of papers by a scientist, again arranged in the ascending order of their citation counts. Quantitatively, these inequalities are captured by the corresponding inequality indices, namely the Kolkata $k$ and the Hirsch $h$ indices, given by the fixed points of these nonlinear functions. In statistical physics of criticality, the fixed points of the Renormalization Group generator functions are studied in their self-similar limit, where its (fractal) structure converges to a unique form. The statistical indices in the social science, however, correspond to the fixed points where the values of the generator function (wealth or citation sizes) are commensurately abundant in fractions or numbers (of persons or papers). We introduce and study these indices for the inequalities of (pre-failure) avalanches, given by their size distributions in the Fiber Bundle Models (FBM) of non-brittle materials. We show how a prior knowledge of the terminal and almost universal value of the $k$ index for a wide range of disorder parameter, can help in predicting an imminent catastrophic breakdown in the model. This observation has also been complemented by noting a similar (but not identical) behavior of the Hirsch index ($h$), redefined for such avalanche statistics., Comment: 8 pages, 9 figures; Phys. Rev. E (in press)

We conduct an analysis of the quasi-normal modes for generic spin perturbations of the Kerr black hole using the isomonodromic method. The strategy consists of solving the Riemann-Hilbert map relating the accessory parameters of the differential equations involved to monodromy properties of the solutions, using the $\tau$-function for the Painlev\'e V transcendent. We show good accordance of the method with the literature for generic rotation parameter $a, Comment: REVTeX 4.2, 17 pages, 7 figures; version 2 with added references and better control of the Stokes phenomenon in the numerical calculations. Results now agree within machine precision to the method of choice when they are both applicable

In nonequilibrium systems, the relative fluctuation of a current has a universal trade-off relation with the entropy production, called the thermodynamic uncertainty relation (TUR). For systems with broken time reversal symmetry, its violation has been reported in specific models or in the linear response regime. Here, we derive a modified version of the TUR analytically in the overdamped limit for general Langevin dynamics with a magnetic Lorentz force causing time reversal broken. Remarkably, this modified version is simply given by the conventional TUR scaled by the ratio of the reduced effective temperature of the overdamped motion to the reservoir temperature, permitting a violation of the conventional TUR. Without the Lorentz force, this ratio becomes unity and the conventional TUR is restored. We verify our results both analytically and numerically in a specific solvable system., Comment: 15 pages

We apply a hyperspherical formulation to a trapped Bose-Einstein condensate with dipolar and contact interactions. Central to this approach is a general correspondence between $K$-harmonic hyperspherical methods and a suitable Gaussian ansatz to the Gross-Pitaevskii equation, regardless of the form of the interparticle potential. This correspondence allows one to obtain hyperspherical potential energies for a wide variety of physical problems. In the case of the dipolar Bose-Einstein condensate, this motivates the inclusion of a beyond-mean-field term within the hyperspherical picture, which allows us to describe the energies and wave functions of excitations of self-bound dipolar droplets outside the mean-field limit.

The use of phase-shifting interferometry (PSI) in the ultra-low-light region would open the way for important applications, such as imaging of phototoxic substances and sensing of ultrafast phenomena. In the ultra-low-light region, the statistical nature of photons can be a dominant source of noise compared with other noise caused by experimental instruments. Here we theoretically derive the precision limit determined by the statistical nature of photons for simultaneously measuring the transmittance and phase of a sample with PSI. We show that the precision of PSI depends on the phase and transmittance themselves. We also show a trade-off relation between transmittance and phase. Then we compare PSI with sequential optimal measurements in which the transmittance and phase of a sample are separately measured for each corresponding optimal measurement. We also discuss the case where the input number of photons fluctuates with a Poisson distribution and show that the fluctuation affects both the transmittance and phase precision for PSI.

The existence of black holes is one of the key predictions of general relativity (GR) and therefore a basic consistency test for modified theories of gravity. In the case of spherical symmetry in GR the existence of an apparent horizon and its regularity is consistent with only two distinct classes of physical black holes. Here we derive constraints that any self-consistent modified theory of gravity must satisfy to be compatible with their existence. We analyze their properties and illustrate characteristic features using the Starobinsky model. Both of the GR solutions can be regarded as zeroth-order terms in perturbative solutions of this model. We also show how to construct nonperturbative solutions without a well-defined GR limit., 13 pages. Published version. Comments welcome!

We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings {in the time domain} by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provides an exact description, at large space-time scales, for arbitrary temperature $T$, particle density, and interactions. At $T=0$ and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low $T>0$ effects of SCS survive and {characterize} explicitly the value of $T$ for which the two distinguishable excitations melt., 12 pages, 7 figures; v2: modified layout; corrected some typos

In the largest, currently known, class of one Quadrillion globally consistent F-theory Standard Models with gauge coupling unification and no chiral exotics, the vector-like spectra are counted by cohomologies of root bundles. In this work, we apply a previously proposed method to identify toric base 3-folds, which are promising to establish F-theory Standard Models with exactly three quark-doublets and no vector-like exotics in this representation. The base spaces in question are obtained from triangulations of 708 polytopes. By studying root bundles on the quark doublet curve $C_{(\mathbf{3},\mathbf{2})_{1/6}}$ and employing well-known results about desingularizations of toric K3-surfaces, we derive a \emph{triangulation independent lower bound} $\check{N}_P^{(3)}$ for the number $N_P^{(3)}$ of root bundles on $C_{(\mathbf{3},\mathbf{2})_{1/6}}$ with exactly three sections. The ratio $\check{N}_P^{(3)} / N_P$, where $N_P$ is the total number of roots on $C_{(\mathbf{3},\mathbf{2})_{1/6}}$, is largest for base spaces associated with triangulations of the 8-th 3-dimensional polytope $\Delta^\circ_8$ in the Kreuzer-Skarke list. For each of these $\mathcal{O}( 10^{15} )$ 3-folds, we expect that many root bundles on $C_{(\mathbf{3},\mathbf{2})_{1/6}}$ are induced from F-theory gauge potentials and that at least every 3000th root on $C_{(\mathbf{3},\mathbf{2})_{1/6}}$ has exactly three global sections and thus no exotic vector-like quark-doublet modes., Comment: 6 pages, 5 figures and 2 tables

Anisotropy parameters describing the angular dependence of the photoionization delay are defined. The formalism is applied to results obtained with the relativistic random phase approximation with exchange for photoionization delay from the outermost $s$-orbitals in selected rare-gas atoms. Any angular dependence in the Wigner delay is induced here by relativistic effects, while the measurable atomic delay exhibits such a dependence also in the nonrelativistic limit. The contributions to the anisotropy from the different sources are disentangled and discussed. For the heavier rare gases, it is shown that measurements of the delay for electrons ejected in specific angles, relative to, e.g., those ejected along the laser polarization, are directly related here to the Wigner delay. For a considerable range of angles, the contributions from the second photon largely get canceled when the results in different angles are compared, and this angle-relative atomic delay is then close to the corresponding Wigner delay.

Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits, usually require the full measurement statistics, which can be challenging to access. In this work, we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources, and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity and on the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise., Comment: 18 pages, 12 figures, 1 table. Comments are very welcome!

We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{K}^{+}$ and ${K}^{+}{K}^{+}{\ensuremath{\pi}}^{+}$. We derive the formalism necessary to extract two- and three-particle infinite-volume scattering amplitudes from the spectrum of such systems in finite volume. We use a relativistic formalism based on an all-orders diagrammatic analysis in generic effective field theory, adopting the methodology used recently to study the case of three nondegenerate particles. We present both a direct derivation, and also a cross-check based on an appropriate limit and projection of the fully nondegenerate formalism. We also work out the threshold expansions for the three-particle K matrix that will be needed in practical applications, both for systems with two identical particles plus a third, and also for the fully nondegenerate theory.

Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial stages or compartments (e.g., exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with compartments are more common than TSI models, largely due to the higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a compartment model with three or four stages for the infected class. We also provide a perspective for adding stages to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an Appendix. Finally, as proof of principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by nonpharmaceutical intervention. Many of the tools described in this paper are available through the software package pyross.

According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily large factor if one aims, instead, to guess the unknown value of a past measurement. For experiments on a single quantum system, the precise assignment of past position and momentum measurement outcomes is accompanied by large uncertainty about their linear combinations, while we show that entanglement with an ancillary system permits accurate retrodiction of any such linear combination. Finally, we show that the outcomes of experiments that jointly measure multiple linear combinations of position and momentum observables by means of ancillary probe particles can also be guessed with no formal lower limit. We present quantitative results for projective measurements and for generalized measurements where all components are prepared in Gaussian states.

We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity. The GED model is a generalization of the Yard-Sale model in which the additional wealth added by economic growth is nonuniformly distributed to the agents according to their wealth in a way determined by the parameter $\lambda$. The model was shown numerically to have a phase transition at $\lambda=1$ and be characterized by critical exponents and critical slowing down. Our mean-field treatment of the GED model correctly predicts the existence of the phase transition, critical slowing down, the values of the critical exponents, and introduces an energy whose probability satisfies the Boltzmann distribution for $\lambda < 1$, implying that the system is in thermodynamic equilibrium in the limit that $N \to \infty$. We show that the values of the critical exponents obtained by varying $\lambda$ for a fixed value of $N$ do not satisfy the usual scaling laws, but do satisfy scaling if a combination of parameters, which we refer to as the Ginzburg parameter, is much greater than one and is held constant. We discuss possible implications of our results for understanding economic systems and the subtle nature of the mean-field limit in systems with both additive and multiplicative noise., Comment: The paper is complemented by simulations of the GED model reported in Kang K. L. Liu,1 N. Lubbers, 1 W. Klein, J. Tobochnik, B. M. Boghosian, and Harvey Gould, "Simulation of a generalized asset exchange model with economic growth and wealth distribution."

Quantum target detection is an emerging application that utilizes entanglement to enhance the sensing of the presence of an object. Although several experimental demonstrations for certain situations have been reported recently, the single-shot detection limit imposed by the Helstrom limit has not been reached because of the unknown optimum measurements. Here we report an experimental demonstration of quantum target detection, also known as quantum illumination, in the single-photon limit. In our experiment, one photon of the maximally entangled photon pair is employed as the probe signal and the corresponding optimum measurement is implemented at the receiver. We explore the detection problem in different regions of the parameter space and verify that the quantum advantage exists even in a forbidden region of the conventional illumination, where all classical schemes become useless. Our results indicate that quantum illumination breaks the classical limit for up to 40%, while approaching the quantum limit imposed by the Helstrom limit. These results not only demonstrate the advantage of quantum illumination, but also manifest its valuable potential of target detection.

An explosive percolation transition is the abrupt emergence of a giant cluster at a threshold caused by a suppression of the growth of large clusters. In this paper, we consider the information entropy of the cluster size distribution, which is the probability distribution for the size of a randomly chosen cluster. It has been reported that information entropy does not reach its maximum at the threshold in explosive percolation models, a result seemingly contrary to other previous results that the cluster size distribution shows power-law behavior and the cluster size diversity (number of distinct cluster sizes) is maximum at the threshold. Here, we show that this phenomenon is due to that the scaling form of the cluster size distribution is given differently below and above the threshold. We also establish the scaling behaviors of the first and second derivatives of the information entropy near the threshold to explain why the first derivative has a negative minimum at the threshold and the second derivative diverges negatively (positively) at the left (right) limit of the threshold, as predicted through previous simulation., Comment: 7 figures, published version

Somehow, our brain and other organisms manage to predict their environment. Behind this must be an input-dependent dynamical system, or recurrent neural network, whose present state reflects the history of environmental input. The design principles for prediction---in particular, what kinds of attractors allow for greater predictive capability---are still unknown. We offer some clues to design principles using an attractor picture when the environment perturbs the system's state weakly, motivating and developing some theory for continuous-time time-varying linear reservoirs along the way. Reservoirs that inherently support only stable fixed points are generically good predictors, while reservoirs with limit cycles are good predictors for noisy periodic input.

We investigate the role of nonclassical temporal correlations in enhancing the performance of ticking clocks in a discrete-time scenario. We show that the problem of optimal models for ticking clocks is related to the violation of Leggett-Garg-type temporal inequalities formulated in terms of, possibly invasive, sequential measurements, but on a system with a bounded memory capacity. Ticking clocks inspire the derivation of a family of temporal inequalities showing a gap between classical and quantum correlations, despite involving no input. We show that quantum ticking-clock models achieving accuracy beyond the classical bound are also those violating Leggett-Garg-type temporal inequalities for finite sequences and we investigate their continuous-time limit. Interestingly, we show that optimal classical clock models in the discrete-time scenario do not have a well-defined continuous-time limit, a feature that is absent in quantum models., Physical Review Research, 3 (3), ISSN:2643-1564

Distributed quantum sensing can provide quantum-enhanced sensitivity beyond the shot-noise limit (SNL) for sensing spatially distributed parameters. To date, distributed quantum sensing experiments have been mostly accomplished in laboratory environments without a real space separation for the sensors. In addition, the post-selection is normally assumed to demonstrate the sensitivity advantage over the SNL. Here, we demonstrate distributed quantum sensing in field and show the unconditional violation (without post-selection) of SNL up to 0.916 dB for the field distance of 240 m. The achievement is based on a loophole free Bell test setup with entangled photon pairs at the averaged heralding efficiency of 73.88%. Moreover, to test quantum sensing in real life, we demonstrate the experiment for long distances (with 10-km fiber) together with the sensing of a completely random and unknown parameter. The results represent an important step towards a practical quantum sensing network for widespread applications., 8 pages, 5 figures

A cold-atom gyroscope as an intrinsic high-precision sensor has, however, one inevitable limitation for its dynamic application lying in the vanishing fringe contrast beyond the rotation-rate limit. Here, we realize the measurement beyond the rotation-rate limit via the tip-tilt mirror compensation technique in a three-pulse cold-atom gyroscope. The contrasts of both fringes at an external rotation rate of ${15}^{\ensuremath{\circ}}$/s or below are fully recovered to about 35%, nearly the same as that in the static condition. We elucidate theoretically that intact rotation information can still be extracted from the phase output even though the mirror completely counteracts its rotation. Before reaching 50% contrast loss, detailed numerical verification shows a two-orders-of-magnitude extension in the dynamic range for the compensated case compared with that without compensation. Further analysis shows that no reduction of sensitivity up to ${60}^{\ensuremath{\circ}}$/s is found for our scheme, whereas other schemes have a trade-off between sensitivity and dynamic range. Whereas other schemes have a trade-off between sensitivity and dynamic range, the simulation shows that no reduction to the sensitivity is found for the measurement beyond the rotation-rate limit in our scheme for up to ${60}^{\ensuremath{\circ}}$/s. These features are especially of major relevance in applications such as inertial sensing and navigation.

We describe a proposal for constructing a lattice theory that we argue may be capable of yielding free Weyl fermions in the continuum limit. The model employs reduced staggered fermions and uses site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. The possibility for such symmetric mass generation is tied to the cancellation of certain discrete anomalies arising in the continuum limit. The latter place strong constraints on the number of lattice fermions -- constraints that are satisfied by this model. We present numerical results for the model in two dimensions which support this sc, 10 pages. 8 figures. Changes to text and figures added. Version to be published in PRD

Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model., Comment: 11 figures

Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case., 14 pages; 3 figures; v3: published version

We present the results of an explicit numerical computation of a novel instanton in Georgi-Glashow SU(2) theory. The instanton is physically relevant as a mediator of Schwinger production of 't Hooft-Polyakov magnetic monopoles from strong magnetic fields. In weak fields, the pair production rate has previously been computed using the worldline approximation, which breaks down in strong fields due to the effects of finite monopole size. Using lattice field theory we have overcome this limit, including finite monopole size effects to all orders. We demonstrate that a full consideration of the internal monopole structure results in an enhancement to the pair production rate, and confirm earlier results that monopole production becomes classical at the Ambjorn-Olesen critical field strength., 9 pages, 4 figures; corrected sign error in Eq. (2)

The Shannon's bound for compression is one of the key restrictions for the compression of quantum information. Here we show that the unitarity of the compression operation imposes new bounds on the compression that are more limiting than Shannon's compression bound. This translates to a no-go theorem for the purification of quantum states. For a specific case of a two-qubit system, our results indicate that it is not possible to distill purity beyond the maximum of the individual purities. We show that this restriction results in the cooling limit of the heat-bath algorithmic cooling techniques. We formalize the limitations imposed by the unitarity of the compression operation in two theorems and use the theorems to show that the limitations of unitarity lead to the cooling limit of heat-bath algorithmic cooling. To this end, we introduce a new optimal cooling technique and show that without the limitations of the unitary operations, the new cooling technique would have exceeded the limit of Heat-bath algorithmic cooling. This work opens up new avenues to understanding the limits of dynamic cooling.

We study the effect of gravity on barrel-shaped droplets on fibers using theoretical analyses, numerical simulations, and experiments. By performing a perturbation analysis in the limit of small Bond numbers and small dimensionless droplet volumes, we formulate a nearly axisymmetric solution that describes the shape of the droplet. The leading-order solution yields the axisymmetric profile and the first-order correction incorporates the effect of gravity. We validate our solution by comparing droplet shape and contact line predictions with experiments and Surface Evolver simulations.

Recently, topological phases in non-Hermitian systems have attracted great attention. In most of these works, disorders are added to the chemical potential or hopping term and the topological transition driven by disordered loss and gain has not been found. In this paper, we investigate the one-dimensional dimerized Kitaev superconductor chain with balanced loss and gain. In the clean limit, the phase diagram is given by calculating the Bloch winding number and real-space energy spectrum. Furthermore, by calculating the disorder-averaged real-space winding number and disorder-averaged real-space energy spectrum, we identify a topological transition driven by the disordered balanced loss and gain. The disorder-averaged inverse participate ratio of each eigenstate, mean inverse participate ratio, and density distribution of the edge mode are also calculated to support the existence of the topological Anderson phase. Finally, we compare our model with the Hermitian disordered Kitaev chain and discuss the possible experimental scheme of our model. Our work offers a minimal start point to explore the interplay between the dissipation and Majorana zero modes in the topological superconductor.

The site and bond percolation problems are conventionally studied on (hyper)cubic lattices, which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now also facilitates the study of ${D}_{n}$ root lattices in $n$ dimensions as well as ${E}_{8}$-related lattices. Here, we consider the percolation problem on ${D}_{n}$ for $n=3$ to 13 and on ${E}_{8}$ relatives for $n=6$ to 9. Precise estimates for both site and bond percolation thresholds obtained from invasion percolation simulations are compared with dimensional series expansion based on lattice animal enumeration for ${D}_{n}$ lattices. As expected, the bond percolation threshold rapidly approaches the Bethe lattice limit as $n$ increases for these high-connectivity lattices. Corrections, however, exhibit clear yet unexplained trends. Interestingly, the finite-size scaling exponent for invasion percolation is found to be lattice and percolation-type specific.

We determine the upper limit on the mass of the lightest neutrino from the most robust recent cosmological and terrestrial data. Marginalizing over possible effective relativistic degrees of freedom at early times ($N_\mathrm{eff}$) and assuming normal mass ordering, the mass of the lightest neutrino is less than 0.037 eV at 95% confidence; with inverted ordering, the bound is 0.042 eV. These results improve upon the strength and robustness of other recent limits and constrain the mass of the lightest neutrino to be barely larger than the largest mass splitting. We show the impacts of realistic mass models, and different sources of $N_\mathrm{eff}$., 5 pages, 2 figures + Appendix. Full dataset available at https://doi.org/10.5281/zenodo.4005381 (v3: Matches version published in PRD)

This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor components of the wavefunction exhibit an increasing number of zeros, resembling the changes in the quantum Hall wavefunction as the Landau level index is increased. The wavefunction zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moire unit cell, while opposite chirality zeros are pushed to the boundaries of the unit cell. The enhanced phase winding at higher magic angles suggests an increased circulating current. Physical implications for scanning tunneling spectroscopy, orbital magnetization and interaction effects are discussed.

Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization, and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks the limit for quantum systems. However, we report in this paper a periodically-modulated nonlinear Schr\"odinger system, in which we interestingly find a way of OTOCs' growth: super-EG. We show that the quantum OTOCs, which stems from the quantum chaotic dynamics, will increase in a super-exponential way. We also find that in the classical limit, the hyper-chaos revealed by a linearly-increasing Lyapunov exponent actually triggers the super-EG of classical OTOCs. The results in this paper break the restraints of EG as the limit for quantum systems, which give us insight into the nature of quantum chaos in various fields of physics from black hole to many-body system.

The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten model realizes bosonic-string theory in ${\mathrm{AdS}}_{3}$ with pure Neveu-Schwarz-Neveu-Schwarz flux. We construct an effective action in the semiclassical limit of the model, which corresponds to a $\mathrm{SL}(2,\mathbb{R})$ spin-chain $\ensuremath{\sigma}$-model. We adopt two complementary points of view. First, we consider the classical action. We identify fast and slow target-space coordinates. We impose a gauge-fixing condition to the former. By expanding the gauge-fixed action in an effective coupling, we obtain the effective action for the slow coordinates. Second, we consider the spin chain of the model. We postulate a set of coherent states to express a transition amplitude in the spin chain as a path integral. We observe that the temporal interval is discretized in terms of the step length of the spatial interval. This relationship implies that the Landau-Lifshitz limit of the spin chain involves both intervals. The limit yields a semiclassical path integral over coherent states, wherein we identify the effective action again.

Optimisation of heat engines at the micro-scale has applications in biological and artificial nano-technology, and stimulates theoretical research in non-equilibrium statistical physics. Here we consider non-interacting overdamped particles confined by an external harmonic potential, in contact either with a thermal reservoir or with a stochastic self-propulsion force (active Ornstein-Uhlenbeck model). A cyclical machine is produced by periodic variation of the parameters of the potential and of the noise. An exact mapping between the passive and the active model allows us to define the effective temperature $T_{eff}(t)$ which is meaningful for the thermodynamic performance of the engine. We show that $T_{eff}(t)$ is different from all other known active temperatures, typically used in static situations. The mapping allows us to optimise the active engine, whatever are the values of the persistence time or self-propulsion velocity. In particular - through linear irreversible thermodynamics (small amplitude of the cycle) - we give explicit formula for the optimal cycle period and phase delay (between the two modulated parameters, stiffness and temperature) achieving maximum power with Curzon-Ahlborn efficiency. In the quasi-static limit, the formula for $T_{eff}(t)$ simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency. A point - overlooked in recent literature - is made about the difficulty in defining efficiency without a consistent definition of effective temperature., 18 pages, 6 pages, submitted for publication

The interpretation of experiments that search for neutrinoless double-$\ensuremath{\beta}$ decay relies on input from nuclear theory. Cirigliano et al. [Phys. Rev. Lett. 120, 202001 (2018)] recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nn\ensuremath{\rightarrow}pp{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ contact term at leading order. They estimated the size of this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about the relative sizes of CIB operators. We show that the assumptions underlying this approximation are justified in the limit of the number of colors, ${N}_{c}$, being large. We also obtain a large-${N}_{c}$ hierarchy among CIB nucleon-nucleon interactions that is in agreement with phenomenological results.

Motivated by gravitational wave observations of binary black hole mergers, we present a procedure to compute the leading-order nonlinear gravitational wave interactions around a Kerr black hole. We describe the formalism used to derive the equations for second-order perturbations. We develop a procedure that allows us to reconstruct the first-order metric perturbation solely from knowledge of the solution to the first-order Teukolsky equation, without the need of Hertz potentials. Finally, we illustrate this metric reconstruction procedure in the asymptotic limit for the first-order quasinormal modes of Kerr. In a companion paper [J. L. Ripley et al., Phys. Rev. D 103, 104018 (2021)] we present a numerical implementation of these ideas.

The CUPID-Mo experiment at the Laboratoire Souterrain de Modane (France) is a demonstrator for CUPID, the next-generation ton-scale bolometric 0νββ experiment. It consists of a 4.2 kg array of 20 enriched Li_{2}^{100}MoO_{4} scintillating bolometers to search for the lepton-number-violating process of 0νββ decay in ^{100}Mo. With more than one year of operation (^{100}Mo exposure of 1.17 kg×yr for physics data), no event in the region of interest and, hence, no evidence for 0νββ is observed. We report a new limit on the half-life of 0νββ decay in ^{100}Mo of T_{1/2}>1.5×10^{24} yr at 90% C.I. The limit corresponds to an effective Majorana neutrino mass ⟨m_{ββ}⟩