Phase Space Research Articles

Unique ergodicity in stochastic electroconvection

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller properties. When the noise forces enough modes in phase space, we obtain the uniqueness of the smooth invariant measure for the Markov transition kernels associated with the model.

Orbit tomography in constants-of-motion phase-space

Abstract Tomographic reconstructions of a 3D fast-ion constants-of-motion phase-space distribution function are computed by inverting synthetic signals based on projected velocities of the fast ions along the diagnostic lines of sight. The fast-ion distribution functions are parameterised by three constants of motion, the kinetic energy, the magnetic moment and the toroidal canonical angular momentum. The reconstructions are computed using both zeroth-order and firstorder Tikhonov regularisation expressed in terms of Bayesian inference to allow uncertainty quantification. In addition to this, a discontinuity appears to be present in the solution across the trapped passing boundary surface in the three-dimensional phase space due to a singularity in the Jacobian of the transformation from position and velocity space to phase space. A method to allow for this apparent discontinuity while simultaneously penalising large gradients in the solution is demonstrated. Finally, we use our new methods to optimise the diagnostic performance of a set of six fans of sightlines by finding where the detectors contribute most complementary diagnostic information for the future COMPASS-Upgrade tokamak.

Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space.

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population-population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important.

M3D-K simulations of beam-driven instabilities in an energetic particle dominant KSTAR discharge

We perform a systematic simulation study of energetic passing particle-driven instabilities in KSTAR using the kinetic-MHD hybrid code M3D-K. Linear simulation results show that the observed n = 1 mode in the early phase of the discharge is the low-frequency fishbone driven by energetic passing beam ions. The mode frequency computed is in a good agreement with the experimental measurement. Nonlinear simulations show that the frequency of the n = 1 mode jumps up to a higher value corresponding to the β-induced Alfvén eigenmode (BAE). In the later phase of the discharge, the simulated n = 5 mode is identified as a BAE in its linear phase. In the nonlinear phase, the n = 5 mode exhibits a similar frequency jump to a higher value of an energetic particle (EP) mode after mode saturation. Analysis of perturbed beam ion distributions in phase space shows that these new modes in nonlinear stages are driven by new resonances due to nonlinearly evolved beam ion distributions. Further simulations of a beam beta scan for the n = 5 mode show that the frequency jump disappears for a sufficiently small beam beta or beam ion drive. This result may explain the non-existence of frequency jump in the experiment. Finally, the impact of toroidal rotation on mode characteristics is investigated, showing that it has a marginal influence on EP driven modes.

Phase space geometry of general quantum energy transitions

Abstract The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory segments along the shell determine the phase of the Wigner oscillations in its interior. The classical transitions between any pair of energy shells, driven by a general external time dependent Hamiltonian, also have a smooth probability density. It is shown here that a further contribution to the transition between the corresponding pair of coarsegrained energy levels, which oscillates with either energy, or the driving time, is determined by four trajectory segments (two in the pair of energy shells and two generated by the driving Hamiltonian) that join exactly to form a closed compound orbit. In its turn, this sequence of segments belongs to the semiclassical expression of a compound unitary operator that 
combines four quantum evolutions: a pair generated by the static internal Hamiltonian and a pair generated by the driving Hamiltonian.
The closed compound orbits are shown to belong to continuous families, which are initially seeded at points where the classical flow generated by both Hamiltonians commute.

On the nature of sub-THz continuum absorption in CO2 gas, its mixture with Ar, and in pure water vapor.

Detailed analysis of the unique broadband millimeter-wave (70-360 GHz) collision-induced absorption spectra in pure CO2 and in its mixture with Ar is presented. The nature of the observed continuum absorption is examined using classical trajectory simulation along with statistical physics consideration. Bimolecular continuum is decomposed in the phase space into separate contributions from the so-called free, quasibound, and true bound molecular pairs, the proportions of which greatly vary with temperature. This partitioning is supported by consideration of the second virial coefficient and excluded volume in pure CO2, Ar, and CO2-Ar. Close similarity between collision-induced absorption in the CO2 containing gases and the water vapor continuum in the subterahertz spectral range is demonstrated. This similarity suggests that the physical principles underlying both continuum absorption phenomena have much in common and, therefore, can be used for continuum modeling.

Unlocking Predictive Capability and Enhancing Sensing Performances of Plasmonic Hydrogen Sensors via Phase Space Reconstruction and Convolutional Neural Networks.

This study innovates plasmonic hydrogen sensors (PHSs) by applying phase space reconstruction (PSR) and convolutional neural networks (CNNs), overcoming previous predictive and sensing limitations. Utilizing a low-cost and efficient colloidal lithography technique, palladium nanocap arrays are created and their spectral signals are transformed into images using PSR and then trained using CNNs for predicting the hydrogen level. The model achieves accurate predictions with average accuracies of 0.95 for pure hydrogen and 0.97 for mixed gases. Performance improvements observed are a reduction in response time by up to 3.7 times (average 2.1 times) across pressures, SNR increased by up to 9.3 times (average 3.9 times) across pressures, and LOD decreased from 16 Pa to an extrapolated 3 Pa, a 5.3-fold improvement. A practical application of remote hydrogen sensing without electronics in hydrogen environments is actualized and achieves a 0.98 average test accuracy. This methodology reimagines PHS capabilities, facilitating advancements in hydrogen monitoring technologies and intelligent spectrum-based sensing.

Black hole — wormhole transitions in two dimensional string theory

We study charged black hole and wormhole solutions of Type 0A/IIA string theory in two dimensions, by analysing their low energy equations of motion at leading order in α′. There is a competition between Euclidean wormholes and near extremal black holes in the thermodynamic ensemble. In a certain regime of phase space, the former can disassociate into the latter. Since such solutions are of string scale near the wormhole throat that takes an AdS2 form, there is a need for an exact worldsheet description. We discuss relevant WZW coset models which we argue will shed light on this problem. Finally, we present appropriate versions of the Type 0A/IIA matrix quantum mechanics models that are expected to describe these geometries.

Electron kinetic effects in back-stimulated Raman scattering bursts driven by broadband laser pulses

We examine electron kinetic effects in broadband-laser-driven back-stimulated Raman scattering (BSRS) bursts using particle-in-cell simulations. These bursts occur during the nonlinear stage, causing reflectivity spikes and generating large numbers of hot electrons. Long-duration simulations are performed to observe burst events, and a simplified model is developed to eliminate the interference of the broadband laser’s random intensity fluctuations. Using the simplified model, we isolate and characterize the spectrum of electron plasma waves. The spectrum changes from a sideband structure to a turbulence-like structure during the burst. A significant asymmetry in the spectrum is observed. This asymmetry is amplified and transferred to electron phase space by high-intensity broadband laser pulses, leading to violent vortex-merging and generation of hot electrons. The proportion of hot electrons increases from 6.76% to 14.7% during a single violent burst event. We demonstrate that kinetic effects profoundly influence the BSRS evolution driven by broadband lasers.

Nonlinear excitation of energetic particle driven geodesic acoustic mode by Alfvén instability in ASDEX-Upgrade tokamak

Abstract Recently, the coexistence of multiple energetic particle driven instabilities was observed in experiments on the ASDEX-Upgrade tokamak[P. Lauber et al., EX 1-1, 27th IAEA Fusion Energy Conference, 22-27 October 2018, Gandhinagar, India]. A hybrid simulation using the MEGA code was performed to investigate the properties of those instabilities. The basic mode properties obtained in the simulations, such as mode frequencies, mode numbers, and inward energetic particle (EP) redistribution, are in good agreement with the experiments. It is found that the energetic particle driven geodesic acoustic mode (EGAM) is initially stable, then zonal flow gradually occurs with the growth of the Alfvén instability, and finally, the EGAM is nonlinearly excited and the amplitude exceeds the Alfvén instability. The dependence of EGAM properties on EP pressure and pitch angle distribution is analyzed. The EGAM amplitude increases with EP pressure. The nonlinearly excited EGAM is a high-frequency branch that appears even under the condition of a slowing-down EP distribution. The resonant particles are also analyzed, but the dominant resonant particles of the EGAM in the linear growth phase are not found because the EGAM does not grow in the linear regime. In the phase space of pitch angle variable Λ and energy E, it is found that initially the Alfvén instability is excited by EPs with poloidal frequency 70 kHz, then, after the saturation of the Alfvén instability, the resonance region moves towards lower energy and touches the EGAM resonance line, and finally, EGAM is excited by the particles with poloidal frequency 50 kHz. This process is a kind of resonance overlap.

Do traffic flow states follow Markov properties? A high-order spatiotemporal traffic state reconstruction approach for traffic prediction and imputation

Assessing traffic states accurately is challenging due to the complex, high-dimensional, and nonlinear nature of traffic systems. This study introduces the innovative High-Order Spatiotemporal Traffic State Reconstruction (HOSTSR) algorithm, designed to track and predict traffic flow dynamics effectively. It combines phase space reconstruction with time delays and high-order neighborhood concepts from graph theory to improve traffic state assessments' accuracy. The algorithm's effectiveness is validated using chi-square tests and the Chapman-Kolmogorov equation to confirm the Markovian properties of traffic flows. A lean autoencoder, informed by prior Markov knowledge of traffic states, is developed for mapping traffic states to real traffic data, proving highly effective for traffic data imputation due to the Markov model's memoryless property. Experimental results from the PeMSD04 and PeMSD08 datasets show that HOSTSR outperforms traditional state reconstruction methods based on delayed coordinate embedding in predicting future traffic flow state based on four key metrics. The autoencoder framework, guided by prior Markov knowledge, shows significant advantages in addressing traffic data gaps in different cases over six baseline models. Gradient sensitivity analysis further evaluates the impact of prior knowledge on improving the autoencoder's interpretability for interpolation efforts.

Computational Spectroscopy of Aqueous Solutions: The Underlying Role of Conformational Sampling.

Fully atomistic multiscale polarizable quantum mechanics (QM)/molecular mechanics (MM) approaches, combined with techniques to sample the solute-solvent phase space, constitute the most accurate method to compute spectral signals in aqueous solution. Conventional sampling strategies, such as classical molecular dynamics (MD), may encounter drawbacks when the conformational space is particularly complex, and transition barriers between conformers are high. This can lead to inaccurate sampling, which can potentially impact the accuracy of spectral calculations. For this reason, in this work, we compare classical MD with enhanced sampling techniques, i.e., replica exchange MD and metadynamics. In particular, we show how the different sampling techniques affect computed UV, electronic circular dichroism, nuclear magnetic resonance shielding, and optical rotatory dispersion of N-acetylproline-amide in aqueous solution. Such a system is a model peptide characterized by complex conformational variability. Calculated values suggest that spectral properties are influenced by solute conformers, relative population, and solvent effects; therefore, particular care needs to be paid for when choosing the sampling technique.

The Evolution of the Phase Space Structure Along Pitchfork and Period-Doubling Bifurcations in a 3D-Galactic Bar Potential

We investigate how the phase space structure of a Three-Dimensional (3D) autonomous Hamiltonian system evolves across a series of successive Two-Dimensional (2D) and 3D pitchfork and period-doubling bifurcations, as the transition of the parent families of Periodic Orbits (POs) from stability to simple instability leads to the creation of new stable POs. Our research illustrates the consecutive alterations in the phase space structure near POs as the stability of the main family of POs changes. This process gives rise to new families of POs within the system, either maintaining the same or exhibiting higher multiplicity compared to their parent families. Tracking such a phase space transformation is challenging in a 3D system. By utilizing the color and rotation technique to visualize the Four-Dimensional (4D) Poincaré surfaces of section of the system, i.e. projecting them onto a 3D subspace and employing color to represent the fourth dimension, we can identify distinct structural patterns. Perturbations of parent and bifurcating stable POs result in the creation of tori characterized by a smooth color variation on their surface. Furthermore, perturbations of simple unstable parent POs beyond the bifurcation point, which lead to the birth of new stable families of POs, result in the formation of figure-8 structures of smooth color variations. These figure-8 formations surround well-shaped tori around the bifurcated stable POs, losing their well-defined forms for energies further away from the bifurcation point. We also observe that even slight perturbations of highly unstable POs create a cloud of mixed color points, which rapidly move away from the location of the PO. Our study introduces, for the first time, a systematic visualization of 4D surfaces of section within the vicinity of higher multiplicity POs. It elucidates how, in these cases, the coexistence of regular and chaotic orbits contributes to shaping the phase space landscape.

2-in-1 Phase Space Sampling for Calculating the Absorption Spectrum of the Hydrated Electron.

The investigation of vibrational effects on absorption spectrum calculations often employs Wigner sampling or thermal sampling. While Wigner sampling incorporates zero-point energy, it may not be suitable for flexible systems. Thermal sampling is applicable to anharmonic systems yet treats nuclei classically. The application of generalized smoothed trajectory analysis (GSTA) as a postprocessing method allows for the incorporation of nuclear quantum effects (NQEs), combining the advantages of both sampling methods. We demonstrate this approach in computing the absorption spectrum of a hydrated electron. Theoretical exploration of the hydrated electron and its embryonic forms, such as water cluster anions, poses a significant challenge due to the diffusivity of the excess electron and the continuous motion of water molecules. In many previous studies, the wave nature of atomic nuclei is often neglected, despite the substantial impact of NQEs on thermodynamic and spectroscopic properties, particularly for hydrogen atoms. In our studies, we examine these NQEs for the excess electrons in various water systems. We obtained structures from mixed classical-quantum simulations for water cluster anions and the hydrated electron by incorporating the quantum effects of atomic nuclei with the filtration of the classical trajectories. Absorption spectra were determined at different theoretical levels. Our results indicate significant NQEs, red shift, and broadening of the spectra for hydrated electron systems. This study demonstrates the applicability of GSTA to complex systems, providing insights into NQEs on energetic and structural properties.

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

Nonstandard Nearly Exact Analysis of the FitzHugh–Nagumo Model

The FitzHugh–Nagumo model has been used empirically to model certain types of neuronal activities. It is also a non-linear dynamical system applicable to chemical kinetics, population dynamics, epidemiology and pattern formation. In the literature, many approaches have been proposed to study its dynamics. In this paper, initially, we have employed cutting-edge tools from discrete dynamics for discretization and fixed points. It has been proven that an exact discrete scheme exists for this paradigm. This project also considers the phase space and integral surfaces of these evolutionary equations. In addition, it carries out a thorough symmetry analysis of this reaction diffusion system to find equivalent systems. Moreover, steady-state solutions are obtained using ansatzes for traveling wave solutions. The existence of infinite traveling wave solutions has also been proven. Yet again, this investigation establishes the potential of symmetry methods to unravel non-linearity. Finally, singular perturbation theory has been employed to obtain analytical approximations and to study stability in different parameter regimes.

Scalar Perturbations in Nonsingular Universes from Interacting Vacuum

Abstract In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit 
to late-time acceleration. Regarding such configurations as background spacetimes we introduce
scalar perturbations in order to examine the stability of these models in a high energy domain.
We explicitly show that the vacuum perturbation is not an independent variable and diverges as
dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics
making the choices for the energy transfer ill defined at least for nonsingular configurations
at the bounce scale.

Leveraging statistical-spectral correlations of random metasurfaces for steganography and multi-wavelength cryptography

The ability to tailor the spectral response of photonic devices is paramount to the advancement of a broad range of applications. The vast design space offered by disordered optical media provides enhanced functionality for spectral tailoring while also making it challenging to map the spectral properties of such complex systems to their structural attributes. In this work, we investigate correlations between the configuration statistics of random metasurfaces and their spectral transmissivity in the visible, and leverage those to develop a reduced phase space. In the latter part of the manuscript, we use this reduced phase space to design a pixelated color filter that hides visual data within a preselected cover image for steganography. Furthermore, we design a pair of color filters that can collectively encrypt a given grayscale image in their spectral transmissivities. We envision such devices to create opportunities for the development of compact, next-generation cryptographic systems. More broadly, the results presented in this manuscript provide new, to the best of our knowledge, avenues for optimizing large-scale random metasurfaces to achieve enhanced optical functionalities for a wide variety of applications.

Self-assembly of nanocrystal checkerboard patterns via non-specific interactions

Checkerboard lattices—where the resulting structure is open, porous, and highly symmetric—are difficult to create by self-assembly. Synthetic systems that adopt such structures typically rely on shape complementarity and site-specific chemical interactions that are only available to biomolecular systems (e.g., protein, DNA). Here we show the assembly of checkerboard lattices from colloidal nanocrystals that harness the effects of multiple, coupled physical forces at disparate length scales (interfacial, interparticle, and intermolecular) and that do not rely on chemical binding. Colloidal Ag nanocubes were bi-functionalized with mixtures of hydrophilic and hydrophobic surface ligands and subsequently assembled at an air–water interface. Using feedback between molecular dynamics simulations and interfacial assembly experiments, we achieve a periodic checkerboard mesostructure that represents a tiny fraction of the phase space associated with the polymer-grafted nanocrystals used in these experiments. In a broader context, this work expands our knowledge of non-specific nanocrystal interactions and presents a computation-guided strategy for designing self-assembling materials.

Normal form and Hopf bifurcation for the memory‐based reaction‐diffusion equation with nonlocal effect

In this paper, we provide the normal form for the Hopf bifurcation of a class of the reaction‐diffusion equation with memory‐based diffusion and nonlocal effect, where the delay is present in the differential term, similar to the chemotaxis model with time delay. The eigenvalue problems and the decomposition of the phase space are discussed in detail. Through a series of variable transformations, we obtain the third‐order truncated normal form of the model constrained on the central manifold and its equivalent equation in polar coordinates. Then, with the help of the dynamic analysis for the finite dimensional equations, the key parameters for determining the direction and stability of the Hopf bifurcation are given. These theoretical results are applied to the Bazykin's model, the stability, Turing bifurcation and Hopf bifurcation of the equilibrium are demonstrated through both theoretical and numerical methods.