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We consider the recent relativistic bit commitment protocol introduced by Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015)] and present a new security analysis against classical attacks. In particular, while the initial complexity of the protocol scales double exponentially with the commitment time, our analysis shows that the correct dependence is only linear. This has dramatic implications in terms of implementation: in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation. [ABSTRACT FROM AUTHOR]

From length scale distributions characterizing frozen amorphous domains, we relate the s ensemble method with standard cooling and aging protocols for formin0 glass. We show that in a class of models where space-time scaling is in harmony with that of experiment, the spatial distributions of excitations obtained with the .v ensemble are identical to those obtained through cooling or aging, but the computational effort for applying the s ensemble is generally many orders of magnitude smaller than that of straightforward numerical simulation of cooling or aging. We find that in contrast to the equilibrium ergodic state, a nonequilibrium length scale characterizes the anticorrelation between excitations and encodes the preparation history of glass states. [ABSTRACT FROM AUTHOR]

We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the 2D3/2 → 2B1/2 transition in calcium, resulting in a transition frequency of f = 346 000 234 867(96) kHz. Furthermore, we determine the isotope shift of this transition and the 2S1/2 → 2P1/2 transition for 42Ca+, 44Ca+, and 48Ca+ ions relative to 40Ca+ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data. [ABSTRACT FROM AUTHOR]

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrix-product operators, designed to capture mixed states of one-dimensional quantum systems. It is a well-known open problem to find an efficient algorithm that decides whether a given matrix-product operator actually represents a physical state that in particular has no negative eigenvalues. We address and answer this question by showing that the problem is provably undecidable in the thermodynamic limit and that the bounded version of the problem is NP-hard (nondeterministic-polynomial-time hard) in the system size. Furthermore, we discuss numerous connections between tensor network methods and (seemingly) different concepts treated before in the literature such as hidden Markov models and tensor trains. [ABSTRACT FROM AUTHOR]

The spin-orbit interaction (SOI) of a two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge/SiGe quantum well structure. We observe weak antilocalization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrate electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained Ge is a purely cubic Rashba system, which is consistent with the spin angular momentum mj = ± 3/2 nature of the HH wave function. [ABSTRACT FROM AUTHOR]

For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to anti-de Sitter space (AdS) but whose numerical evolution does not result in black hole formation. According to the AdS/conformal field theory (CFT) dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-time-scale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasiperiodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem. [ABSTRACT FROM AUTHOR]

We present a thermodynamic theory for a generic population of M individuals distributed into N groups (clusters). We construct the ensemble of all distributions with fixed M and N, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to regular thermodynamics. We treat the emergence of a so-called giant component as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of superdiffusion, in the sense that there is a logarithmic correction to the linear growth in time of the meansquared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time range accessible to numerical simulations. We compare our simulations to analytical results for the variance of the anomalously rescaled limiting normal distributions. [ABSTRACT FROM AUTHOR]

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid-state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there has been no systematic computational technique of the multiple series representations of N-fold MB integrals for N>2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e., logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained, the method also allows, in general, the determination of a single "master series" for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this Letter, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers. [ABSTRACT FROM AUTHOR]

The S=1 Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the S=3/2 AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental problem of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound Δ>0.006 on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives an analytical, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion numerically by performing state-of-the-art DMRG calculations on the subsystem. [ABSTRACT FROM AUTHOR]

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature Tc with the carrier density n predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasilocal. In contrast, we show that any well-defined nonlocal potential leads to a "superconducting dome," i.e., a nonmonotonic Tc(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity. [ABSTRACT FROM AUTHOR]

We establish a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe ansatz equations that yield the Hagedorn temperature of planar N=4 super Yang-Mills theory at any value of the 't Hooft coupling. We solve these equations perturbatively at weak coupling via the associated Y system, confirming the known results at tree level and one-loop order as well as deriving the previously unknown two-loop Hagedorn temperature. Finally, we comment on solving the equations at finite coupling. [ABSTRACT FROM AUTHOR]

We use a numerical solution of the deterministic time-dependent Ginzburg-Landau (TDGL) equations to determine the response induced by a probe field in a material quenched into a superconducting state. We characterize differences in response according to whether the probe is applied before, during, or after the phase stiffness has built up to its final steady-state value. We put an emphasis on the extent to which superfluid response requires a non-negligible phase stiffness, which for the considered quench has to build up dynamically. A key finding is that the time-dependent phase stiffness controls the likelihood of phase slips as well as the magnitude of the electromagnetic response. Additionally, we address the electromagnetic response expected if the probe itself is strong enough to activate phase slip processes. If the probe is applied before phase stiffness is sufficiently built up, we find that phase slips occur so that the vector potential is compensated and no long-term supercurrent is induced, while if it is applied at sufficient phase stiffness a weak probe pulse will induce a state with a long-lived supercurrent. If the probe is strong enough to activate the phase slip process, the supercurrent state will only be metastable with a lifetime that scales logarithmically with the amplitude of fluctuations in the magnitude of the order parameter. Finally, we study the response to experimentally motivated probe fields (electric field that integrates to zero). Interestingly, depending on the relative time difference of the probe field to the buildup of superconductivity, long-lived supercurrents can be induced even though the net change in vector potential is zero. [ABSTRACT FROM AUTHOR]

One of the central ideas regarding anomalies in topological phases of matter is that they imply the existence of higher-dimensional physics, with an anomaly in a D-dimensional theory typically being canceled by a bulk (D+1)-dimensional symmetry-protected topological phase (SPT). We demonstrate that for some topological phases with reflection symmetry, anomalies may actually be canceled by a D-dimensional SPT, provided that it comes embedded in an otherwise trivial (D+1)-dimensional bulk. We illustrate this for the example of ZN topological order enriched with reflection symmetry in (2+1)D, and along the way establish a classification of anomalous reflection symmetry fractionalization patterns. In particular, we show that anomalies occur if and only if both electric and magnetic quasiparticle excitations possess nontrivial fractional reflection quantum numbers. [ABSTRACT FROM AUTHOR]

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations. [ABSTRACT FROM AUTHOR]

We investigate the spin-stripe mechanism responsible for the peculiar nanometer modulation of the incommensurate magnetic order that emerges between the vector-chiral and the spin-density-wave phase in the frustrated zigzag spin-1/2 chain compound β-TeVO4. A combination of magnetic-torque, neutron-diffraction, and spherical-neutron-polarimetry measurements is employed to determine the complex magnetic structures of all three ordered phases. Based on these results, we develop a simple phenomenological model, which exposes the exchange anisotropy as the key ingredient for the spin-stripe formation in frustrated spin systems. [ABSTRACT FROM AUTHOR]

We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial, and power-law degree distributions. The mean, mode, and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illuminating the connection between the two distributions. [ABSTRACT FROM AUTHOR]

The rock-paper-scissors game is a paradigmatic model for biodiversity, with applications ranging from microbial populations to human societies. Research has shown, however, that mobility jeopardizes biodiversity by promoting the formation of spiral waves, especially if there is no conservation law in place for the total number of competing players. First, we show that even if such a conservation law applies, mobility still jeopardizes biodiversity in the spatial rock-paper-scissors game if only a small fraction of links of the square lattice is randomly rewired. Secondly, we show that zealots are very effective in taming the amplitude of oscillations that emerge due to mobility and/or interaction randomness, and this regardless of whether the later is quenched or annealed. While even a tiny fraction of zealots brings significant benefits, at 5% occupancy zealots practically destroy all oscillations regardless of the intensity of mobility, and regardless of the type and strength of randomness in the interaction structure. Interestingly, by annealed randomness the impact of zealots is qualitatively the same as by mobility, which highlights that fast diffusion does not necessarily destroy the coexistence of species, and that zealotry thus helps to recover the stable mean-field solution. Our results strengthen the important role of zealots in models of cyclic dominance, and they reveal fascinating evolutionary outcomes in structured populations that are a unique consequence of such uncompromising behavior. [ABSTRACT FROM AUTHOR]

It is commonly assumed in percolation theories that at most one percolating cluster can exist in a network. We show that several coexisting percolating clusters (CPCs) can emerge in networks due to limited mixing, i.e., a finite and sufficiently small number of interlinks between network modules. We develop an approach called modular message passing (MMP) to describe and verify these observations. We demonstrate that the appearance of CPCs is an important source of inaccuracy in previously introduced percolation theories, such as the message passing (MP) approach, which is a state-of-the-art theory based on the belief propagation method. Moreover, we show that the MMP theory improves significantly over the predictions of MP for percolation on synthetic networks with limited mixing and also on several real-world networks. These findings have important implications for understanding the robustness of networks and in quantifying epidemic outbreaks in the susceptible-infected-recovered (SIR) model of disease spread. [ABSTRACT FROM AUTHOR]

We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent clustering are extracted from the evolved networks and used to construct random networks with the prescribed distributions. In the analysis of these reconstructed networks it turns out that the degree distribution alone is not sufficient to generate the spectral scaling and the degree-dependent clustering has only an indirect influence. The two-point correlations are found to be the dominant characteristic for the power-law scaling over a broader eigenvalue range. [ABSTRACT FROM AUTHOR]

In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field. [ABSTRACT FROM AUTHOR]

The relaxation process of a diffusive ring becomes underdamped if the bias (so-called affinity) exceeds a critical threshold value, also known as the delocalization transition. This is related to the spectral properties of the pertinent stochastic kernel. We find the dependence of the relaxation rate on the affinity and on the length of the ring. Additionally we study the implications of introducing a weak link into the circuit and illuminate some subtleties that arise while taking the continuum limit of the discrete model. [ABSTRACT FROM AUTHOR]

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by the analysis of particular physical systems and do not necessarily apply to general situations. The central concepts in this paper--the swatch and the cloth--provide a description of the local topology of a cell complex that is general (any physical system that can be represented as a cell complex is admissible) and complete (any statistical question about the local topology can be answered from the cloth). Furthermore, this approach allows a distance to be defined that measures the similarity of the local topology of two cell complexes. The distance is used to identify a steady state of a model grain boundary network, quantify the approach to this steady state, and show that the steady state is independent of the initial conditions. The same distance is then employed to show that the long-term properties in simulations of a specific model of a dislocation network do not depend on the implementation of dislocation intersections. [ABSTRACT FROM AUTHOR]

We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)]. Our investigation further justifies the definition of quantum work via two-point energy measurements. [ABSTRACT FROM AUTHOR]

Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory that characterizes the ability of a linear readout network, the perceptron, to classify objects from variable neural responses. We show how the readout perceptron capacity depends on the dimensionality, size, and shape of the object manifolds in its input neural representation. [ABSTRACT FROM AUTHOR]

While originally discovered in the context of the Gaussian unitary ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters, the profile develops a rarefaction wave while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For a Fermi-Pasta-Ulam type anharmonic chain, we will demonstrate that the time-integrated current has a deterministic contribution, linear in time t, and fluctuations of size t1/3 with a Tracy-Widom distributed random amplitude. [ABSTRACT FROM AUTHOR]

Following on our previous work [S. Delong, B. E. Griffith, E. Vanden-Eijnden, and A. Donev, Phys. Rev. E 87, 033302 (2013)], we develop temporal integrators for solving Langevin stochastic differential equations that arise in fluctuating hydrodynamics. Our simple predictor-corrector schemes add fluctuations to standard second-order deterministic solvers in a way that maintains second-order weak accuracy for linearized fluctuating hydrodynamics. We construct a general class of schemes and recommend two specific schemes: an explicit midpoint method and an implicit trapezoidal method. We also construct predictor-corrector methods for integrating the overdamped limit of systems of equations with a fast and slow variable in the limit of infinite separation of the fast and slow time scales. We propose using random finite differences to approximate some of the stochastic drift terms that arise because of the kinetic multiplicative noise in the limiting dynamics. We illustrate our integrators on two applications involving the development of giant nonequilibrium concentration fluctuations in diffusively mixing fluids. We first study the development of giant fluctuations in recent experiments performed in microgravity using an overdamped integrator. We then include the effects of gravity and find that we also need to include the effects of fluid inertia, which affects the dynamics of the concentration fluctuations greatly at small wave numbers. [ABSTRACT FROM AUTHOR]

The solution of the inverse scattering problem for the one-dimensional Schrödinger equation is given by the Marchenko equation. Recently, a Marchenko-type equation has been derived for three-dimensional (3D) acoustic wave fields, whose solution has been shown to recover the Green's functions from points within the medium to its exterior, using only single-sided scattered data. Here we extend this approach to 3D vectorial wave fields that satisfy the elastodynamic wave equation and recover Green's functions from points interior to an elastic, solid-state medium from purely external and one-sided measurements. The method is demonstrated in a solid-earth-like model to construct Green's functions using only subsurface sources, from earth-surface force and deformation sources and particle velocity and stress measurements. [ABSTRACT FROM AUTHOR]

A vortex sheet formalism is used to search for equilibrium shapes in the centrifugally driven interfacial elastic fingering problem. We study the development of interfacial instabilities when a viscous fluid surrounded by another of smaller density flows in the confined environment of a rotating Hele-Shaw cell. The peculiarity of the situation is associated to the fact that, due to a chemical reaction, the two-fluid boundary becomes an elastic layer. The interplay between centrifugal and elastic forces leads to the formation of a rich variety of stationary shapes. Visually striking equilibrium morphologies are obtained from the numerical solution of a nonlinear differential equation for the interface curvature (the shape equation), determined by a zero vorticity condition. Classification of the various families of shapes is made via two dimensionless parameters: an effective bending rigidity (ratio of elastic to centrifugal effects) and a geometrical radius of gyration. [ABSTRACT FROM AUTHOR]

The embedding of a time series provides a basic tool to analyze dynamical properties of the underlying chaotic system. To this purpose, the choice of the embedding dimension and lag is crucial. Although several methods have been devised to tackle the issue of the optimal setting of these parameters, a conclusive criterion to make the most appropriate choice is still lacking. An accepted procedure to rank different embedding methods relies on the evaluation of the maximum Lyapunov exponent (MLE) out of embedded time series that are generated by chaotic systems with explicit analytic representation. The MLE is evaluated as the local divergence rate of nearby trajectories. Given a system, embedding methods are ranked according to how close such MLE values are to the true MLE. This is provided by the so-called standard method in a way that exploits the mathematical description of the system and does not require embedding. In this paper we study the dependence of the finite-time MLE evaluated via the divergence rate method on the embedding dimension and lag in the case of time series generated by four systems that are widely used as references in the scientific literature. We develop a completely automatic algorithm that provides the divergence rate and its statistical uncertainty. We show that the uncertainty can provide useful information about the optimal choice of the embedding parameters. In addition, our approach allows us to find which systems provide suitable benchmarks for the comparison and ranking of different embedding methods. [ABSTRACT FROM AUTHOR]

We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between elastic and fracture energies. The power law exponent (8/11) is in close agreement with experiments. We also show that a second (asymptotic) regime, with an exponent of 9/8, emerges for small distances between the two crack tips due to the finite transverse curvature of the elastic ridge joining them. [ABSTRACT FROM AUTHOR]