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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.

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

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

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

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!

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.

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

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 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)

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.

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}⟩

Spin-exchange collisions among alkali-metal atoms affect the coherence time and gyromagnetic ratio of atoms by redistributing the ground-state population. We theoretically study the interactions between magnetic fields and atoms in the presence of spin-exchange collisions. Using the modified Bloch equations derived from the density-matrix equation in a low spin-polarization limit, we obtain explicit formulas describing the role of spin-exchange collisions in the interactions between atoms and magnetic fields, especially the nonresonant radio-frequency fields, which are widely used to manipulate atoms. The results derived from these equations agree well with density-matrix simulations and previous experimental results, and provide a simple and precise way to quantitatively analyze the effect of spin-exchange collisions on atoms. Our paper is helpful to gain physical insight into the spin-exchange collisions and optimize the performance of atom-based precision measurement instruments.

Analyzing gamma-ray sources leads to an upper limit on how many antimatter stars could exist in the Milky Way.

The oscillating-barrier model was used by B\"uttiker and Landauer to determine a ``traversal time for tunneling.'' The model sets a timescale but is not the physically measured flight time of a wave packet scattered on the oscillating-barrier potential. In this paper we show that the flight time in the limit of a narrow-in-momentum wave packet is given by the reflected phase time associated with the various branches of the scattered particle. This is but another example which establishes that tunneling flight times are a reflection of the Wigner phase times. As such, the oscillating-barrier model does not add any new information about tunneling flight times which has not been elucidated previously using static barrier models.

It is generally taken for granted that our Universe is free of antimatter objects and domains. This certitude has recently been challenged by the possible detection of anti-helium nuclei by AMS-02. Should the observation be confirmed, the existence of nearby antistars would make a plausible hypothesis to explain the origin of the antinuclei. In this paper we use the 10-years Fermi Large Area Telescope (LAT) gamma-ray source catalog to set constraints on the abundance of antistars around the Sun. We identify in the catalog 14 antistar candidates not associated with any objects belonging to established gamma-ray source classes and with a spectrum compatible with baryon-antibaryon annihilation. We use them along with an estimate of the LAT sensitivity to antistars to set upper limits on the local antistar fraction $f_{\bar{\ast}}$ with respect to normal stars. We provide parametric limits as a function of the closest antistar mass, velocity, and surrounding matter density. We also employ a novel Monte~Carlo method to set limits for a few hypotheses about the antistar population. For a population with properties equivalent to those of regular stars concentrated in the Galactic disk we obtain $f_{\bar{\ast}} < 2.5 \times 10^{-6}$ at 95\% confidence level, which is 20 times more constraining than limits previously available. For a primordial population of antistars distributed in the Galactic halo we obtain new local upper limits which decrease as a function of antistar mass $M$ from $f_{\bar{\ast}} < 0.2$ at 95\% confidence level for $M = 1 \; M_\odot$ to $f_{\bar{\ast}} < 1.6 \times 10^{-4}$ at 95\% confidence level for $M = 10 \; M_\odot$. By combining these limits with existing microlensing constraints for lighter objects in the Magellanic clouds, we infer that a primordial population of halo antistars must have a density lower than $\mathcal{O}(10^{-5}\;\text{pc}^{-3})$ to $\mathcal{O}(10^{-2}\;\text{pc}^{-3})$ depending on their masses. Our limits can constrain models for the origin and propagation of antinuclei in cosmic rays., Physical Review D, American Physical Society, 2021

The quantum kicked rotor is well-known to display dynamical localization in the non-interacting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate remains debated beyond mean-field. Here we study the kicked Lieb-Liniger model in the few-body limit. We show that for any interaction strength, two kicked interacting bosons always dynamically localize, in the sense that the energy of the system saturates at long time. However, contrary to the non-interacting limit, the momentum distribution $\Pi(k)$ of the bosons is not exponentially localized, but decays as $\mathcal C/k^4$, as expected for interacting quantum particles, with Tan's contact $\mathcal C$ which remains finite at long time. We discuss how our results will impact the experimental study of kicked interacting bosons., Comment: v1) 10 pages, 10 figures; v2) minor typos corrected, published version

We investigate the statistics of articulation points and bredges (bridge-edges) in complex networks in which bonds are randomly removed in a percolation process. Articulation points are nodes in a network which, if removed, would split the network component on which they are located into two or more separate components, while bredges are edges whose removal would split the network component on which they are located into two separate components. Both articulation points and bredges play an important role in processes of network dismantling and it is therefore useful to know the evolution of the probability of nodes or edges to be articulation points and bredges, respectively, when a fraction of edges is randomly removed from the network in a percolation process. Due to the heterogeneity of the network, the probability of a node to be an articulation point, or the probability of an edge to be a bredge will not be homogeneous across the network. We therefore analyze full distributions of articulation point probabilities as well as bredge probabilities, using a message-passing or cavity approach to the problem, as well as a deconvolution of these distributions according to degrees of the node or the degrees of both adjacent nodes in the case of bredges. Our methods allow us to obtain these distributions both for large single instances of networks as well as for ensembles of networks in the configuration model class in the thermodynamic limit of infinite system size. We also derive closed form expressions for the large mean degree limit of Erd\H{o}s-R\'enyi networks., Comment: 15 pages, 10 multipart figures

A general analytical model is established to study the change in the signal-to-noise ratio (SNR) of the spatially noisy optical signal after passing through a subwavelength-aperture system. The corresponding spatial resolution limit is redefined based on Shannon's theory of information, and the expression is analytically given derived from nonparaxial vectoral diffraction theory. Contrary to the conventional wisdom, it is demonstrated both analytically and numerically that the SNR of the optical signal will increase with the propagation distance due to the presence of the subwavelength aperture and the corresponding spatial resolution could, thus, exceed the traditional Abbe-Rayleigh diffraction limit even though when the input SNR is low. The theoretical result provides perspectives for optimizing optical resolution and is general, that can be extended to other sciences, such as x-ray imaging and quantum imaging.

Using the Lindblad equation approach, we derive the range of the parameters of an interacting one-dimensional electronic chain connected to two reservoirs in the large bias limit in which an optimal working point (corresponding to a change in the monotonicity of the stationary current as a function of the applied bias) emerges in the nonequilibrium stationary state. In the specific case of the one-dimensional spinless fermionic Hubbard chain, we prove that an optimal working point emerges in the dependence of the stationary current on the coupling between the chain and the reservoirs, both in the interacting and in the noninteracting case. We show that the optimal working point is robust against localized defects of the chain, as well as against a limited amount of quenched disorder. Eventually, we discuss the importance of our results for optimizing the performance of a quantum circuit by tuning its components as close as possible to their optimal working point.

Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space and in weakly-coupled systems. Here, we propose a general criterion for the existence of a well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In such systems, we show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale, such as the lattice spacing. As an explicit example, we study a random unitary circuit with tunable interactions. In this model, we show that in the weakly interacting limit, the above criterion is satisfied, and there is a prolonged window of exponential growth. Our results are based on numerical simulations of both Clifford and universal random circuits supported by an analytical treatment.

We propose a simple model based on the assumption that the varying fine structure constant $\ensuremath{\alpha}$ is an effect of the cosmological expansion to investigate the relation between the varying $\ensuremath{\alpha}$ and the cosmological components. For a spatially flat, homogeneous, and isotropic universe, the current proportion of cosmological components and age of the universe predicted by the model are consistent with the cosmological observations. Furthermore, the predicted current variation rate of $\ensuremath{\alpha}$ is also close to the atomic clock measurements. For the early universe, we predict a very strict constraint, which is compatible with the upper limit given by the investigations of cosmic microwave background and big bang nucleosynthesis.

We show that the presented in Phys.Rev.B, v.101, 214312 (2020) theoretical expressions for longitudinal current spectral function $C^L(k,\omega)$ and dispersion of collective excitations are not correct. Indeed, they are not compatible with the continuum limit and $C^L(k,\omega\to 0)$ contradicts the continuity equation., Comment: Submitted to Phys.Rev.B

Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Even though there exist numerous nonequivalent definitions of graph curvature, none is known to converge in any limit to any traditional definition of curvature of a Riemannian manifold. Here we show that Ollivier curvature of random geometric graphs in any Riemannian manifold converges in the continuum limit to Ricci curvature of the underlying manifold, but only if the definition of Ollivier graph curvature is properly generalized to apply to mesoscopic graph neighborhoods. This result establishes the first rigorous link between a definition of curvature applicable to networks and a traditional definition of curvature of smooth spaces.

We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit. We derive exact results for the two-time correlation functions and the speed of convergence. The {\em de Almedia-Thouless} stability criterion of the static problem is found to be necessary and sufficient for the global convergence of the random sequential dynamics., Accepted for publication in Physical Review E Letter

We present explicit evaluations of quantum speed limit times pertinent to the Markovian dynamics of an open continuous-variable system. Specifically, we consider the standard setting of a cavity mode of the quantum radiation field weakly coupled to a thermal bosonic reservoir. The evolution of the field state is ruled by the quantum optical master equation, which is known to have an exact analytic solution. Starting from a pure input state, we employ two indicators of how different the initial and evolved states are, namely, the fidelity of evolution and the Hilbert-Schmidt distance of evolution. The former was introduced by del Campo {\em et al.} who derived a time-independent speed limit for the evolution of a Markovian open system. We evaluate it for this field-reservoir setting, with an arbitrary input pure state of the field mode. The resultant formula is then specialized to the coherent and Fock states. On the other hand, we exploit an alternative approach that employs both indicators of evolution mentioned above. Their rates of change have the same upper bound, and consequently provide a unique time-dependent quantum speed limit. It turns out that the associate quantum speed limit time built with the Hilbert-Schmidt metric is tighter than the fidelity-based one. As apposite applications, we investigate the damping of the coherent and Fock states by using the characteristic functions of the corresponding evolved states. General expressions of both the fidelity and the Hilbert-Schmidt distance of evolution are obtained and analyzed for these two classes of input states. In the case of a coherent state, we derive accurate formulas for their common speed limit and the pair of associate limit times., Comment: 6 figures

A wide variety of imaging systems have been designed to measure phase variations, with applications from physics to biology and medicine. In this work, we theoretically compare the precision of phase estimations achievable with classical phase microscopy techniques, operated at the shot-noise limit. We show how the Cram\'{e}r-Rao bound is calculated for any linear optical system, including phase-contrast microscopy, phase-shifting holography, spatial light interference microscopy, and local optimization of wavefronts for phase imaging. Through these examples, we demonstrate how this general framework can be applied for the design and optimization of classical phase microscopes. Our results show that wavefront shaping is required to design phase microscopes with optimal phase precision.

The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.

We study the transitions between the different color states of a static quark-antiquark pair, singlet and octet, in a thermal medium. This is done non-perturbatively exploiting the infinite mass limit of QCD. This study is interesting because it can be used for future developments within the framework of Effective Field Theories (EFTs) and because it can be combined with other techniques, like lattice QCD or AdS/CFT, to gain non-perturbative information about the evolution of quarkonium in a medium. We also study the obtained expressions in the large $N_{c}$ limit. This allows us to learn lessons that are useful to simplify phenomenological models of quarkonium in a plasma., 32 pages, 14 figures. Matches published version

We report on sub-cycle terahertz light-field emission of electrons from tungsten nanotips under extreme conditions corresponding to a Keldysh parameter $\gamma_K\approx10^{-4}$. Local peak THz fields up to 40~GV/m are achieved at the apex of an illuminated nanotip, causing sub-cycle cold-field electron emission and acceleration in the quasi-static field. By simultaneous measurement of the electron bunch charge and energy distribution, we perform a quantitative test of quasi-static Fowler-Nordheim tunnelling theory under field conditions that completely suppress the tunnel barrier. Very high bunch charges of $\sim10^6$ electrons/pulse are observed, reaching maximum energies of 3.5~keV after acceleration in the local field. The energy distribution and emission current show good agreement with Fowler-Nordheim theory even in this extreme field regime. Extending this model to the single-shot regime under these conditions predicts peak electron distributions with a spectral purity of $10^{-4}$. THz field-induced reshaping and sharpening of the nanotip is observed, reducing the tip radius from 120~nm to 35~nm over roughly $10^9$ THz shots. These results indicate THz-driven nanotips in the extreme field limit are promising electron sources for ultrafast electron diffraction and microscopy., Comment: 7 pages, 4 figures, Supplemental material (5 pages, 5 figures)

In this paper, we study a particular deformation of the Jackiw-Teitelboim gravity recently considered by Maxfield, Turiaci, and independently by Witten. We will compute the partition function of this model as well as its higher order correlators to all orders in genus expansion in the low temperature limit for small perturbations. In this limit, the results match with those obtained from the Airy limit of a Hermitian random matrix ensemble. Using this result, we will also study the free energy of the model. One observes that although the annealed free energy has pathological behaviors, under certain assumptions, the quenched free energy evaluated by replica trick exhibits the desired properties at low temperatures.

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with $n-$multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For $n\geq1$, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent ${2n+1}$. A simple theory based on Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the $n\to \infty$ limit, and accordingly exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile non-equilibrium phases, which we illustrate with a random multipolar discrete time crystal., Comment: 5+5 pages, 4+7 figures, accepted in P.R.L

It is widely accepted that inverse square Levy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the previously visited target, which becomes revisitable again with high probability, i.e., non-destructive foraging [Nature 401, 911 (1999)]. The precise conditions for the validity of this Levy flight foraging hypothesis (LFH) have been widely described in the literature [Phys. Life Rev. 14, 94 (2015)]. Nevertheless, three objecting claims to the LFH have been raised recently for $d \geq 2$: (i) the capture rate $\eta$ has linear dependence on the target density $\rho$ for all values of the Levy index $\alpha$; (ii) "the gain $\eta_{max}/\eta$ achieved by varying $\alpha $ is bounded even in the limit $\rho \to 0 $" so that "tuning $\alpha$ can only yield a marginal gain"; (iii) depending on the values of the radius of detection $a$, the restarting distance $l_c$ and the scale parameter $s$, the optimum is realized for a range of $\alpha$ [Phys. Rev. Lett. 124, 080601 (2020)]. Here we answer each of these three criticisms in detail and show that claims (i)-(iii) do not actually invalidate the LFH. Our results and analyses restore the original result of the LFH for non-destructive foraging.

Composite particles---atoms, molecules, or microspheres---are unique tools for testing joint quantum and general relativistic effects, macroscopic limits of quantum mechanics, and searching for new physics. However, all studies of the free propagation of these particles find that they delocalise into separate internal energy components, destroying their spatial coherence. This renders them unsuitable for experimental applications, as well as theoretical studies where they are used as idealised test masses or clocks. Here we solve this problem by introducing a new class of states with minimal uncertainty in space-time that fully overcome the delocalisation. The relevant physics comes from minimising the uncertainty between position and velocity, rather than position and momentum, while directly accounting for mass as an operator. Our results clarify the nature of composite particles, providing a currently missing theoretical tool with direct relevance for studies of joint foundations of quantum and relativistic phenomena, which removes a roadblock that could limit near-future quantum tests using composite particles., Comment: 5 figures, version 4 updated text, reordering of sections, new appendix on contractive states

We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel regime. Then by examining the convergence of the localization length, in the limit of infinite hopping range, we revisit the problem of localization criteria in this model and investigate the conditions under which it can be violated. Our results reveal possibilities of having delocalized states by tuning the long-range hopping., Comment: 5 pages, 3 figures

We show that the predictions of spatially smeared particle detectors coupled to quantum fields are not generally covariant outside the pointlike limit. This lack of covariance manifests itself as an ambiguity in the time-ordering operation. We analyze how the breakdown of covariance affects typical detector models in quantum field theory such as the Unruh-DeWitt model. Specifically, we show how the violations of covariance depend on the state of the detectors-field system, the shape and state of motion of the detectors, and the spacetime geometry. Furthermore, we provide the tools to explicitly evaluate the magnitude of the violation, and identify the regimes where the predictions of smeared detectors are either exactly or approximately covariant in perturbative analyses., Comment: 12 pages. RevTeX 4.1. V2. Corrected minor typos

In contrast to five-dimensional Schwarzschild-Tangherlini and Myers-Perry backgrounds, we show that there are stable bound orbits of massive/massless particles in five-dimensional black lens backgrounds, in particular, the supersymmetric black lens with $L(2,1)$ and $L(3,1)$ topologies. We also show that in the zero-energy limit of massless particles, there exist stable circular orbits on the evanescent ergosurfaces., 25 pages, 24 figures

Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial dimension, the quantum walk can be "promoted" to a QCA that, in the long-wavelength limit, gives rise to the Dirac quantum field theory (QFT) for noninteracting fermions. This QCA/QFT correspondence has both theoretical and practical applications, but there are obstacles to similar constructions in two or more spatial dimensions. Here we show that a method of construction employing distinguishable particles confined to the completely antisymmetric subspace yields a QCA in two spatial dimensions that gives rise to the 2D Dirac QFT. Generalizing to 3D will entail some additional complications, but no conceptual barriers. We examine how this construction evades the "no go" results in earlier work., 12 pages, no figures

Strong-field above-threshold detachment (ATD) is analyzed in the low-frequency (or adiabatic) limit. The explicit form of ATD amplitude is obtained within a developed low-frequency approximation. We show that in the low-frequency limit, the atomic structure effects are introduced in the ATD amplitude through the $T$ matrix, which in the limiting case coincides with the amplitude of elastic electron scattering. The rescattering part of ATD amplitude is evaluated in terms of the closed real classical electron trajectories. We further discuss the behavior of ATD amplitude near the caustic rescattering energies (classical energies for which two trajectories merge into a single one) of photoelectrons. Comparison of developed analytic theory with the numerical solution of time-dependent Schr\"odinger equation is presented for linearly polarized and time-delayed bicircular fields. Based on the analytical description, we predict an enhancement of ATD yield for time-delayed bicircular fields, which is similar to previous findings for the high harmonic yield [M.V. Frolov et al., Phys. Rev. Lett. 120, 263203 (2018)].

We study an optomechanical (OM) system with optical and mechanical modes interacting through a dispersive linear and quadratic optomechanical coupling (QOC) in an unresolved sideband limit. The presence of a QOC plays a crucial role in altering the effective OM interaction and the spring constant of the mechanical resonator. The choice of a positive QOC in the system increases the spring constant, inducing a `stiffer mode.' The existence of this stiffer mode leads to unconventional behavior in the total displacement noise consisting of imprecision, backaction, and thermal noises. We further show that unlike the conventional OM system wherein the optimal total displacement noise is limited by the imprecision and backaction noises, it is due to the competing imprecision and thermal noise, making it feasible to observe displacement sensing below the conventional standard quantum limit.

We discuss vortex solutions of the Abelian Higgs model in the limit of large winding number n. We suggest a framework where a topological quantum number n is associated with a ratio of dynamical scales and a systematic expansion in inverse powers of n is then derived in the spirit of effective field theory. The general asymptotic form of giant vortices is obtained. For critical coupling the axially symmetric vortices become integrable in the large-n limit and we present the corresponding analytic solution. The method provides simple asymptotic formulas for the vortex shape and parameters with accuracy that can be systematically improved, and can be applied to topological solitons of other models. After including the next-to-leading terms the approximation works remarkably well down to n=1.

We investigate the role of the effective range on the bulk viscosity of $s$- and $p$-wave Fermi gases. At resonance, the presence of the effective range breaks the scale invariance of the system, and hence results in a non-zero bulk viscosity. However, we show that the effective range plays a very different role in the two cases. In the $s$-wave case, the role of the effective range is perturbative, and its contribution to the bulk viscosity vanishes in the limit of zero effective range. On the other hand, the effective range in $p$-wave Fermi gases leads to a non-zero bulk viscosity, even in the zero-range limit. We setup the general diagrammatic approach to compute the bulk viscosity spectral function that includes the effects of the effective range. We then compute the analytic expressions for the spectral function in the high temperature limit, at low- and high-frequencies. We also derive the sum rules for the bulk viscosity spectral function for both $s$- and $p$-wave gases.

International audience; Propagation of waves in materials that exhibit stealth-hyperuniform long range correlations is investigated. By using a modal decomposition of the field that takes multiple scattering into account at all orders, we study the impact of the concentration of particles on the transparency of such materials at low frequency. An upper frequency limit for transparency is defined that include both the particles size and the degree of stealthiness. We show that the independent scattering approximation is not relevant to calculate elastic mean free paths when wavelength become comparable to the size of particles. We find that transparency is very robust with regard to the degree of heterogeneity of the host random medium and the polydispersity of particles. Finally, it is shown that resonances can be used as frequency filter.

We investigate diffusion of excitation in one- and two-dimensional lattices with random onsite energies and deterministic long-range couplings (hopping) inversely proportional to the distance. Three regimes of diffusion are observed in strongly disordered systems: ballistic motion at short time, standard diffusion for intermediate times, and a stationary phase (saturation) at long times. We propose an analytical solution valid in the strong-coupling regime which explains the observed dynamics and relates the ballistic velocity, diffusion coefficient, and asymptotic diffusion range to the system size and disorder strength via simple formulas. We show also that in the long-time asymptotic limit of diffusion from a single site the occupations form a heavy-tailed power-law distribution.

We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of the spin current density $\mathcal J^s$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a non-trivial universal behavior close to the XX limit. It is controlled by the scattering length $L^*\propto V^{-2}$, where $V$ is the strength of the integrability breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasi-ballistic" regime at length scales much shorter than $L^*$. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on Matrix Product Operator numerical simulations and agree with perturbative analytical calculations., 13 pages, 9 figures

Cold Dark Stars made of self-gravitating fermions in the degenerate limit are constructed in General Relativity and in R-square gravity, $f(R)=R+\alpha R^2$. The properties of the resulting Cold Dark Stars in both theories of gravity are studied. It is found that the same gravitational potential is generated for different election of the parameters of the model, such as the mass of the fermion, the self-interacting strength or the value of $\alpha$, thus, a possible confusion in the determination of the dark matter properties and the favored theory of gravity might arise., Comment: Accepted for publication in Physical Review D

A geometric superinductor made of a tightly wound aluminum wire can achieve an impedance about 5 times larger than a hypothesized fundamental limit.

When a muon bound in an atom decays, there is a small probability that the daughter electron remains bound. That probability is evaluated. Surprisingly, a significant part of the rate is contributed by the negative energy component of the wave function, neglected in a previous study. A simple integral representation of the rate is presented. In the limit of close muon and electron masses, an analytic formula is derived.