Phase Space Research Articles

Supersymmetric smooth distributions of M2-branes as AdS solitons

We show that the singularities of certain distributions of M2-branes can be removed by adding a Wilson loop around a compact direction along the brane. The holographic coordinate naturally ends up before the singularity and the resulting spacetime provides an AdS soliton configuration, albeit possibly supersymmetric. We study the phase space diagram of these M2-branes distributions endowed with Wilson loops and show that different distributions are interconnected, providing a rich structure of phase transitions at zero temperature.

Towards Modelling Mechanical Shaking Using Potential Energy Surfaces: A Toy Model Analysis

In this work, we formalize the effect of mechanical shaking by using various forms of an externally exerted force, which may be constant or may be position-dependent, and we examine the changes in the potential energy surfaces that quantify the chemical reaction. We use a simple toy model to model the potential energy surfaces of a chemical reaction, and we study the effect of a constant or position-dependent externally exerted force for various forms of the force. As we demonstrate, the effect of the force can be quite dramatic on the potential energy surfaces, which acquire new stationary points and new Newton trajectories that are distinct from the original ones that were obtained in the absence of mechanochemical effects. We also introduce a new approach to mechanochemical interactions, using a dynamical systems approach for the Newton trajectories. As we show, the dynamical system attractor properties of the trajectories in the phase space are identical to the stationary points of the potential energy surfaces, but the phase space contains much more information regarding the possible evolution of the chemical reaction—information that is quantified by the existence of unstable or saddle fixed points in the phase space. We also discuss how an experimental method for a suitable symmetric liquid solution substance might formalize the effect of shaking via various forms of external force, even in the form of an extended coordinate-dependent force matrix. This approach may experimentally quantify the Epstein effect of shaking in chemical solutions via mechanochemistry methods.

Relativistic corrections to prompt double charmonium hadroproduction near threshold

We calculate the relativistic corrections to prompt J/ψ pair and J/ψ+ψ(2S) hadroproduction through the color singlet channel within the framework of nonrelativistic-QCD (NRQCD) factorization. The short-distance coefficients are obtained by matching full-QCD and NRQCD calculations at the partonic level, in which both squared amplitude and phase space are expanded in v2. We find that such an expansion of the phase space spoils the convergence of NRQCD factorization near the production threshold. To fix this problem, we propose to modify the matching between full QCD and NRQCD by adopting the physical phase space. In this modified approach, the theoretical uncertainties due to the choice of charm quark mass mc are largely reduced and the overall agreement of our predictions with LHC data is significantly improved, both for total and differential cross sections. Published by the American Physical Society 2024

Notes on thermodynamics of Schwarzschild-like bumblebee black hole

In this work, we revisited the thermodynamics of Schwarzschild-like bumblebee black hole using Iyer–Wald covariant phase space formalism. With a non zero vacuum expectation value, the bumblebee field is responsible for spontaneously breaking the Lorentz symmetry. As the bumblebee field is non-minimally coupled to gravity, we showed that the thermodynamic variables will be different from the counterpart in Einstein gravity. Especially, by using Iyer–Wald formalism, we found that the black hole entropy also differs from the result obtained from Wald entropy formula. Like Horndeski gravity, this mismatch is due to the divergence of bumblebee one-form field at the horizon. After figuring out the thermodynamics, we also briefly discussed the evaporation behavior of Schwarzschild like bumblebee black hole. We found that although bumblebee field has no influence on the critical impact factor, it can influence the black hole evaporation time.

Approaching Maximal Precision of Hong-Ou-Mandel Interferometry with Nonperfect Visibility.

In quantum mechanics, the precision achieved in parameter estimation using a quantum state as a probe is determined by the measurement strategy employed. The quantum limit of precision is bounded by a value set by the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, these conditions cannot be achieved, so precision never reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this Letter, we provide a model for precision limits in two-photon Hong-Ou-Mandel interferometry using coincidence statistics for nonperfect visibility and temporally unresolved measurements. We show that the scaling of precision with visibility depends on the effective area in time-frequency phase space occupied by the state used as a probe, and we find that an optimal scaling exists. We demonstrate our results experimentally for different states in a setup where the visibility can be controlled and reaches up to 99.5%. In the optimal scenario, a ratio of 0.97 is observed between the experimental precision and the quantum limit, establishing a new benchmark in the field.

N3LL resummation of one-jettiness for Z -boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the color-singlet plus jet production process pp→(γ*/Z→ℓ+ℓ−)+jet at hadron colliders up to the fourth logarithmic order (N3LL). This is the first resummation at this order for processes involving three colored partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for color-singlet plus jet production matched to parton showers in the framework. Published by the American Physical Society 2024

Matter relative to quantum hypersurfaces

We explore the canonical description of a scalar field in 1+1 dimensional Minkowski space as a parametrized field theory on an extended phase space that includes additional embedding fields that characterize spacetime hypersurfaces X relative to which the scalar field is described. This theory is quantized via the Dirac prescription and physical states of the theory are used to define conditional wave functionals |ψϕ[X]⟩ interpreted as the state of the field relative to the hypersurface X, thereby extending the Page-Wootters formalism to quantum field theory. It is shown that this conditional wave functional satisfies the Tomonaga-Schwinger equation, thus demonstrating the formal equivalence between this extended Page-Wootters formalism and standard quantum field theory. We also construct relational Dirac observables and define a quantum deparametrization of the physical Hilbert space leading to a relational Heisenberg picture, which are both shown to be unitarily equivalent to the Page-Wootters formalism. Moreover, by treating hypersurfaces as quantum reference frames, we extend recently developed quantum frame transformations to changes between classical and nonclassical hypersurfaces. This allows us to exhibit the transformation properties of a quantum field under a larger class of transformations, which leads to a frame-dependent particle creation effect. Published by the American Physical Society 2024

Bulk-boundary thermodynamics of charged black holes in higher-derivative theory

The connection between bulk and boundary thermodynamics in Einstein–Maxwell theory is well established using AdS/CFT correspondence. In the context of general higher-derivative gravity coupled to a U(1) gauge field, we examine the resemblance of the first law of thermodynamics between bulk and boundary, followed by an extended phase space description on both sides. Higher-derivative terms related to different powers of the string theory parameter α′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha '$$\\end{document} emerged from a consistent truncation in the bulk supergravity action. We demonstrate that one must include the fluctuation of α′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha '$$\\end{document} in the bulk thermodynamics as a bookkeeping tool to match the bulk first law and Smarr relation with the boundary side. Consequently, the Euler relation and the boundary first law are altered by adding two central charges (a,c).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ exttt{a}}, {\ exttt{c}}).$$\\end{document} To support our general conclusion, we consider the black hole in Gauss–Bonnet gravity and the general four-derivative theory. Finally, we examine the bulk and boundary aspects of the extended phase space description for higher-derivative-corrected black holes.

Flux Quantization on Phase Space

Flux Quantization on Phase Space

Data-driven traffic signal adaptive control algorithm integrating vehicle perception and traffic flow data

Due to the equipment error, environmental interference and data transmission delay of vehicle flow detection, the accuracy and real-time performance of vehicle perception and traffic flow data will be affected to some extent, resulting in poor traffic signal control effect. Therefore, a data-driven traffic signal adaptive control algorithm is designed by integrating vehicle perception and traffic flow data. To complete the modeling of urban traffic, the discrete distribution and continuous distribution of traffic are obtained. Based on this research environment, the DV-hop localization algorithm is improved to sense the vehicle position. Based on the phase space reconstruction of traffic flow time series and vehicle location information, traffic flow data is predicted. Based on the driving of traffic data, the vehicle types are divided into small, medium and large three categories, and the impact weights are assigned respectively, and the weight values affecting the final allocation of green time are obtained to realize the allocation of green time. The experimental results show that: The research algorithm can not only predict the traffic flow intensity effectively, but also the predicted results are highly coincident with the actual traffic flow intensity. Vehicle arrival rates are higher, vehicle delays are shorter, and vehicles stop fewer times on average.

Geometrically parametrised reduced order models for studying the hysteresis of the Coanda effect in finite element-based incompressible fluid dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behaviour of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behaviour in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

Vortex-induced rotation of a square cylinder under the influence of Reynolds number and density ratio

Numerical simulations are carried out on the vortex-induced rotations of a freely rotatable rigid square cylinder in a two-dimensional uniform cross-flow. A range of Reynolds numbers between 40 and 150 and density ratios between 0.1 and 10 are considered. Results show eight different characteristic regimes, expanding the classification of Ryu & Iaccarino (J. Fluid Mech., vol. 813, 2017, pp. 482–507). New regimes include the transition and wavy rotation regimes; in the ${\rm \pi}$ -limited oscillation regime we observe multipeak subregimes. Moment-generating mechanisms of these regimes and subregimes are further elucidated. A phenomenon related to the influence of density ratio is the tooth-like shape of the ${\rm \pi} /2$ -limit oscillation regime observed in the regime map, which is explained as a result of the imbalance relation between the main frequencies of rotation response and the vortex shedding frequency. In addition, existence of multiple regimes and multistable states are discussed, indicating multiple stable attractive structures in phase space.

Nanoscale spin ordering and spin screening effects in tunnel ferromagnetic Josephson junctions

Magnetic Josephson junctions (MJJs) have emerged as a prominent playground to explore the interplay between superconductivity and ferromagnetism. A series of fascinating experiments have revealed striking phenomena at the superconductor/ferromagnet (S/F) interface, pointing to tunable phase transitions and to the generation of unconventional spin-triplet correlations. Here, we show that the Josephson effect, being sensitive to phase space variation on the nanoscale, allows a direct observation of the spin polarization of the S/F interface. By measuring the temperature dependence of the Josephson magnetic field patterns of tunnel MJJs with strong and thin F-layer, we demonstrate an induced nanoscale spin order in S along the superconducting coherence length at S/F interface, i.e., the inverse proximity effect, with the first evidence of full spin screening at very low temperatures, as expected by the theory. A comprehensive phase diagram for spin nanoscale ordering regimes at S/F interfaces in MJJs has been derived in terms of the magnetic moment induced in the S-layer. Our findings contribute to drive the design and the tailoring of S/F interfaces also in view of potential applications in quantum computing.

Two-loop amplitudes for tt¯H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}H $$\\end{document} production: the quark-initiated Nf-part

We present numerical results for the two-loop virtual amplitude entering the NNLO corrections to Higgs boson production in association with a top quark pair at the LHC, focusing, as a proof of concept of our method, on the part of the quark-initiated channel containing loops of massless or massive quarks. Results for the UV renormalised and IR subtracted two-loop amplitude for each colour structure are given at selected phase-space points and visualised in terms of surfaces as a function of two-dimensional slices of the full phase space.

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms

Non-thermal advanced fuel fusion trades the requirement of a large amount of recirculating tritium in the system for that of large recirculating power. Phase space engineering technologies utilizing externally injected electromagnetic fields can be applied to meet the challenge of maintaining non-thermal particle distributions at a reasonable cost. The physical processes of the phase space engineering are studied from a theoretical and algorithmic perspective. It is emphasized that the operational space of phase space engineering is limited by the underpinning symplectic dynamics of charged particles. The phase space incompressibility according to the Liouville theorem is just one of many constraints, and Gromov's non-squeezing theorem determines the minimum footprint of the charged particles on every conjugate phase space plane. In this sense and level of sophistication, the mathematical abstraction of phase space engineering is symplectic topology. To simulate the processes of phase space engineering, such as the Maxwell demon and electromagnetic energy extraction, and to accurately calculate the minimum footprints of charged particles, recently developed structure-preserving geometric algorithms can be used. The family of algorithms conserves exactly, on discretized spacetime, symplecticity and thus incompressibility, non-squeezability, and symplectic capacities. The algorithms apply to the dynamics of charged particles under the influence of external electromagnetic fields as well as the charged particle–electromagnetic field system governed by the Vlasov–Maxwell equations.

Experimental study on the disturbance of microbubble liquid jets

The presence of microbubble significantly influences the rheological properties of a jet, thereby considerably increasing the complexity of the jet instability problem. However, the instability of microbubble jets has been rarely studied, and their breakup mechanism remains obscure. The present study was focused on conducting a comprehensive analysis of bubble jet flows. A high-precision experimental system was constructed to extract the time-series signals of each cross-sectional profile along the axial direction of a jet. Glycerol solutions with three different bubble volume fractions were prepared, and the standard deviation, spectral relationship, and nonlinear dynamical behavior (i.e., autocorrelation, phase space trajectory, Poincaré section, and Lyapunov exponent) were studied. The detailed development process of small surface disturbances in space was assessed, and the influence of variations in the bubble volume fraction on the nonlinear dynamics of the jet was examined. The results demonstrate that microbubbles can significantly change the energy transfer relationship between various sections of a jet and enhance the periodicity of the signal.

On the Ryll-Nardzewski fixed point property in convex uniform spaces

In this paper, we introduce the concept of a convex uniform space as a natural generalization of locally convex spaces, and a fixed point property as a semigroup formulation of the famous Ryll-Nardzewski fixed point theorem, and study its non-linear counterpart in this framework. The Nardzewski's fixed point theorem is a beautiful result in fixed point theory that ensures the existence of a common fixed point for any noncontracting semigroup of continuous affine self-mappings on a non-void weakly compact convex set in a separated locally convex space. We establish that in a separated convex uniform space satisfying a certain property (P), any noncontracting finite semigroup of contraction mappings of a non-empty bounded closed convex subset possesses a common fixed point. In case where the underlying space is admissible, we prove that this result is extendable to arbitrary noncontracting semigroups without condition (P) if we assume that the phase space is weakly compact and convex.

Lagrangian approach for analysis of acoustic energy transport in open cavity flows

The energy transport in aero-acoustics is investigated in the Lagrangian frame. First, based on finite-time Lyapunov exponent (FTLE) and momentum potential theory, a Lagrangian approach is proposed to identify transport barriers of acoustic energy. Specifically, the method, named relative flux gradient (RFG), is presented in detail. Then, to verify the method, it is applied to analytical fields, showing that it could reveal the wavefronts and energy transport barriers depending on the time interval of computation. Moreover, RFG is applied to analyze a simulated flow field of an open cavity flow, and the results are compared with the Lagrangian coherent structures identified by FTLE, demonstrating great similarity. Importantly, the differences between the structures are further analyzed, illustrating several transport channels that correspond to the Rossiter mode and showing a complex interaction between acoustic and vorticity modes. Finally, the relationship between the identified transport barriers and the acoustic behaviors in Eulerian frame is studied in detail. The results show that the transport barriers identified by RFG significantly impact the orbits in phase space, and in particular, RFG has the potential to illustrate and analyze the transport of acoustic energy in complex flow fields in a quantitative way: one method for direct analysis of acoustic phenomena in complex flow regions.

Dynamical Modeling and Qualitative Analysis of a Delayed Model for CD8 T Cells in Response to Viral Antigens.

Although the immune effector CD8 T cells play a crucial role in clearance of viruses, the mechanisms underlying the dynamics of how CD8 T cells respond to viral infection remain largely unexplored. Here, we develop a delayed model that incorporates CD8 T cells and infected cells to investigate the functional role of CD8 T cells in persistent virus infection. Bifurcation analysis reveals that the model has four steady states that can finely divide the progressions of viral infection into four states, and endows the model with bistability that has ability to achieve the switch from one state to another. Furthermore, analytical and numerical methods find that the time delay resulting from incubation period of virus can induce a stable low-infection steady state to be oscillatory, coexisting with a stable high-infection steady state in phase space. In particular, a novel mechanism to achieve the switch between two stable steady states, time-delay-based switch, is proposed, where the initial conditions and other parameters of the model remain unchanged. Moreover, our model predicts that, for a certain range of initial antigen load: 1) under a longer incubation period, the lower the initial antigen load, the easier the virus infection will evolve into severe state; while the higher the initial antigen load, the easier it is for the virus infection to be effectively controlled and 2) only when the incubation period is small, the lower the initial antigen load, the easier it is to effectively control the infection progression. Our results are consistent with multiple experimental observations, which may facilitate the understanding of the dynamical and physiological mechanisms of CD8 T cells in response to viral infections.