Phase Space Research Articles

Late time dynamics in SUSY saddle-dominated scrambling through higher-point OTOC

In this article, we propose higher-point out-of-time-order correlators (OTOCs) as a tool to differentiate chaotic from saddle-dominated dynamics in late times. As a model, we study the scrambling dynamics in supersymmetric quantum mechanical systems. Using the eigenstate representation, we define the 2N-point OTOC using two formalisms, namely the ’Tensor Product formalism’ and the ’Partner Hamiltonian formalism’. We analytically find that the 2N-point OTOC for the supersymmetric 1D harmonic oscillator is in exact agreement with that of the 1D bosonic harmonic oscillator system. We show that the higher-point OTOC is a more sensitive measure of scrambling than the usual 4-point OTOC. To demonstrate this, we analyze a supersymmetric sextic 1D oscillator, for which the bosonic partner system has an unstable saddle in the phase space, while the saddle is absent in the fermionic counterpart. For such a system, we show that the saddle-dominated scrambling, higher anharmonic potential effects, and the supersymmetric OTOC exhibit similar dynamics due to supersymmetry constraints. Finally, we illustrate that the late-time dynamics of the higher-point OTOC become oscillatory after the peak for saddle-dominated scrambling and anharmonic oscillator systems. We propose the higher-point OTOC as a probe of late-time dynamics in non-chaotic systems that exhibit fast early-time scrambling.

The dynamics around the collinear points of the elliptic three-body problem: A normal form approach

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating-pulsating barycentric frame, taking the true anomaly as independent variable. We consider the Hamiltonian modeling this problem in the extended phase space and we implement a normal form to make a center manifold reduction. The normal form provides an approximate solution for the Cartesian coordinates, which allows us to construct several kinds of orbits, most notably planar and vertical Lyapunov orbits, and halo orbits. We compare the analytical results with a numerical simulation, which requires special care in the selection of the initial conditions.

An adaptive feature mode decomposition-guided phase space feature extraction method for rolling bearing fault diagnosis

Abstract The extraction of fault features from rolling bearings is a challenging and highly important task. Since they have complex operating conditions and are usually under a strong noise background. In this study, a novel approach termed phase space feature extraction guided by an adaptive feature mode decomposition (AFMDPSFE) is proposed to detect subtle faults in rolling bearings. Initially, a new method using Kullback-Leiber divergence is introduced to automatically select the optimal mode number and filter length for the decomposition of vibration signals, facilitating the automatic extraction of optimal components and ensuring efficient screening. This eliminates the need for manual configuration of feature mode decomposition parameters. Furthermore, a criterion that could determine two crucial parameters to capture system dynamics characteristics in phase space reconstruction is embedded into AFMDPSFE algorithm. Subsequently, a series of high-dimensional independent components is derived. The envelope spectrum of the principal component exhibiting the highest kurtosis value is computed to achieve fault identification, consequently enhancing the separation of signal from noise. Both simulations and experimental results confirm the effectiveness of AFMDPSFE approach. A comparison analysis shows the excellent performance of AFMDPSFE in extracting fault features from significant noise interference.

Concatenated backward ray mapping on the compound parabolic concentrator

Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface. The original algorithm (Filosa, ten Thije Boonkkamp and IJzerman in J Math Ind 11(1):4, 2021) is limited to optical systems consisting of only straight surfaces; we generalize it to accommodate curved surfaces. The algorithm is applied to a standard optical system, the compound parabolic concentrator. We compare the accuracy and speed of the generalized algorithm, the original algorithm and Monte Carlo ray tracing. The results show that the generalized algorithm outperforms both other methods.

Assessment of the runaway electron load distribution in ITER during 3D MHD induced beam termination

In ITER, disruption-born runaway electrons (REs), unless mitigated, are expected to form a several Mega-Ampere beam that ultimately intercepts the first wall leading to melting of the plasma facing components. Developing a successful mitigation strategy therefore requires modeling that takes into account the coupling between REs and the MHD during the formation and termination of the beam, along with estimates for the wall loads that can be compared to design values. Using the JOREK code, this work aims to provide the latter by presenting a novel model for collisions between REs and the wall and applying it to a beam termination scenario in ITER. To this end, the transport of REs is modeled by tracing particles in the fields calculated by preceding simulations of the disruption event where REs were treated in the fluid picture and self-consistently coupled to the MHD. The resulting heat loads are found to be highly localized in both the poloidal and toroidal directions, with 3D features also playing an important role in the appearance of hot spots. Peak loads were on the order of 107−108Jm2 . The load distribution was found to only be weakly sensitive to the initial phase space distribution of the REs when decoupled from the fields, while modifying properties of the underlying MHD yielded notable differences in wetted area and peak loads, in particular for cases with higher resistivity.

Four-dimensional phase-space reconstruction of flat and magnetized beams using neural networks and differentiable simulations

Beams with cross-plane coupling or extreme asymmetries between the two transverse phase spaces are often encountered in particle accelerators. Flat beams with large transverse-emittance ratios are critical for future linear colliders. Similarly, magnetized beams with significant cross-plane coupling are expected to enhance the performance of electron cooling in hadron beams. Preparing these beams requires precise control and characterization of the four-dimensional transverse phase space. In this study, we employ generative phase-space reconstruction techniques to rapidly characterize magnetized and flat-beam phase-space distributions using a conventional quadrupole-scan method. The reconstruction technique is experimentally demonstrated on an electron beam produced at the Argonne Wakefield Accelerator and successfully benchmarked against conventional diagnostics techniques. Specifically, we show that predicted beam parameters from the reconstructed phase-space distributions (e.g., as magnetization and flat-beam emittances) are in excellent agreement with those measured from the conventional diagnostic methods. Published by the American Physical Society 2024

Reverse Intersystem Crossing Dynamics in Vibronically Modulated Inverted Singlet-Triplet Gap System: A Wigner Phase Space Study.

We inspect the origin of the inverted singlet-triplet gap (INVEST) and slow change in the reverse intersystem crossing (rISC) rate with temperature, as recently observed. A Wigner phase space study reveals that, though INVEST is found at equilibrium geometry, variation in the exchange interaction and the doubles-excitation for other geometries in the harmonic region leads to non-INVEST behavior. This highlights the importance of nuclear degrees of freedom for the INVEST phenomenon, and in this case, geometric puckering of the studied molecule determines INVEST and the associated rISC dynamics.

Phase space reconstruction technique for beam optimization in the Low Energy High Intensity Proton Accelerator (LEHIPA)

Phase space reconstruction technique for beam optimization in the Low Energy High Intensity Proton Accelerator (LEHIPA)

Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model

Reaction-diffusion models describing interactions between vegetation and water reveal the emergence of several types of patterns and travelling wave solutions corresponding to structures observed in real-life. Increasing their accuracy by also considering the ecological factor known as autotoxicity has lead to more involved models supporting the existence of complex dynamic patterns. In this work, we include an additional carrying capacity for the biomass in a Klausmeier-type vegetation-water-autotoxicity model, which induces the presence of two asymptotically small parameters: ɛ, representing the usual scale separation in vegetation-water models, and δ, directly linked to autotoxicity. We construct three separate types of homoclinic travelling pulse solutions based on two different scaling regimes involving ɛ and δ, with and without a so-called superslow plateau. The relative ordering of the small parameters significantly influences the phase space geometry underlying the construction of the pulse solutions. We complement the analysis by numerical continuation of the constructed pulse solutions, and demonstrate their existence (and stability) by direct numerical simulation of the full partial differential equation model.

Dynamical stability and phase space analysis of an Emergent Universe with non-interacting and interacting fluids

Dynamical stability and phase space analysis of an Emergent Universe with non-interacting and interacting fluids

Wavelet Transform, Reconstructed Phase Space, and Deep Learning Neural Networks for EEG-Based Schizophrenia Detection.

This study proposes an innovative expert system that uses exclusively EEG signals to diagnose schizophrenia in its early stages. For diagnosing psychiatric/neurological disorders, electroencephalogram (EEG) testing is considered a financially viable, safe, and reliable alternative. Using the reconstructed phase space (RPS) and the continuous wavelet transform, the researchers maximized the differences between the EEG nonstationary signals of normal and schizophrenia individuals, which cannot be observed in the time, frequency, or time-frequency domains. This reveals significant information, highlighting more distinguishable features. Then, a deep learning network was trained to enhance the accuracy of the resulting image classification. The algorithm's efficacy was confirmed through three distinct methods: employing 70% of the dataset for training, 15% for validation, and the remaining 15% for testing. This was followed by a 5-fold cross-validation technique and a leave-one-out classification approach. Each method was iterated 100 times to ascertain the algorithm's robustness. The performance metrics derived from these tests - accuracy, precision, sensitivity, F1 score, Matthews correlation coefficient, and Kappa - indicated remarkable outcomes. The algorithm demonstrated steady performance across all evaluation strategies, underscoring its relevance and reliability. The outcomes validate the system's accuracy, precision, sensitivity, and robustness by showcasing its capability to autonomously differentiate individuals diagnosed with schizophrenia from those in a state of normal health.

ATEP: An advanced transport model for energetic particles

Abstract In this paper we report on the implementation and verification of a phase- space resolved energetic particle (EP) transport model. It is based on a first-principle theoretical framework, i.e. the system of non-linear gyrokinetic equations and the related transport equations. Its focus is primarily directed toward understanding the meso-scale character of EPs and its consequences. Compared to the conventional description of thermal radial transport via a one-dimensional radial diffusion equation, the newly developed model is three-dimensional using canonical constants-of-motion (CoM) variables. The model does not assume diffusive processes to be dominant a priori, instead the EP fluxes are self-consistently calculated and directly evolved in CoM space. We use the EP-Stability workflow and the HAGIS code to determine the phase space fluxes explicitly either in the limit of constant mode amplitudes or an energy-conserving quasi-linear model. As an application of the model the transport of neutral-beam-generated EPs due to a toroidal Alfv ́en eigenmode in an ITER plasma is investigated. As there are no sources and collisions taken into account so far (for an extension of the model see the companion paper ref. [1]), the results cannot be considered as an exhaustive study, but rather as a practical demonstration of the conceptual framework on the way to a comprehensive reduced description of burning plasmas.

Dynamics of the epidemiological Predator-Prey system in advective environments.

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.

Polarized and unpolarized off-shell $H^\ast\to ZZ\rightarrow 4\ell$ decay above the $2m_Z$ threshold

Abstract An analysis of the off-shell $H^\ast\rightarrow ZZ \rightarrow \overline{\ell}_1\ell_1\overline{\ell}_2\ell_2$ decay width is presented for both unpolarized and polarized $Z$ gauge bosons in the scenario with the most general $H^*ZZ$ vertex function, which is given in terms of two $CP$-even ($\hat b_Z$ and $\hat c_Z$) and one $CP$-odd ($\tilde b_Z$) anomalous couplings.
 The SM contributions to the $H^*ZZ$ coupling up to the one-loop level are also included. Explicit analytic results for the unpolarized and polarized $H^\ast\rightarrow ZZ \rightarrow \overline{\ell}_1\ell_1\overline{\ell}_2\ell_2$ square amplitudes and the four-body phase space are presented, out of which several observable quantities can be obtained straightforwardly. As far as the numerical analysis is concerned, a cross-check is performed via Madgraph, where our model was implemented with the aid of FeynRules.
We then consider the most stringent bounds on anomalous complex $H^*ZZ$ couplings and analyze the effects of the polarizations of the $Z$ gauge bosons through the polarized $H^\ast\rightarrow ZZ \rightarrow \overline{\ell}_1\ell_1\overline{\ell}_2\ell_2$ decay width as well as left-right and forward-backward asymmetries, which are found to be sensitive to new-physics effects. Particular focus is put on the effects of the absorptive parts of the anomalous $H^*ZZ$ couplings, which have been largely overlooked up to now in LHC analyses. It is found that the studied observable quantities, particularly the left-right asymmetries, can be helpful to look for effects of $CP$-violation in the $H^*ZZ$ coupling and set bounds on the absorptive parts. For completeness, we also analyze the case of unpolarized $Z$ gauge bosons.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

Probing the quantum nature of gravity using a Bose-Einstein condensate

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The general complex scalar field theory with a quadratic self-interaction term has been considered in the presence of a gravitational wave. The gravitational wave perturbation is then considered as a sum of discrete Fourier modes in the momentum space. Varying the action and making use of the principle of least action, one obtains two equations of motion corresponding to the gravitational perturbation and the time-dependent part of the pseudo-Goldstone boson. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonical commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. The entries of the covariance matrix now involves a stochastic contribution which results in an operatorial stochastic structure of the quantum Fisher information. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. It always has a finite value if the gravitons are initially in a squeezed state with high enough squeezing. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in a decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing. Published by the American Physical Society 2024

Thermodynamics of Magnetic Black Holes with Nonlinear Electrodynamics in Extended Phase Space

We study Einstein’s gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, f(0)=1, and corrections to the Reissner–Nordström solution are in the order of O(r−3) when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated to coupling are computed and depicted. We calculate the Gibbs free energy and the heat capacity showing that first-order and second-order phase transitions take place.

Surface crack detection on selective laser melting printed Inconel 718 using a laser generated ultrasound technique and phase space reconstruction

Abstract In the field of metallic additive manufacturing, Selective Laser Melting (SLM) has become a predominant technology due to its advantages of short production cycles, high precision, and low cost. It is frequently employed in the production of complex parts. This paper proposes the use of a scanning laser line source, in conjunction with the singular value decomposition method, to reconstruct phase space and identify surface cracks in SLM specimens. The scanning laser line source addresses the limitations of a single line source, which is often unable to accurately detect tiny cracks. By comparing experimental and simulation data, the results demonstrate that the scanning laser line source can effectively compensate for some of the detection deficiencies of a single line source.

Learning Feynman integrals from differential equations with neural networks

We perform an exploratory study of a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural networks to approximate the solution to the differential equations satisfied by the Feynman integrals. This approach relies neither on a canonical form of the differential equations, which is often a bottleneck for the analytical techniques, nor on the availability of a large dataset, and after training yields essentially instantaneous evaluation times. We provide a proof-of-concept implementation within the PyTorch framework, and apply it to a number of one- and two-loop examples, achieving a mean magnitude of relative difference of around 1% at two loops in the physical phase space with network training times on the order of an hour on a laptop GPU.

The dressing field method for diffeomorphisms: a relational framework

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M) -invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic ‘extended bracket’ for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Frölicher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M) -theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent ( diff(M) ) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M) -invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the ‘dressed’ (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.

Thermodynamics of charged AdS black hole surrounded by quintessence in restricted phase space

Thermodynamics of charged AdS black hole surrounded by quintessence in restricted phase space