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As a promising candidate for exhibiting quantum computational supremacy, Gaussian Boson Sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS --- in the form of an inequality between the input squeezing parameter, the overall transmission rate and the quality of photon detectors. Our result serves as a non-classicality test that must be passed by any quantum computationalsupremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss., 13 pages, 4 figures, final version accepted for publication in Physical Review Letters

The observation of maximally rotating neutron stars (in comparison to nonrotating ones) may provide more information on the behavior of nuclear matter at high densities. We provide a theoretical treatment concerning the effects of the upper bound of the sound speed in dense matter on the bulk properties of maximally rotating (at mass-shedding limit) neutron stars. In particular, we consider two upper bounds for the speed of sound, $v_s = c$ and $v_s = c/\sqrt{3}$, and the one provided by the relativistic kinetic theory. We investigate to what extent the possible predicted (from various theories and conjectures) upper bounds on the speed of sound constrain the ones of various key quantities, including the maximum mass and the corresponding radius, Keplerian frequency, Kerr parameter and moment of inertia. We mainly focus on the lower proposed limit, $v_{s}=c/\sqrt{3}$, and we explore in which mass region a rotating neutron star collapses to a black hole. In any case, useful relations of the mentioned bulk properties with the transition density are derived and compared with the corresponding nonrotating cases. We concluded that the proposed limit $v_{s}=c/\sqrt{3}$ leads to dramatic decrease on the values of the maximum mass, Kerr parameter and moment of inertia preventing a neutron star to reach values which derived with the consideration of realistic equations of state or from other constraints. Possible measurements of the Kerr parameter and moment of inertia would shed light on these issues and help to reveal the speed of sound bound in dense matter., Comment: v1: 8 pages, 10 figures, 2 tables. v2: 10 pages, 15 figures, 3 tables; sections, tables, figures and references had been added. v3: 12 pages, 10 figures, 5 tables; accepted for publication in Phy. Rev. D

We analyze a new model for growing networks, the constrained Leath invasion percolation model. Cluster dynamics are characterized by bursts in space and time. The model quantitatively reproduces the observed frequency-magnitude scaling of earthquakes in the limit that the occupation probability approaches the critical bond percolation probability in d=2. The model may have application to other systems characterized by burst dynamics.

We formulate and solve the Eliashberg equations on the imaginary frequency axis at temperatures below $T_c$ in the weak-coupling limit. We find an excellent scaling at all temperatures, for a given coupling strength, and the normalized order parameter exhibits a BCS-like temperature dependence. The hybrid real-imaginary axis equations are also solved to obtain numerically exact analytic continuations from the imaginary frequency axis to the real frequency axis. This provides a determination of the gap edge, which, in the weak-coupling limit, is identical to the order parameter from the imaginary axis. The analytical result for the zero-temperature gap edge deviates from the BCS result by a factor of $1/\sqrt{e}$, which was also obtained for the transition temperature $T_c$. We show that the normalized gap function on both the real and imaginary frequency axes, for an electron-phonon Einstein spectrum ($\delta$-function) of a given strength, is a universal function of frequency, independent of temperature. The $1/\sqrt{e}$ correction is a result of this non-trivial frequency dependence in the gap function. This modification, in the gap edge and in $T_{c}$, serves to preserve various dimensionless ratios to their BCS values., Comment: 11 pages, 8 figures

This letter exposes a tight connection between the thermodynamic efficiency of information processing and predictive inference. A generalized lower bound on dissipation is derived for partially observable information engines which are allowed to use temperature differences. It is shown that the retention of irrelevant information limits efficiency. A data representation strategy is derived from optimizing a fundamental physical limit to information processing: minimizing the lower bound on dissipation leads to a data compression method that maximally retains relevant, predictive, information. In that sense, predictive inference emerges as the strategy that least precludes energy efficiency., Comment: Accepted for publication in Physical Review Letters

We propose a continuous-variable quantum secret sharing (CV-QSS) protocol in which the quantum states are prepared passively using a thermal source. In our protocol, one player splits the output of a thermal source into two spatial modes with the help of a beam splitter, then he (or she) measures one of the correlated thermal states and sends the others to the secure station of the adjacent player in sequence after using appropriate optical attenuation, which waives the necessity of employment of high extinction ratio modulators with good stability. Therefore, the proposed protocol provides convenient implementation in QSS framework. Moreover, our scheme is immune to Trojan horse attacks. We derive the security bounds for our protocol against both eavesdroppers and dishonest players. Furthermore, we can achieve tighter bound of QSS distance by considering the finite-size effect, which is more practical than that obtained in the asymptotic limit.

We study the null geodesics extending from the near-horizon region out to the far region in the background of the Schwarzschild and the singly-spinning Myers-Perry black holes in the large dimension limit. We find that in this limit the radial integrals of these geodesics can be obtained by using the method of matched asymptotic expansions. If the motion of the photon is confined to the equator plane, then all geodesic equations are solvable analytically. The study in this paper may provide a toy model to analyze the observables relevant to the electromagnetic phenomena occurring near the black holes., Comment: 19 pages,v2: minor changes, references added, accepted version

Aiming to combine density functional theory (DFT) and wave-function theory, we study a mapping from the many-body interacting system to an effectively interacting Kohn-Sham system instead of a noninteracting Kohn-Sham system. Because a ground state of effectively interacting systems requires having a solution for the correlated many-body wave functions, this provides a natural framework to many-body wave-function theories such as the configuration interaction and the coupled-cluster method in the formal theoretical framework of DFT. Employing simple one-dimensional two-electron systems—namely, the one-dimensional helium atom, the hydrogen molecule, and the heteronuclear diatomic molecule—we investigate properties of many-body wave functions and exact exchange-correlation potentials of effectively interacting Kohn-Sham systems. As a result, we find that the asymptotic behavior of the exact exchange-correlation potential can be controlled by optimizing that of the effective interaction. Furthermore, the typical features of the exact noninteracting Kohn-Sham system, namely, a spiky feature and a step feature in the exchange-correlation potential for the molecular dissociation limit, can be suppressed by a proper choice of the effective interaction. These findings open a possibility to construct numerically robust and efficient exchange-correlation potentials and functionals based on the effectively interacting Kohn-Sham scheme., This work was supported by the European Research Council (Grant No. ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM), and JST-CREST under Grant No. JP-MJCR16N5. Support by the Flatiron Institute, a division of the Simons Foundation, is acknowledged. S.A.S. gratefully acknowledges a fellowship from the Alexander von Humboldt Foundation.

We consider a formulation for the Hopf functional differential equation which governs statistical solutions of the Navier-Stokes equations. By introducing an exponential operator with a functional derivative, we recast the Hopf equation as an integro-differential functional equation by the Duhamel principle. On this basis we introduce a successive approximation to the Hopf equation. As an illustration we take the Burgers equation and carry out the approximations to the leading order.\ud Scale-invariance of the statistical Navier-Stokes equations in d-dimensions is formulated and contrasted with that of the deterministic Navier-Stokes equations. For the statistical Navier-Stokes equations, critical scale-invariance is achieved for the characteristic functional of the d-th derivative of the vector potential in d-dimensions. The deterministic equations corresponding to this choice of the dependent variable acquire the linear Fokker-Planck operator under dynamic scaling. In three dimensions it is the vorticity gradient that behaves like a fundamental solution (more precisely, source-type solution) of deterministic Navier-Stokes equations in the long-time limit.\ud Physical applications of these ideas include study of a self-similar decaying profile of fluid flows. Moreover, we reveal typical physical properties in the late stage evolution by combining statistical scale-invariance and the source-type solution. This yields an asymptotic form of the Hopf functional\ud in the long-time limit, improving the well-known Hopf-Titt solution. In particular, we present analyses for the Burgers equations to illustrate the main ideas and indicate a similar analysis for the Navier-Stokes equations.

We present a theory of nonradiative recombination (NRR) with an emphasis on the so far little-explored dynamic effect in the process. We show that it can significantly enhance the NRR rate over that of a static midgap level as suggested by the Shockley-Read-Hall theory, whereby offering an alternative explanation to the long-lasting discrepancy between theory and experiment for semiconductors. As an illustration, we show that dynamic NRR can take place at the $DX$ center in Si-doped GaAs which, combined with a modified ABC model at high carrier-density limit, makes it possible to verify the theory directly by experiment.

L\'{e}vy walk is a practical model and has wide applications in various fields. Here we focus on the effect of an external constant force on the L\'{e}vy walk with the exponent of the power-law distributed flight time $\alpha\in(0,2)$. We add the term $F\eta(s)$ ($\eta(s)$ is the L\'{e}vy noise) on a subordinated Langevin system to characterize such a constant force, being effective on the velocity process for all physical time after the subordination. We clearly show the effect of the constant force $F$ on this Langevin system and find this system is like the continuous limit of the collision model. The first moments of velocity processes for these two models are consistent. In particular, based on the velocity correlation function derived from our subordinated Langevin equation, we investigate more interesting statistical quantities, such as the ensemble- and time-averaged mean squared displacements. Under the influence of constant force, the diffusion of particles becomes faster. Finally, the super-ballistic diffusion and the non-ergodic behavior are verified by the simulations with different $\alpha$., Comment: 11 pages, 2 figures

An electronic phase-field crystal model is proposed where the thermodynamics of electrons are considered in a free-energy-functional formulation. The free-electron-gas system is considered initially as the noninteracting limit of the model. The excess free-energy contribution to the functional is incorporated by including Coulombic repulsions among electrons and exchange-correlation interactions. The evolution of an electron mean field is considered in the low-temperature limit using diffusive dynamics. Three-dimensional Wigner crystallization can be achieved from the model when the density of the system is lowered sufficiently. Through this approach, we are able to provide insight into topological defect formation and evolution during Wigner crystallization.

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems., 26 pages, 12 figures

We propose a new definition of ``horizon molecules'' in causal set theory following pioneering work by Dou and Sorkin. The new concept applies for any causal horizon and its intersection with any spacelike hypersurface. In the continuum limit, as the discreteness scale tends to zero, the leading behavior of the expected number of horizon molecules is shown to be the area of the horizon in discreteness units, up to a dimension dependent factor of order one. We also determine the first order corrections to the continuum value, and show how such corrections can be exploited to obtain further geometrical information about the horizon and the spacelike hypersurface from the causal set.

The generalized Einstein relation (GER) for nonergodic processes is investigated within the framework of the generalized Langevin equation. The conditions for anomalous relaxation such as long-tail decay and non-vanishing velocity autocorrelation function (VAF) are proposed and distinguished. For the stationary nonergodic process, if the initial preparation of the particle velocity is non-thermal, an asymptotic GER occurs in a departure from the usual result. It is shown that the GER holding is a necessary condition rather than a full condition for the system being close to equilibrium. For the nonergodic process of the second type due to cutoff of high frequencies, the VAF oscillates with time, the GER holds but the equilibrium fails in the long-time limit. Applications to some practical examples confirm the present theoretical findings.

We consider the chiral Lagrangian for baryon fields with J^P =\frac{1}{2}^+ or J^P =\frac{3}{2}^+ quantum numbers as constructed from QCD with up, down and strange quarks. The specific class of counter terms that are of chiral order Q^3 and contribute to meson-baryon interactions at the two-body level is constructed. Altogether we find 24 terms. In order to pave the way for realistic applications we establish a set of 22 sum rules for the low-energy constants as they are implied by QCD in the large-N_c limit. Given such a constraint there remain only 2 independent unknown parameters that need to be determined by either Lattice QCD simulations or directly from experimental cross section measurements. At subleading order we arrive at 5 parameters.

This paper presents a theoretical framework for the phase description of limit-torus solutions to partial differential equations with constraints. The theory is illustrated in two-dimensional incompressible Navier-Stokes flow systems. The author further analyzes the spatiotemporal phase synchronization between a pair of weakly coupled systems of traveling and oscillating thermal convection.

We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a nonequilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, i.e., the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics.

In this paper, motivated by a general interest in the stochastic thermodynamics of small systems, we derive an exact expression-via path integrals-for the conditional probability density of a two-dimensional harmonically confined Brownian particle acted on by linear mixed flow. This expression is a generalization of the expression derived earlier by Foister and Van De Ven [J. Fluid Mech. 96, 105 (1980)10.1017/S0022112080002042] for the case of the corresponding free Brownian particle, and reduces to it in the appropriate unconfined limit. By considering the long-time limit of our calculated probability density function, we show that the flow-driven Brownian oscillator attains a well-defined steady state. We also show that, during the course of a transition from an initial flow-free thermal equilibrium state to the flow-driven steady state, the integral fluctuation theorem, the Jarzynski equality, and the Bochkov-Kuzovlev relation are all rigorously satisfied. Additionally, for the special cases of pure rotational flow we derive an exact expression for the distribution of the heat dissipated by the particle into the medium, and for the special case of pure elongational flow we derive an exact expression for the distribution of the total entropy change. Finally, by examining the system's stochastic thermodynamics along a reverse trajectory, we also demonstrate that in elongational flow the total entropy change satisfies a detailed fluctuation theorem.

N=2 three dimensional Supergravity with internal $R-$symmetry generators can be understood as a two dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to be flat limit of a generalised Liouville theory, up to zero modes. The reduced phase space description can also be explained as a gauged chiral Wess-Zumino-Witten model. We show that both these descriptions possess identical gauge and global (quantum N=2 superBMS$_3$) symmetries., Comment: 20+2 pages. arXiv admin note: text overlap with arXiv:1905.10239

Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation upon the increasing ratio of the positive and negative feedback strengths is observed, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with large burst frequencies and the L\'{e}vy limit applies to proteins with large burst sizes. We derive the analytic steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and its two macroscopic limits, generalizing the results obtained in [Chaos 26:043108, 2016]. We also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting model proposed in [Phys. Rev. Lett. 97:168302, 2006]. Our analytic results are further applied to study the structure of gene expression noise in a coupled gene circuit and a complete decomposition of noise in terms of five different biophysical origins is provided., Comment: 27 pages, 7 figures

We consider transverse momentum dependent gluon distributions inside both unpolarized and transversely polarized protons and show how they can be probed by looking at azimuthal modulations in ep→eJ/ψ jet X. We find that the contribution due to quark induced subprocesses is always suppressed in the considered kinematic regions, accessible in principle at a future electron-ion collider. Our model-independent estimates of the maximal values of these asymmetries allowed by positivity bounds suggest the feasibility of their measurement. In addition, by adopting the McLerran-Venugopalan model for the unpolarized and linearly polarized gluon densities, we study the behavior of the cos2ϕ asymmetries in the small-x limit.

The existence of quasi-long range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including of two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay., Comment: 19 pages, 9 figures, published version

A famous example of gauge/gravity duality is the result that the entropy density of strongly coupled ${\cal N}=4$ SYM in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at finite temperature $T$ for all couplings $\lambda$ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at $\lambda=0$ to exactly 4/5 of the Stefan-Boltzmann limit at $\lambda=\infty$. Calculating the retarded energy-momentum tensor correlator in the scalar channel at $\lambda=\infty$, I find that it has two logarithmic branch cuts originating at $\omega=\pm 4 T \ln \frac{1+\sqrt{5}}{2}$, but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic CFTs in 2+1 dimensions.

Driven periodic elastic systems such as charge-density waves (CDWs) pinned by impurities show a nontrivial, glassy dynamical critical behavior. Their proper theoretical description requires the functional renormalization group. We show that their critical behavior close to the depinning transition is related to a much simpler model, $O(n)$ symmetric ${\ensuremath{\phi}}^{4}$ theory in the unusual limit of $n\ensuremath{\rightarrow}\ensuremath{-}2$. We demonstrate that both theories yield identical results to four-loop order and give both a perturbative and a nonperturbative proof of their equivalence. As we show, both theories can be used to describe loop-erased random walks (LERWs), the trace of a random walk where loops are erased as soon as they are formed. Remarkably, two famous models of non-self-intersecting random walks, self-avoiding walks and LERWs, can both be mapped onto ${\ensuremath{\phi}}^{4}$ theory, taken with formally $n=0$ and $n\ensuremath{\rightarrow}\ensuremath{-}2$ components. This mapping allows us to compute the dynamic critical exponent of CDWs at the depinning transition and the fractal dimension of LERWs in $d=3$ with unprecedented accuracy, $z(d=3)=1.6243\ifmmode\pm\else\textpm\fi{}0.001$, in excellent agreement with the estimate $z=1.62400\ifmmode\pm\else\textpm\fi{}0.00005$ of numerical simulations.

A modified periodic boundary condition adequate for non-hermitian topological systems is proposed. Under this boundary condition a topological number characterizing the system is defined in the same way as in the corresponding hermitian system and hence, at the cost of introducing an additional parameter that characterizes the non-hermitian skin effect, the idea of bulk-edge correspondence in the hermitian limit can be applied almost as it is. We develop this framework through the analysis of a non-hermitian SSH model with chiral symmetry, and prove the bulk-edge correspondence in a generalized parameter space. A finite region in this parameter space with a nontrivial pair of chiral winding numbers is identified as topologically nontrivial, indicating the existence of a topologically protected edge state under open boundary., Comment: 8 pages, 6 figures with 11 panels, updated version

In this paper we propose a practical quantum key distribution protocol based on geometrically uniform states and a standard decoy state technique. The protocol extends the ideas used in SARG04 to the limit where the core quantum communication is secure against unambiguous state discrimination and provides some level of inherent resistance to photon number splitting attacks. Additional decoy state overlay ensures its conformity to the conventional security requirements. The protocol security is analyzed by an explicit construction of the most optimal unitary attack, which is known to reach the tight security bound in the case of BB84., 7 pages, 3 figures

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop `dressing tails' of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-$S$ limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in light of the limitations set by cavity dissipation., v3: Published version. Included more data and updated the figures accordingly

If the time evolution of a system can be understood classically, then there must exist an underlying probability distribution for the variables describing the system at all times. It is well known that for systems described by a single time-evolving dichotomic variable $Q$ and for which a given set of temporal correlation functions are specified, a necessary set of conditions for the existence of such a probability are provided by the Leggett-Garg (LG) inequalities. Fine's theorem in this context is the non-trivial result that a suitably augmented set of LG inequalities are both necessary and sufficient conditions for the existence of an underlying probability. We present a proof of Fine's theorem for the case of measurements on a dichotomic variable at an abitrary number of times, thereby generalizing the familiar proofs for three and four times. We demonstrate how the LG framework and Fine's theorem can be extended to the case in which all possible two-time correlation functions are measured (instead of the partial set of two-time correlators normally studied). We examine the limit of a large number of measurements for both of the above cases., 29 pages Latex, 6 figures. Revised. Accepted for publication in Physical Review A

Confining light to scales beyond the diffraction limit, quantum plasmonics supplies an ideal platform to explore strong light-matter couplings. The light-induced localized surface plasmons (LSPs) on the metal-dielectric interface acting as a quantum bus have wide potential in quantum information processing; however, the loss nature of light in the metal hinders their application. Here we propose a mechanism to make the reversible energy exchange and the multipartite quantum correlation of a collective of quantum emitters (QEs) mediated by the LSPs persistent. Via investigating the quantized interaction between the QEs and the LSPs supported by a spherical metal nanoparticle, we find that the diverse signatures of the quantized QE-LSP coupling in the steady state, including the complete decay, population trapping, and persistent oscillation, are essentially determined by the different number of bound states formed in the energy spectrum of the QE-LSP system. Enriching our understanding on the light-matter interactions in a lossy medium, our result is instructive in the design of quantum devices using plasmonic nanostructures.

We study the use of the complex-Langevin equation (CLE) to simulate lattice QCD at a finite chemical potential ($\mu$) for quark-number, which has a complex fermion determinant that prevents the use of standard simulation methods based on importance sampling. Recent enhancements to the CLE specific to lattice QCD inhibit runaway solutions which had foiled earlier attempts to use it for such simulations. However, it is not guaranteed to produce correct results. Our goal is to determine under what conditions the CLE yields correct values for the observables of interest. Zero temperature simulations indicate that for moderate couplings, good agreement with expected results is obtained for small $\mu$ and for $\mu$ large enough to reach saturation, and that this agreement improves as we go to weaker coupling. For intermediate $\mu$ values these simulations do not produce the correct physics. We compare our results with those of the phase-quenched approximation. Since there are indications that correct results might be obtained if the CLE trajectories remain close to the $SU(3)$ manifold, we study how the distance from this manifold depends on the quark mass and on the coupling. We find that this distance decreases with decreasing quark mass and as the coupling decreases, i.e. as the simulations approach the continuum limit., Comment: 26 pages, 12 postscript figures, LaTeX source. V3 version accepted for publication. Extensive revisions from previous versions

Strutinsky's method is reviewed through a new understanding. This method depends on two free parameters: The smoothing parameter and the order of the curvature correction. It turns out that this method is nothing but a compromise between two fundamental conditions which are the so-called asymptotic limit which comes from the so-called remainder which imposes a small as possible smoothing parameter and the smoothing condition which forces that parameter to be, at least, slightly larger than the intershell spacing. In this paper, to find the best value of the smoothing parameter, a new criterion is proposed instead of the plateau condition. This new criterion is much more clear and free from ambiguities of the usual plateau condition. It is also found that the second free parameter, i.e., the order of the curvature correction, plays an accessory role since, it is connected intimately to the smoothing parameter, when the smoothing is realized. This paper provides a new and definitive insight into Strutinsky's method and its relationship with semiclassical methods.

Starting with the general stress-tensor commutation relations consistent with the Poincaré algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in d>2 conformal field theories.

Quantum phase transitions are studied in the nonchiral p-clock chain, and a new explicitly U(1)-symmetric clock model, by monitoring the ground-state fidelity susceptibility. For p≥5, the self-dual Zp-symmetric chain displays a double-hump structure in the fidelity susceptibility with both peak positions and heights scaling logarithmically to their corresponding thermodynamic values. This scaling is precisely as expected for two Beresinskii-Kosterlitz-Thouless (BKT) transitions located symmetrically about the self-dual point, and so confirms numerically the theoretical scenario that sets p=5 as the lowest p supporting BKT transitions in Zp-symmetric clock models. For our U(1)-symmetric, non-self-dual minimal modification of the p-clock model we find that the phase diagram depends strongly on the parity of p and only one BKT transition survives for p≥5. Using asymptotic calculus we map the self-dual clock model exactly, in the large p limit, to the quantum O(2) rotor chain. Finally, using bond-algebraic dualities we estimate the critical BKT transition temperatures of the classical planar p-clock models defined on square lattices, in the limit of extreme spatial anisotropy. Our values agree remarkably well with those determined via classical Monte Carlo for isotropic lattices. This work highlights the power of the fidelity susceptibility as a tool for diagnosing the BKT transitions even when only discrete symmetries are present.

We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an over-critical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second, the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit, we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances. We also obtain the marginal spatial and angular densities in the under-critical regime where the foragers behave like individuals as well as in the over-critical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.

We study the $\ensuremath{\theta}$ dependence of the continuum limit of 2D $U(N)$ gauge theories defined on compact manifolds, with special emphasis on spherical ($g=0$) and toroidal ($g=1$) topologies. We find that the coupling between $U(1)$ and $SU(N)$ degrees of freedom survives the continuum limit, leading to observable deviations of the continuum topological susceptibility from the $U(1)$ behavior, especially for $g=0$, in which case deviations remain even in the large $N$ limit.

Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intra-cavity squeezing, and optomechanical entanglement. We further apply an analogous analysis to the multimode optomechanical system of two mechanical and one cavity mode and find conditional mechanical Einstein-Podolski-Rosen entanglement and genuinely tripartite optomechanical entanglement. Our analysis is of direct relevance for state-of-the-art optomechanical experiments that have entered the backaction-dominated regime., 4 pages + appendix. 4 figures

Edge dynamics is relevant to various real-world systems with complex network topological features. An edge dynamical system is controllable if it can be driven from any initial state to any desired state in finite time with appropriate control inputs. Here a framework is proposed to study the impact of correlation between in- and out-degrees on controlling the edge dynamics in complex networks. We use the maximum matching and direct acquisition methods to determine the controllability limit, i.e., the limit of acceptable change of the edge controllability by adjusting the degree correlation only. Applying the framework to plenty complex networks, we find that the controllability limits are ubiquitous in model and real networks. Arbitrary edge controllability in between the limits can be achieved by properly adjusting the degree correlation. Moreover, a nonsmooth phenomenon occurs in the upper limits, and exponential and power-law scaling behaviors are widespread in the approach or separation speed between the upper and lower limits.

The space charge limit (SCL) of emission from photocathodes sets an upper limit on the performance of both high- and low-field electron guns. Generally, one is forced to strike a compromise between the space charge limit and the cathode's intrinsic emittance (I. Bazarov et al., Phys. Rev. Lett., 102,104801(2009)). However, it is possible to nearly eliminate the SCL due to the image charge by engineering the topography of the cathode's surface. A cathode with a surface plasma frequency below the frequency spectrum of the accelerating electrons will greatly reduce the bunch's image charge or polarization of the cathode, resulting in a small image-charge field. Thereby mitigating the cathode's space charge limit. In the work presented here, a theory for the image-charge field produced by a disk of charge being accelerated from the cathode surface is developed to include the frequency-dependent behavior of surface dielectric function on the fields seen by the beam. The paper applies this theory to mitigate the SCL of a novel cathode based upon a wire-array metasurface. It is shown that such meta-cathodes should have negligible space charge limits for photoelectric, thermionic and field emission., Comment: 20 pages and 13 figures

We study the model of growing filament against a wall proposed by Peskin, Odell, and Oster [Biophys. J. 65, 316 (1993)BIOJAU0006-349510.1016/S0006-3495(93)81035-X] using the ratio of chemical to diffusion timescales as a small expansion parameter. A detailed multiple-scale analysis allows us to fully describe the spatiotemporal evolution toward a steady-state distribution for the wall-tip distance, including chemical effects, in very good agreement with numerical simulations. Implications on the quasistatic approximation, where the force on the wall is allowed to vary slowly in time, are discussed. A corrected force-velocity relationship together with explicit expressions of the relevant timescales are provided.

We study the effects of disorder on the topological Chern insulating phase in the Harper--Hofstadter--Hatsugai (HHH) model. The model with half flux has a bulk band gap and thus exhibits a nontrivial topological phase. We consider two typical types of disorder: on-site random disorder and the Aubry--Andre type quasi-periodic potential. Using the coupling matrix method, we clarify the global topological phase diagram in terms of the Chern number. The disorder modifies the gap closing behavior of the system. This modification induces the Chern insulating phase even in the trivial phase parameter regime of the system in the clean limit. Moreover, we consider an interacting Rice--Mele model with disorder, which can be obtained by dimensional reduction of the HHH model. Moderately strong disorder leads to an increase in revival events of the Chern insulator at a specific parameter point., Comment: 8 pages, 7 figures, accepted in Phys. Rev. B

For waves described by the focusing nonlinear Schrödinger equation (FNLS), we present an effective dispersion relation (EDR) that arises dynamically from the interplay between the linear dispersion and the nonlinearity. The form of this EDR is parabolic for a robust family of "generic" FNLS waves and equals the linear dispersion relation less twice the total wave action of the wave in question multiplied by the square of the nonlinearity parameter. We derive an approximate form of this EDR explicitly in the limit of small nonlinearity and confirm it using the wave-number-frequency spectral (WFS) analysis, a Fourier-transform based method used for determining dispersion relations of observed waves. We also show that it extends to the FNLS the universal EDR formula for the defocusing Majda-McLaughlin-Tabak (MMT) model of weak turbulence. In addition, unexpectedly, even for some spatially periodic versions of multisolitonlike waves, the EDR is still a downward shifted linear-dispersion parabola, but the shift does not have a clear relation to the total wave action. Using WFS analysis and heuristic derivations, we present examples of parabolic and nonparabolic EDRs for FNLS waves and also waves for which no EDR exists.

We demonstrate that in the continuous limit the etching mechanism yields the Kardar-Parisi-Zhang (KPZ) equation in a ($d+1$)-dimensional space. We show that the parameters $\ensuremath{\nu}$, associated with the surface tension, and $\ensuremath{\lambda}$, associated with the nonlinear term of the KPZ equation, are not phenomenological, but rather they stem from a new probability distribution function. The Galilean invariance is recovered independently of $d$, and we illustrate this via very precise numerical simulations. We obtain firsthand the coupling parameter as a function of the probabilities. In addition, we strengthen the argument that there is no upper critical limit for the KPZ equation.

We study the massive scalar field Sorkin-Johnston (SJ) Wightman function restricted to a flat 2D causal diamond of linear dimension L. Our approach is two-pronged. In the first, we solve the central SJ eigenvalue problem explicitly in the small mass regime, upto order (mL)^4. This allows us to formally construct the SJ Wightman function up to this order. Using a combination of analytic and numerical methods, we obtain expressions for the SJ Wightman function both in the center and the corner of the diamond, to leading order. We find that in the center, it is more like the massless Minkowski Wightman function than the massive one, while in the corner it corresponds to that of the massive mirror. In the second part, in order to explore larger masses, we perform numerical simulations using a causal set approximated by a flat 2D causal diamond. We find that in the center of the diamond the causal set SJ Wightman function resembles the massless Minkowski Wightman function for small masses, as in the continuum, but beyond a critical value it resembles the massive Minkowski Wightman function as expected. Our calculations suggest that unlike the massive Minkowski vacuum, the SJ vacuum has a well-defined massless limit, which mimics the behavior of the Pauli Jordan function underlying the SJ construction. In the corner of the diamond, moreover, it agrees with the mirror vacuum for all masses, and not, as might be expected, with the Rindler vacuum., Comment: 49 pages, 22 figures. Erratum added at the end of the paper. The erratum is published in Phys. Rev. D. (Phys. Rev. D. 104, 089901)

We study 3d N=2 Chern-Simons (CS) quiver theories on S3 and Σg×S1. Using localization results, we examine their partition functions in the large rank limit and requiring the resulting matrix models to be local, find a large class of quiver theories that include quivers in one-to-one correspondence with the ADE^ Dynkin diagrams. We compute explicitly the partition function on S3 for D^ quivers and that on Σg×S1 for AD^ quivers, which lead to certain predictions for their holographic duals. We also provide a new and simple proof of the “index theorem,” extending its applicability to a larger class of theories than considered before in the literature.

We develop the effective medium theory (EMT) to calculate the effective ``refractive index'' of quantum dot array for electron waves in graphene. It can be used to design electron metamaterials which will control the flow of graphene electrons by achieving any desirable effective ``refractive index.'' Here the coherent-potential approximation is adopted to derive the analytic formulation of the effective ``refractive index,'' which has been successfully used in the EMT of electromagnetic metamaterials. The EMT is valid beyond the long-wavelength limit. The region of validity is identified by the comparison of the energy band structures obtained by the EMT and the rigorous multiple scattering theory. We also provide the expressions for effective ``refractive indices'' in the frame of the long-wavelength theory and the Maxwell-Garnett theory so that a simple estimation can be done in the long-wavelength limit. We perform the simulation of the electron density distribution around a metamaterial with circular cross-section composed of smaller quantum dots. The simulation results show excellent agreement with the equal-size effective circular potential, verifying the effectiveness of our theory to design electron metamaterials. Finally, we show that even though these quantum dots that make up the metamaterial are disordered, the electron density distribution is almost the same as that around the effective one again and the effective medium theory is still applicable.

We present a model description of the bound $^{19}\mathrm{B}$ isotope in terms of a $^{17}\mathrm{B}\ensuremath{-}n\ensuremath{-}n$ three-body system where the two-body subsystems $^{17}\mathrm{B}\ensuremath{-}n$ and $n\ensuremath{-}n$ are unbound (virtual) states close to the unitary limit. The $^{19}\mathrm{B}$ ground state is well described in terms of two-body potentials only, and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be naturally used to describe the recently discovered resonant states in $^{20,21}\mathrm{B}$.

Recently, emission linewidths of single defect centers in layered hexagonal boron nitride down to 50 MHz were reported, close to the lifetime limit. The linewidths were extracted from time traces of laser scanning photoluminescence excitation experiments. At the same time, temporal blinking was affecting the measured time traces even in the absence of a frequency scanning the excitation laser. I argue here that the reported temporal blinking timescale is consistent with the observed transients, implying that the interpretation as spectral shapes and thus the extracted linewidths are invalid.