Perturbation Strengths Research Articles

Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches

We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.

Exceptional point sensing via energy loss profile in a non-Hermitian system

The heightened sensitivity observed in non-Hermitian systems at exceptional points (EPs) has garnered significant attention. Typical EP sensor implementations rely on precise measurements of spectra and importantly, for real time sensing measurements, the EP condition ceases to hold as the perturbation increases over time, thereby preventing the use of high sensitivity at the EP point. In this work, we present an new approach to EP sensing which goes beyond these two traditional constraints. Firstly, instead of measuring the spectra, our scheme of EP based sensing is based on the observation of decay length of the optical mode in finite size gratings, which is validated via coupled mode theory as well as full wave electrodynamic simulations. Secondly, for larger perturbation strengths, the EP is spectrally shifted instead of being destroyed — this spectral shift of the EP is calibrated and using this look-up table, we propose continuous real time detection by varying the excitation laser wavelength. As a proof of principle of our technique, we present an application to the sensing of coronavirus particles, which shows unprecedented limit of detection. Furthermore, our analysis includes calculation of the signal-to-noise ratio, revealing that EP sensors offer advantage when classical technical noise dominates over fundamental noise. These findings will contribute to the expanding field of exceptional point based sensing technologies for real time applications beyond spectral measurements.

Cross section sensitivity to perturbation strengths in distorted waves for double electron capture by alpha particles from helium targets

Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second-order methods. The perturbation strength is parametrized by the Sommerfeld factor (the quotient of the nuclear charge and the relative velocity of the colliding particles). At each fixed impact energy, the sought sensitivity is monitored by gradually modifying the nuclear charges in the Sommerfeld factors. These factors reside in the Coulomb distortions of the unperturbed channels states. The focus is on the electronic distortions through the eikonal Coulomb logarithmic phases and the full Coulomb waves. The logarithmic phases are the constituents of the compound phases for the net charges of the two heavy scattering aggregates in relative motions. A striking perturbation strength sensitivity of the obtained total cross sections is recorded.

Adversarial attack and training for deep neural network based power quality disturbance classification

Power quality disturbance (PQD) can significantly affect the normal operation of the power system. Deep neural network (DNN) can classify PQD with extremely high accuracy. However, adversarial attacks can drastically degrade the performance of DNN, which raises security issues for DNN-based PQD classification. At present, there are few researches on adversarial attacks and their defenses in PQD classification. In this study, we first adopt convolutional neural network-long short-term memory (CNN-LSTM) to classify PQD signals. Then we propose an adversarial attack algorithm for PQD classification, i.e., momentum iterative-fast gradient sign method (MI-FGSM). MI-FGSM generates adversarial perturbations along the gradient direction of the loss function by incorporating momentum during iterations. Finally, we propose a defense algorithm to defend against adversarial attacks, i.e., iterative adversarial training (IAT). IAT can improve the robustness of the classification model by making it learn to minimize the worst loss caused by multi-class adversarial perturbation strengths. The experimental results demonstrate that compared with the fast gradient sign method, the MI-FGSM produces smaller perturbations and can further reduce the classification accuracy of CNN-LSTM. In addition, compared with the most advanced adversarial training defense algorithm in PQD classification, IAT can effectively enhance the robustness of the CNN-LSTM against adversarial attacks.

DeepPatch: Maintaining Deep Learning Model Programs to Retain Standard Accuracy with Substantial Robustness Improvement

Maintaining a deep learning (DL) model by making the model substantially more robust through retraining with plenty of adversarial examples of non-trivial perturbation strength often reduces the model’s standard accuracy. Many existing model repair or maintenance techniques sacrifice standard accuracy to produce a large gain in robustness or vice versa. This article proposes DeepPatch, a novel technique to maintain filter-intensive DL models. To the best of our knowledge, DeepPatch is the first work to address the challenge of standard accuracy retention while substantially improving the robustness of DL models with plenty of adversarial examples of non-trivial and diverse perturbation strengths. Rather than following the conventional wisdom to generalize all the components of a DL model over the union set of clean and adversarial samples, DeepPatch formulates a novel division of labor method to adaptively activate a subset of its inserted processing units to process individual samples. Its produced model can generate the original or replacement feature maps in each forward pass of the patched model, making the patched model carry an intrinsic property of behaving like the model under maintenance on demand. The overall experimental results show that DeepPatch successfully retains the standard accuracy of all pretrained models while improving the robustness accuracy substantially. However, the models produced by the peer techniques suffer from either large standard accuracy loss or small robustness improvement compared with the models under maintenance, rendering them unsuitable in general to replace the latter.

Criticality in transient behavior of coupled oscillator system toward chimera and synchronization.

Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, while how the system is steering toward different final destinies upon spatially localized perturbation is still unknown. Through a systematic numerical analysis of the evolution of the spatiotemporal patterns of multi-chimera states, we uncover a critical behavior of the system in transient time toward either chimera or synchronization as the final stable state. We measure the critical values and the transient time of chimeras with different numbers of clusters. Then, based on an adequate verification, we fit and analyze the distribution of the transient time, which obeys power-law variation process with the increase in perturbation strengths. Moreover, the comparison between different clusters exhibits an interesting phenomenon, thus we find that the critical value of odd and even clusters will alternatively converge into a certain value from two sides, respectively, implying that this critical behavior can be modeled and enabling the articulation of a phenomenological model.

The replicator equation in stochastic spatial evolutionary games

We study the multi-type stochastic evolutionary game with death–birth updating in expanding spatial populations of size N→∞. The model is a voter model perturbation. For typical eligible populations, we require perturbation strengths satisfying 1/N≪w≪1. Under these conditions, the main results prove that the vector density processes of type obey an extended replicator equation in the limit, and the normalized fluctuations converge to a Gaussian process subject to the Wright–Fisher covariance function. In particular, we obtain a positive resolution of a conjecture from [34] that the replicator equation extends to many non-regular graphs.

Cluster perturbation theory. VII. The convergence of cluster perturbation expansions.

The convergence of the recently developed cluster perturbation (CP) expansions [Pawlowski et al., J. Chem. Phys. 150, 134108 (2019)] is analyzed with the double purpose of developing the mathematical tools and concepts needed to describe these expansions at general order and to identify the factors that define the rate of convergence of CP series. To this end, the CP energy, amplitude, and Lagrangian multiplier equations as a function of the perturbation strength are developed. By determining the critical points, defined as the perturbation strengths for which the Jacobian becomes singular, the rate of convergence and the intruder and critical states are determined for five small molecules: BH, CO, H2O, NH3, and HF. To describe the patterns of convergence for these expansions at orders lower than the high-order asymptotic limit, a model is developed where the perturbation corrections arise from two critical points. It is shown that this model allows for rationalization of the behavior of the perturbation corrections at much lower order than required for the onset of the asymptotic convergence. For the H2O, CO, and HF molecules, the pattern and rate of convergence are defined by critical states where the Fock-operator underestimates the excitation energies, whereas the pattern and rate of convergence for BH are defined by critical states where the Fock-operator overestimates the excitation energy. For the NH3 molecule, both forms of critical points are required to describe the convergence behavior up to at least order 25.

Splitting of localized disturbances in viscoelastic channel flow

We examine the response of an inertialess viscoelastic channel flow to localized perturbations. We thus performed an experiment in which we perturbed the flow using a localized velocity pulse and probed the perturbed fluid packet downstream from the perturbation location. While for low Weissenberg numbers the perturbed fluid reaches the measurement location as a single velocity pulse, for sufficiently high Weissenberg numbers and perturbation strengths, a random number of pulses arrive at the measurement location. The average number of pulses observed increases with the Weissenberg number. This observation constitutes a transition to a novel elastic pulse-splitting regime. Our results suggest a possible new direction for studying the elastic instability of viscoelastic channel flows at high elasticity through the growth of localized perturbations.

Influences of Randomly Uncertain Factors on Dynamic Coefficients of an Interlocking Labyrinth Seal-Rotor System

Many randomly uncertain factors inevitably arise when gas flows through a labyrinth seal, and the orbit of the rotor center will not rotate along a steady trajectory, as previously studied. Here, random uncertainty is considered in an interlocking labyrinth seal-rotor system to investigate the fluctuations of dynamic coefficients. The bounded noise excitation is introduced into the momentum equation of the gas flow, and as a result, the orbit of the rotor center is expressed as the combination of an elliptic trajectory with the bounded noise perturbation. Simulation results of the coefficients under randomly uncertain perturbations with various strengths are comparatively investigated with the traditional predictions under ideal conditions, from which the influences of random uncertain factors on dynamic coefficients are analyzed in terms of the rotor speed, pressure difference, and inlet whirl velocity. It is shown that the deviation levels of the dynamic coefficients are directly related to the random perturbations and routinely increase with such perturbation strengths, and the coefficients themselves may exhibit distinct variation patterns against the rotor speed, pressure difference, and inlet whirl velocity.

Lift in the vertical shear of a southerly jet embedded in a uniform westerly flow

AbstractA new mechanism is proposed as a potential cause for the one‐third of warm season severe nocturnal convection in the US Great Plains that develops in environments without the presence of air‐mass boundaries of fronts or mesoscale systems. This mechanism is tested in two‐ and three‐dimensional models. Results show strong ascent (∼1.0 m·s−1), sufficient for nocturnal convection initiation, arising from interactions of mean westerly zonal wind with the vertical shear of a northern vortex and also perturbation westerly winds that are created by the Coriolis torque on the Great Plains southerly low‐level jet. The interaction involving the northern vortex results in organized strong ascent on the east side of the vortex from the near‐surface level to the top of the model atmosphere, and also a weak upward acceleration near the centre of the vortex. In simulations with westerly wind perturbations, strong and organized ascent occurs above and on the east side of the westerly perturbation winds. The upward motion in these simulations relies on both mechanical forcing from non‐hydrostatic pressure perturbations and buoyant acceleration caused by interactions of the westerly zonal wind and the vertical shear in the vortex or the perturbation westerly wind. Statistical tests confirm that these interactions, not the northern vortex or westerly perturbation itself and related shear, are essential for the simulated vertical motion. Additional sensitivity analysis indicates robust ascent across a wide range of westerly perturbation or northern vortex strengths. The vertical motion profile is not sensitive to the horizontal grid spacing of the model, at least at or below 4 km, but to the morphology of westerly wind perturbations. The latter suggests where improvement could be made to increase the accuracy of model prediction of nocturnal convective storms in the US Great Plains.

Typical relaxation of perturbed quantum many-body systems

We substantially extend our relaxation theory for perturbed many-body quantum systems from ((2020) Phys. Rev. Lett. 124 120602) by establishing an analytical prediction for the time-dependent observable expectation values which depends on only two characteristic parameters of the perturbation operator: its overall strength and its range or band width. Compared to the previous theory, a significantly larger range of perturbation strengths is covered. The results are obtained within a typicality framework by solving the pertinent random matrix problem exactly for a certain class of banded perturbations and by demonstrating the (approximative) universality of these solutions, which allows us to adopt them to considerably more general classes of perturbations. We also verify the prediction by comparison with several numerical examples.

A simplified strategy for titrating gene expression reveals new relationships between genotype, environment, and bacterial growth.

A lack of high-throughput techniques for making titrated, gene-specific changes in expression limits our understanding of the relationship between gene expression and cell phenotype. Here, we present a generalizable approach for quantifying growth rate as a function of titrated changes in gene expression level. The approach works by performing CRISPRi with a series of mutated single guide RNAs (sgRNAs) that modulate gene expression. To evaluate sgRNA mutation strategies, we constructed a library of 5927 sgRNAs targeting 88 genes in Escherichia coli MG1655 and measured the effects on growth rate. We found that a compounding mutational strategy, through which mutations are incrementally added to the sgRNA, presented a straightforward way to generate a monotonic and gradated relationship between mutation number and growth rate effect. We also implemented molecular barcoding to detect and correct for mutations that ‘escape’ the CRISPRi targeting machinery; this strategy unmasked deleterious growth rate effects obscured by the standard approach of ignoring escapers. Finally, we performed controlled environmental variations and observed that many gene-by-environment interactions go completely undetected at the limit of maximum knockdown, but instead manifest at intermediate expression perturbation strengths. Overall, our work provides an experimental platform for quantifying the phenotypic response to gene expression variation.

Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability-breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

Impurity resonance effects in graphene versus impurity location, concentration, and sublattice occupation

Unique electronic band structure of graphene with its semi-metallic features near the charge neutrality point is sensitive to impurity effects. Using the Lifshitz and Anderson impurity models, we study in detail the disorder induced spectral phenomena in the electronic band structure of graphene, namely, the formation of resonances, quasi-gaps, bound states, impurity sub-bands, and their overall impact on the electronic band restructuring and the associated Mott-like metal-insulator transitions. We perform systematic analytical and numerical study for realistic impurities, both substitutional and adsorbed, focusing on those effects that stem from the impurity adatoms locations (top, bridge, and hollow positions), concentration, host sublattice occupation, perturbation strengths, etc. Possible experimental and practical implications are discussed as well.

Predicting steady states of one-dimensional collisionless gravitating systems

Building on the development of a Hermite-Legendre analysis of one-dimensional gravitating collisionless systems, we present a technique for determining the steady states of such systems. This provides an important component for understanding the physics involved in the relaxation of these kinds of systems. As the dark matter structures in the universe should have traits in common with these systems, insight into this relaxation can provide clues to larger astrophysical questions. For large perturbation strengths, we determine physically motivated parameter ranges for the simplest families of steady states as well as their stability. We also demonstrate that any set of initial conditions in the linear regime can be resolved into unique time-independent and time-dependent modes. Combinations of time-independent modes then describe the steady state of any system linearly perturbed from equilibrium. These results highlight the importance of initial conditions over relaxation mechanisms in the evolution of these systems.

Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions

We study properties of eigenfunctions of perturbed systems, given on the eigenbases of unperturbed, integrable systems. For a given pair of perturbed and unperturbed systems, with respect to the energy of each perturbed state, the unperturbed basis states can be divided into two groups: one in the classically-allowed region and the other in the classically-forbidden region; correspondingly, the eigenfunction of the perturbed state is also divided into two parts. In the semiclassical limit, it is shown that, making use of components of the eigenfunction in its classically-allowed region, its components in the classically-forbidden region can be written in the form of a convergent perturbation expansion, which is valid for all perturbation strengths.

Three-body fragmentation dynamics of OCS3+ induced by intermediate energy Ne4+ ion impact

The fragmentation experiment of OCS3+ induced by 56 keV/u Ne4+ ions is performed using reaction microscope, and the corresponding dissociation dynamics is investigated. By detecting the three fragment ions in coincidence, the three-dimensional (3D) momenta of all ions and the corresponding kinetic energy release (KER) distributions are reconstructed. It is found that a peak maximum of the KER distribution is locates at about 25 eV, and a shoulder structure appears around 18 eV. This result is consistent with previous heavy ion experimental results with different perturbation strengths. Taking into account that the KER distribution is related to the initial state population of the OCS3+ parent ions, it can be concluded that the perturbation strength is not a decisive parameter leading to the initial state population of OCS3+ ions. We also reconstruct the Newton diagram and Dalitz plot for the three-body fragmentation of OCS3+ ion, from which the sequential dissociation is distinguished from nonsequential dissociation clearly. By analyzing the kinetic energy of ions from each fragmentation process, we find that the KER peak at 25 eV corresponds to nonsequential dissociation process, but the shoulder at 18 eV arises from both sequential and nonsequential dissociation processes. This phenomenon suggests that the parent OCS3+ ions in ground state and low excitation states tend to fragment through sequential dissociation, while those in high excitation states tend to fragment through nosequential dissociation. Furthermore, we reconstruct the KER distributions in the second fragmentation step of sequential dissociation, whose peak maximum is at 6.2 eV, corresponding to X3, 1+ and 1 metastable states of CO2+ ion. A similar KER distribution is obtained for the second fragmentation step of the OCS4+ ion. By comparing our experimental results with previous ones, we conclude that the origin of sequential dissociation process is the existence of metastable state, and the reconstructed KER in the second step reflects the initial state information about the metastable state.

Simulation study of Landau damping near the persisting to arrested transition

A one-dimensional electrostatic filtered Vlasov–Poisson simulation study is discussed. The transition from persisting to arrested Landau damping that is produced by increasing the strength of a sinusoidal perturbation on a background Vlasov–Poisson equilibrium is explored. Emphasis is placed on observed features of the electron phase-space distribution when the perturbation strength is near the transition value. A single ubiquitous waveform is found perturbing the space-averaged phase-space distribution at almost any time in all of the simulations; the sole exception is the saturation stage that can occur at the end of the arrested damping scenario. This waveform contains relatively strong, very narrow structures in velocity bracketing $\pm v_{\text{res}}$ – the velocities at which electrons must move to traverse the dominant field mode wavelength in one of its oscillation periods – and propagating with $\pm v_{\text{res}}$ respectively. Local streams of electrons are found in these structures crossing the resonant velocities from low speed to high speed during Landau damping and from high speed to low speed during Landau growth. At the arrest time, when the field strength is briefly constant, these streams vanish. It is conjectured that the expected transfer of energy between electrons and field during Landau growth or damping has been visualized for the first time. No evidence is found in the phase-space distribution to support recent well-established discoveries of a second-order phase transition in the electric field evolution. While trapping is known to play a role for larger perturbation strengths, it is shown that trapping plays no role at any time in any of the simulations near the transition perturbation strength.

Non-linear dense core formation in the dark cloud L1517

We present a solution for the observed core fragmentation of filaments in the Taurus L1517 dark cloud which previously could not be explained (Hacar et. al 2011). Core fragmentation is a vital step for the formation of stars. Observations suggest a connection to the filamentary structure of the cloud gas but it remains unclear which process is responsible. We show that the gravitational instability process of an isothermal cylinder can account for the exhibited fragmentation under the assumption that the perturbation grows on the dominant wavelength. We use numerical simulations with the code RAMSES, estimate observed column densities and line-of-sight velocities and compare them to the observations. A critical factor for the observed fragmentation is that cores grow by redistributing mass within the filament and thus the density between the cores decreases over the fragmentation process. This often leads to wrong dominant wavelength estimates as it is strongly dependent on the initial central density. We argue that non-linear effects also play an important role on the evolution of the fragmentation. Once the density perturbation grows above the critical line-mass, non-linearity leads to an enhancement of the central core density in comparison to the analytical prediction. Choosing the correct initial conditions with perturbation strengths of around 20\%, leads to inclination corrected line-of-sight velocities and central core densities within the observational measurement error in a realistic evolution time.