Saddle-point Configuration Research Articles

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

Quartic Gradient Flow

Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to introduce a gradient-flow-like equation in such a way that all the fluctuations around the saddle-point have eigenvalues that are square of the eigenvalues of the original quadratic operator. We illustrate how the method works for the Euclidean bounce and sphalerons.

Sphaleron in the Higgs Triplet Model

The Higgs triplet model (HTM) extends the Standard Model (SM) by one complex triplet scalar (also known as the type-II seesaw model), offering a simple and viable way to account for nonzero neutrino masses. On the other hand, the nontrivial couplings of the triplet to the gauge fields and to the SM Higgs field are expected to influence the topological vacuum structure of the SM, and consequently, the energy and the field configuration of the electroweak sphaleron. The sphaleron process plays a crucial role in dynamically generating the baryon asymmetry of the Universe. In this work, we study the vacuum structure of the gauge and Higgs fields and calculate the saddle-point sphaleron configuration in the HTM. The coupled nonlinear equations of motion of the sphaleron are solved using the spectral method. We find the inclusion of the triplet scalar could in principle significantly change the sphaleron energy compared with the SM. Nevertheless, at zero temperature, the current stringent experimental constraint on the vacuum expectation value of the triplet suppresses the difference. Interestingly, we find that there still exists some narrow parameter space where the sphaleron energy can be enhanced up to 30% compared with the SM case.

Aging mechanisms of nanoceria and pathways for preserving optimum morphology

Thermal aging can modify the unique properties of a nanomaterial via structural change. Mechanistic understanding of the aging process, including accelerated aging under high-temperature operating conditions, is a first step towards property preservation via controlling, limiting, or suppressing aging-related processes. Here, we use molecular dynamics to simulate thermal aging of ceria nanocubes and nanorods, which transform into nanopolyhedra; comparisons with experimental TEM images are presented alongside. We find that morphology changes proceed via the turbulent mobility of CexOy surface clusters from one part of the nanoceria to another. For nanorods and nanocubes, catalytically important {100} and {110} surfaces are eroded, whereas the relative area of {111} surfaces increase. Detailed analysis of the simulations reveals that atoms in the CexOy clusters do not all move simultaneously. Rather, (-O-Ce-O-Ce-O-)n ‘chains’ (subsets of the larger CexOy clusters) move with collective motion, while the atoms inside the chains move in a ‘worm-like’ fashion. This reduces the activation energy barrier associated with all the atoms in the chain simultaneously moving into an activated (saddle point) configuration. We predict gadolinium-doped ceria nanocubes, charge-compensated by oxygen vacancies, age faster than undoped and fully oxidised ceria nanocubes. In particular, dopants that increase catalytic activity, may also accelerate aging by introducing oxygen vacancies that break the (-O-Ce-O-Ce-O-)n chains into smaller chains with reduced activation energies. Accordingly, we advocate that when doping is used to confer catalytic activity, experiment should also target the collective motion of surface (-O-Ce-O-Ce-O-)n chains to maximise thermal stability.

Numerical investigation of dislocation climb under stress and irradiation

We investigate the influence of elastic properties of point defects on dislocation climb under stress and irradiation. For this purpose, elastic dipole tensors and diaelastic polarizabilities are evaluated in aluminum for vacancies and self-interstitial atoms in their stable and saddle configurations, using density functional theory calculations. These parameters are introduced in an object kinetic Monte-Carlo code and a continuous diffusion model to estimate the stress dependence of dislocation climb, using a dipole of straight dislocations. We show that both parameters have an influence on absorption of point defects under stress, in agreement with previous analytical models. However, the effect of dipole tensor is found only 5 times larger than polarizability, whereas models predict a factor up to 30. In addition, including polarizability reverses the stress angular dependence when a uniaxial stress is applied orthogonal to the dislocation line, so in general polarizability cannot be ignored for simulations under applied stress. Further comparison with analytical models shows that they give a good description of angular dependence, provided saddle point configuration of point defects is not too anisotropic. For vacancies, which are strongly anisotropic in their saddle configuration, models fail to reproduce quantitatively lattice effects on stress angular dependence observed in simulations. Calculations show that dislocation climb velocity under irradiation is expected to be the highest if the stress is approximately orthogonal to the dislocation line, especially along the Burgers vector, and the lowest if the stress is applied close to the 〈100〉 direction with the largest projection on the dislocation line.

Extreme events and instantons in Lagrangian passive scalar turbulence models.

The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. The statistics of the passive scalar exhibit complex behavior even in the presence of a Gaussian velocity field. This paper is concerned with two Lagrangian turbulence models that are based on the recent fluid deformation model, but adding a passive scalar field with uniform mean gradient. For a range of Reynolds numbers, these models can reproduce the statistics of passive scalar turbulence. For these models, we demonstrate how events of extreme passive scalar gradients can be recovered by computing the instanton, i.e., the saddle-point configuration of the associated stochastic field theory. It allows us to both reproduce the heavy-tailed statistics associated with passive scalar turbulence, and recover the most likely mechanism leading to such extreme events. We further demonstrate that events of large negative strain in these models undergo spontaneous symmetry breaking.

Diffusion as a possible mechanism controlling the production of superheavy nuclei in cold fusion reactions

The fusion probability for the production of superheavy nuclei in cold fusion reactions was investigated and compared with recent experimental results for $^{48}$Ca, $^{50}$Ti, and $^{54}$Cr incident on a $^{208}$Pb target. Calculations were performed within the fusion-by-diffusion model (FbD) using new nuclear data tables by Jachimowicz et al. It is shown that the experimental data could be well explained within the framework of the FbD model. The saturation of the fusion probability at bombarding energies above the interaction barrier is reproduced. It emerges naturally from the physical effect of the suppression of contributions of higher partial waves in fusion reactions and is related to the critical angular momentum. The role of the difference in values of the rotational energies in the fusion saddle point and contact (sticking) configuration of the projectile-target system is discussed.

New Method for Calculation of Radiation Defect Dipole Tensor and Its Application to Di-Interstitials in Copper

The effect of external and internal elastic strain fields on the anisotropic diffusion of radiation defects (RDs) can be taken into account if one knows the dipole tensor of saddle-point configurations of the diffusing RDs. It is usually calculated by molecular statics, since the insufficient accuracy of the available experimental techniques makes determining it experimentally difficult. However, for an RD with multiple crystallographically non-equivalent metastable and saddle-point configurations (as in the case of di-interstitials), the problem becomes practically unsolvable due to its complexity. In this paper, we used a different approach to solving this problem. The molecular dynamics (MD) method was used to calculate the strain dependences of the RD diffusion tensor for various types of strain states. These dependences were used to determine the dipole tensor of the effective RD saddle-point configuration, which takes into account the contributions of all real saddle-point configurations. The proposed approach was used for studying the diffusion characteristics of RDs, such as di-interstitials in FCC copper (used in plasma-facing components of fusion reactors under development). The effect of the external elastic field on the MD-calculated normalized diffusion tensor (ratio of the diffusion tensor to a third of its trace) of di-interstitials was fully consistent with analytical predictions based on the kinetic theory, the parameters of which were the components of the dipole tensors, including the range of non-linear dependence of the diffusion tensor on strains. The results obtained allowed for one to simulate the anisotropic diffusion of di-interstitials in external and internal elastic fields, and to take into account the contribution of di-interstitials to the radiation deformation of crystals. This contribution can be significant, as MD data on the primary radiation damage in copper shows that ~20% of self-interstitial atoms produced by cascades of atomic collisions are combined into di-interstitials.

Insights into MnAl-C nano-twin defects by micromagnetic characterization

MnAl-C is a prominent candidate for the replacement of rare earth magnets with a moderate energy density product. Crystallographic defects have a strong effect on magnetization properties. In this work, we show the influence of twinning defects in the nanometer regime on the quality of the magnet. Standard micromagnetic simulations and computations of the saddle point configuration for magnetization reversal highlight the importance of optimizing the fraction of and reducing the width of crystallographic twin defects. Switching field distributions and the maximum possible coercive field for ideal microstructures without defects are estimated using a reduced order micromagnetic model.

Disentanglement approach to quantum spin ground states: field theory and stochastic simulation

While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.

Hysteresis and Fréedericksz thresholds for twisted states in chiral nematic liquid crystals: Minimum-energy path approach

We study minimum-energy pathways (MEPs) between the branches of metastable helical structures in chiral nematic liquid crystals (CNLCs) subjected to the electric field applied across the cell. By performing stability analysis we have found that, for the branches with non-vanishing half-turn number, the threshold (critical) voltage of the Fréedericksz transition is an increasing function of the free twisting wave number. The curves for the threshold voltage depend on the elastic anisotropy and determine the zero-field critical free twisting number where the director out-of-plane fluctuations destabilize the CNLC helix. For each MEP passing through a first order saddle point we have computed the energy barrier as the energy difference between the saddle-point and the initial structures at different values of the applied field. In our calculations, where the initial approximation for a MEP at the next step was determined by the MEP obtained at the previous step, the electric field dependence of the energy barrier is found to exhibit the hysteresis. This is the hysteresis of electrically driven transition of the saddle-point configuration between the planar and the tilted structures involving out-of-plane director deformations. It turned out that, by contrast to the second-order Fréedericksz transition, this transition is first order and we have studied how it depends on the zenithal anchoring energy strength.

Properties of heaviest nuclei with [formula omitted] and [formula omitted

We systematically determine ground-state and saddle-point shapes and masses for 1305 heavy and superheavy nuclei with Z=98–126 and N=134–192, including odd-A and odd–odd systems. From these we derive static fission barrier heights, one- and two-nucleon separation energies, and Qα values for g.s. to g.s. transitions. Our study is performed within the microscopic–macroscopic method with the deformed Woods–Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy taken as the smooth part. We use parameters of the model that were fitted previously to masses of even–even heavy nuclei. For systems with odd numbers of protons, neutrons, or both, we use a standard BCS method with blocking. Ground-state shapes and energies are found by the minimization over seven axially-symmetric deformations. A search for saddle-points was performed by using the ”imaginary water flow” method in three consecutive stages, using five- (for nonaxial shapes) and seven-dimensional (for reflection-asymmetric shapes) deformation spaces. Calculated ground-state mass excess, nucleon separation- and Qα energies, total, macroscopic (normalized to the macroscopic energy at the spherical shape) and shell corrections energies, and deformations are given for each nucleus in Table 1. Table 2 contains calculated properties of the saddle-point configurations and the fission barrier heights. In Tables 3-7, are given calculated ground-state, inner and outer saddle-point and superdeformed secondary minima characteristics for 75 actinide nuclei, from Ac to Cf, for which experimental estimates of fission barrier heights are known. These results are an additional test of our model.

Supersymmetric phases of 4d mathcal{N} = 4 SYM at large N

We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N ) mathcal{N} = 4 super Yang-Mills theory on S3× S1 with one chemical potential τ . The saddle-point configurations are labelled by points (m, n) on the lattice Λτ = ℤτ + ℤ with gcd(m, n) = 1. The eigenvalues at a given saddle are uniformly distributed along a string winding (m, n) times along the (A, B) cycles of the torus ℂ/Λτ . The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of (0, 1) and (1, 0) agree with that of pure AdS5 and the supersymmetric AdS5 black hole, respectively. The black hole saddle dominates the canonical ensemble when τ is close to the origin, and there are new saddles that dominate when τ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit τ → 0.

Pure gravity and conical defects

We revisit the spectrum of pure quantum gravity in AdS3. The computation of the torus partition function will — if computed using a gravitational path integral that includes only smooth saddle points — lead to a density of states which is not physically sensible, as it has a negative degeneracy of states for some energies and spins. We consider a minimal cure for this non-unitarity of the pure gravity partition function, which involves the inclusion of additional states below the black hole threshold. We propose a geometric interpretation for these extra states: they are conical defects with deficit angle 2π(1 − 1/N), where N is a positive integer. That only integer values of N should be included can be seen from a modular bootstrap argument, and leads us to propose a modest extension of the set of saddle-point configurations that contribute to the gravitational path integral: one should sum over orbifolds in addition to smooth manifolds. These orbifold states are below the black hole threshold and are regarded as massive particles in AdS, but they are not perturbative states: they are too heavy to form multi-particle bound states. We compute the one-loop determinant for gravitons in these orbifold backgrounds, which confirms that the orbifold states are Virasoro primaries. We compute the gravitational partition function including the sum over these orbifolds and find a finite, modular invariant result; this finiteness involves a delicate cancellation between the infinite tower of orbifold states and an infinite number of instantons associated with PSL(2, ℤ) images.

Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory

The knowledge of vortex nucleation barriers is crucial for applications of superconductors, such as single-photon detectors and superconductor-based qubits. Contrarily to the problem of finding energy minima and critical fields, there are no controllable methods to explore the energy landscape, identify saddle points, and compute associated barriers. Similar problems exist in high-energy physics where the saddle-point configurations are called sphalerons. Here, we present a generalization of the string method to gauge field theories, which allows the calculation of energy barriers in superconductors. We solve the problem of vortex nucleation, assessing the effects of the nonlinearity of the model, complicated geometry, surface roughness, and pinning.

KdV-charged black holes

We construct black hole geometries in AdS3 with non-trivial values of KdV charges. The black holes are holographically dual to quantum KdV Generalized Gibbs Ensemble in 2d CFT. They satisfy thermodynamic identity and thus are saddle point configurations of the Euclidean gravity path integral. We discuss holographic calculation of the KdV generalized partition function and show that for a certain value of chemical potentials new geometries, not the conventional BTZ ones, are the leading saddles.

Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves

A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatio-temporal wave field configurations, which can be defined using the mathematical framework of Large Deviation Theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves that originate from a simple linear superposition mechanism (in weakly nonlinear conditions) or from a nonlinear focusing one (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.

Atomic diffusion mediated by vacancy defects in L12-Zr3Al: A first-principles study

Systematic first-principles calculations based on density functional theory have been performed to determine the self-diffusion mechanism of Zr3Al. The formation energies of four intrinsic point defects were calculated and the relationship between concentration of different point defects and temperature was determined. Then, the effect of defect types on the stability of the system was explored after analyzing the electronic density of different supercells. In addition, the minimum energy pathways (MEPs) and the saddle point configurations during Zr or Al atom migration were calculated using the climbing image nudged elastic band method (CI-NEB). The energetic results show that the VZr-mediated nearest neighbor (NN) jump mechanism is the feasible migration mechanism for Zr atom and dominant Al atom diffusion mechanism is the antisite assisted (AS) mechanism because of the lowest diffusion activation energy barrier. The present study lays the foundation for further investigation, including solute-diffusion in Zr3Al and quantitative calculation of diffusion coefficients, and provides theoretical guideline for further design and improvement of the crucial diffusion-mediated properties of Zr3Al.

First-principles study of diffusion and interactions of hydrogen with silicon, phosphorus, and sulfur impurities in nickel

Using density functional theory (DFT), we systematically study the effect of Si, P, and S impurities on the diffusion and binding of an H atom in a face-centered-cubic (FCC) Ni lattice. First, we quantify binding energies of an H atom to a vacancy, an impurity atom, and a vacancy-impurity atom defect pair. The energetics of H interactions show that a vacancy-impurity atom defect pair with larger binding energy traps the H atom more strongly and correlates with electronic bonding. Next, we study how the impurities influence diffusion of an H atom by using the Climbing Image Nudged Elastic band method to evaluate the Minimum Energy Path and the energy barrier for diffusion. The H atom preferentially diffuses between tetrahedral to octahedral (T-O) interstitial positions in pure Ni and when impurities are present. However, the activation energy significantly decreases from 0.95 eV in pure Ni to 0.47 eV, 0.52 eV, and 0.46 eV, respectively, in the presence of Si, P, and S impurities, which speeds up H diffusion. We rationalize this by comparing the bonding character of the saddle point configuration and changes in the electronic structure of Ni for each system. Notably, these analyses correlate the lower values of the activation energies to a local atomic strain in a Ni lattice. Our DFT study also validates the hypothesis of Berkowitz and Kane that P increases the H diffusion and, thereby, significantly increases H embrittlement susceptibility of Ni. We report a similar effect for Si and S impurities in Ni.

Surface Diffusion of Fe and Cu on Fe (001) Under Electric Field Using First-Principles Calculations.

First-principles calculations were performed to determine the Fe on Fe (001) evaporation field and to characterize the surface diffusion of Fe and Cu on Fe (001) and on a step structure under an applied electric field. The evaporation field of Fe on Fe (001) was calculated by the nudged elastic band (NEB) method, using the combination of the effective screening medium and constant electrode potential methods to obtain a condition of constant electric field. The calculated evaporation field of Fe on Fe (001) was 32.4 V/nm, which agrees well with the experimental value. In the surface diffusion of Fe and Cu on Fe (001) and on a step structure, the activation barrier energies were determined by the NEB method with constant applied electric field. It was found that Cu diffuse more easily on the Fe (001) and step structure than Fe under an applied electric field. The activation barrier energy of surface diffusion in the saddle point configuration is small when the distance between Cu and Fe on the surface is larger, and the activation barrier energy becomes smaller when passing through a path far away from the surface due to the effect of the electric field.