Phase Space Research Articles

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

Abstract We investigate the evolution of a flat Emergent Universe obtained with a non-linear equation of state (nEoS) in Einstein’s general theory of Relativity. The nEoS is equivalent to three different types of barotropic cosmic fluids, which are found from the nEoS parameter. The EU began expanding initially with no interactions among the cosmic fluids. However, one can assume an interaction that sets in at a time t ⩾ t i in the cosmic fluids, we study the evolution of the EU that accommodates the present observed Universe. We adopt dynamical system analysis to study the critical points of the autonomous system and the evolutionary behavior of an EU with or without interaction among the cosmic fluid components. We also study the stability of critical points and plot the phase portraits. The density parameters and the corresponding cosmological parameters are determined for both the non-interacting and interacting phases of the evolutionary dynamics of the Universe.

Triple points of gravitational AdS solitons and black holes

We present a triple point of a new kind for general relativity, at which two gravitational solitons can coexist with a planar black hole in anti–de Sitter space. Working in the context of nonlinear electrodynamics, we obtain simple, sensible spacetimes for which the thermodynamics can be studied in an analytic manner. The spacetimes are charged under the nonlinear electrodynamics leading to an electric charge for black holes and a magnetic flux for solitons. In the grand-canonical ensemble, we show that the phase space of the theory is very rich, containing reentrant phase transitions, as well as triple points, for small values of the coupling controlling the nonlinearity of the electrodynamics Lagrangian. Published by the American Physical Society 2024

Quantum signatures of the mixed classical phase space for three interacting particles in a circular trap

Quantum signatures of the mixed classical phase space for three interacting particles in a circular trap

The quasilocal energy and thermodynamic first law in accelerating AdS black holes

We scrutinize the conserved energy of an accelerating AdS black hole by employing the off-shell quasilocal formalism, which amalgamates the ADT formalism with the covariant phase space approach. In the presence of conical singularities in the accelerating black hole, the energy expression is articulated through the surface term derived from our formalism. The essence of our analysis of the quasilocal energy resides in the surface contributions coming from the conical singularities as well as the conventional radial boundary. Consequently, the resultant conserved quasilocal energy naturally conforms the thermodynamic first law for the black hole without necessitating any augmentation of thermodynamic variables.

Phase space path integral approach to the kinetics of black hole phase transition

Phase space path integral approach to the kinetics of black hole phase transition

Criticality of central charges for Gauss–Bonnet black holes

Employing extended phase space formalism, we study critical phenomenon of A-charge and C-charge for holographic theories dual to Gauss–Bonnet black holes. We find an universal critical Gauss–Bonnet coupling, giving rise to an universal ratio between the two central charges at the critical point. This leads to a new intepretation for critical behavior of Gauss–Bonnet black holes in terms of the boundary degrees of freedoms, although the solutions are electrically neutral. Another novel feature is for either of the central charges, the transition temperature is beyond the critical point but is upper bounded by causality of the boundary theories.

Tunneling Currents in the Hyperbolic Phase Space.

We introduce the quantum currents for quantum systems with an SU(1,1) dynamic symmetry group whose evolution is governed by a non-linear Hamiltonian possessing a continuous spectrum and apply them to the analysis of the tunneling dynamics on the hyperbolic phase space.

On the charge algebra of causal diamonds in three dimensional gravity

Covariant phase space methods are applied to the analysis of a causal diamond in 2+1-dimensional pure Einstein gravity. It is found that the reduced phase space is parametrized by a family of charges with a dual geometrical interpretation: they are geometric observables on the corner of the diamond, and they generate diffeomorphisms. The Poisson brackets among them close into an algebra. Knowledge of the corner charges therefore permits reconstruction of the diamond geometry, which realizes a form of local holography. The results are contrasted with the literature, and the path to a quantum description of spacetime geometry is discussed.

ATEP: an advanced transport model for energetic particles

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 Alfvén 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 (Meng et al 2024 Nucl. Fusion accepted)), 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.

Virtual QCD corrections to gg → ZZ: top-quark loops from a transverse-momentum expansion

We present the virtual corrections due to the top-quark loops for the process gg → ZZ at next-to-leading order in QCD. The associated two-loop box diagrams are computed using a small-transverse-momentum expansion. Our results are then merged with those available in the complementary energy region, obtained via a high-energy expansion, in order to provide an analytic result that is valid in the whole phase space. The results presented allow for an efficient modelling of the signal-background interference as well as the irreducible background in off-shell Higgs production.

Inclusive cross section measurements in final states with and without protons for charged-current νμ -Ar scattering in MicroBooNE

A detailed understanding of inclusive muon neutrino charged-current interactions on argon is crucial to the study of neutrino oscillations in current and future experiments using liquid argon time projection chambers. To that end, we report a comprehensive set of differential cross section measurements for this channel that simultaneously probe the leptonic and hadronic systems by dividing the channel into final states with and without protons. Measurements of the proton kinematics and proton multiplicity of the final state are also presented. For these measurements, we utilize data collected with the MicroBooNE detector from 6.4×1020 protons on target from the Fermilab booster neutrino beam at a mean neutrino energy of approximately 0.8 GeV. We present in detail the cross section extraction procedure, including the unfolding, and model validation that uses data to model comparisons and the conditional constraint formalism to detect mismodeling that may introduce biases to extracted cross sections that are larger than their uncertainties. The validation exposes insufficiencies in the overall model, motivating the inclusion of an additional data-driven reweighting systematic to ensure the accuracy of the unfolding. The extracted results are compared to a number of event generators and their performance is discussed with a focus on the regions of phase space that indicate the greatest need for modeling improvements. Published by the American Physical Society 2024

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.

Linear operator theory of phase mixing

Abstract We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrödinger-type equations. For illustrative purposes, we consider the classical phase mixing of a non-interacting distribution function in a quartic potential. Solutions are determined perturbatively relative to a harmonic oscillator. We impose a form of coarse-graining by choosing a finite dimensional basis to represent the distribution function and time evolution operators, which sets a minimum length scale on phase space structure. We observe a relationship between the dimension of the representation and the multiplicity of the harmonic oscillator eigenvalues. System dynamics are understood in terms of degenerate subspaces of the linear operator spectra. Each subspace is associated with a mode of the harmonic oscillator, the first two being bending and breathing structures. The quartic potential splits the degenerate eigenvalues within each subspace. This facilitates the formation of spiral structure as deformations from the harmonic oscillator modes. We ultimately argue that this construction provides a promising avenue for study of self-interacting systems experiencing phase mixing, which is an outstanding problem in the context of the Gaia DR2 vertical phase space spirals.

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.

Experimental study on combustion instability characteristics in a pre-chamber natural gas engine under lean burn conditions

Pre-chamber jet ignition is a key technology for future high-efficiency natural gas (NG) engines. It can achieve fast and stable combustion through excellent ignition performance. However, there are still some challenges, such as high combustion instability near the lean burn limit and the narrow engine operating range. Therefore, this paper investigates the combustion instability of a pre-chamber NG engine under ultra-diluted conditions by experimental method. At two engine loads, experiments are carried out with different jet ignition intensity schemes to study the effect of jet ignition intensity on the cyclic combustion variations. Then, the combustion instability characteristics of the pre-chamber NG engine are studied by cyclic variation analysis and phase space reconstruction. The results show that with the increase in the jet ignition intensity, the cyclic combustion variations decrease, and the cyclic variation coefficient of the indicated mean effective pressure decreases to below 2%. The lean burn limit of the pre-chamber natural gas engine is extended to an excess air ratio of 2.0. The operation instability of the pre-chamber NG engine is mainly due to cyclic variations in the ignition and combustion process. The nonlinear dynamic analysis shows that the combustion process in the lean burn pre-chamber NG engine behaves with chaotic characteristics under the operating conditions of low jet ignition intensity. As the jet ignition intensity increases, the combustion stability is improved and the cycle-to-cycle variations change from fairly deterministic to more stochastic behavior. The chaotic characteristics of the combustion process become weaker. In conclusion, it is of great importance to generate stable and high ignition intensity jets for reducing combustion instability and improving combustion efficiency in lean burn pre-chamber NG engines.

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

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.

Operation of Rf Systems During Joint Booster and Nuclotron Sessions

The article discusses the results of commissioning of RF systems of the NICA injection complex and plans for their further development. The preparation of the injection complex for injection into the collider requires an increase in the beam intensity in the Nuclotron outlet by about two orders of magnitude. Obtaining the required intensity will be achieved by accumulating the beam on injection energy using electronic cooling and reducing acceleration losses. This will require optimization of all systems of the complex, including a significant reduction in losses associated with RF systems. The experience allows us to choose the optimal strategy for the further development of HF systems. The main directions are: (1) accumulation of the beam in the longitudinal phase space during injection into the Booster, (2) reduction of the growth of the longitudinal emittance during acceleration, (3) bypass of the beam clot-in-clot from the Booster to the Nuclotron without growth of the longitudinal emittance, and (4) minimizing losses during acceleration and beam bypasses. The latter requires matching the acceleration rate with the capabilities of existing HF systems.