Points In Phase Space Research Articles

Two-loop mixed QCD-EW corrections to charged current Drell-Yan

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the W-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the W-boson mass within their radius of convergence in a negligible amount of time.

Improving metrology with quantum scrambling in a spin-1 Bose-Einstein condensate coupled to a cavity

Spinor Bose-Einstein condensate is an ideal candidate for implementing the many-body entanglement, quantum measurement and quantum information processing owing to its inherent spin-mixing dynamics. Here we present a system of an 87Rb atomic spin-1 Bose-Einstein condensate coupled to an optical ring cavity, in which cavity-mediated nonlinear interactions give rise to saddle points in the semiclassical phase space, providing a general mechanism for exponential fast scrambling and metrological gain augment. We theoretically study metrological gain and fidelity out-of-time-ordered correlator based on time-reversal protocols and demonstrate that exponential rapid scrambling dynamics can enhance quantum metrology. In addition, we use the out-of-time-ordered correlator to probe dynamical phase transitions. This work is useful to understand the intrinsic relation between the concepts from different subfields of quantum science.

Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering

We investigate the photon emission in pion-pion and pion-proton scattering in the soft-photon limit where the photon energy ω→0. The expansions of the π−π0→π−π0γ and the π±p→π±pγ amplitudes, satisfying the energy-momentum relations, to the orders ω−1 and ω0 are derived. We show that these terms can be expressed completely in terms of the on-shell amplitudes for π−π0→π−π0 and π±p→π±p, respectively, and their partial derivatives with respect to s and t. The structure term which is nonsingular for ω→0 is determined to the order ω0 from the gauge-invariance constraint using the generalized Ward identities for pions and the proton. For the reaction π−π0→π−π0γ we discuss in detail the soft-photon theorems in the versions of both Low and Weinberg. We show that these two versions are different and must not be confounded. Weinberg’s version gives the pole term of a Laurent expansion in ω of the amplitude for π−π0→π−π0γ around the phase-space point of zero radiation. Low’s version gives an approximate expression for the above amplitude at a fixed phase-space point, corresponding to nonzero radiation. Clearly, the leading and next-to-leading terms in theses two approaches must be, and are indeed, different. We show their relation. We also discuss the expansions of differential cross sections for π−π0→π−π0γ with respect to ω for ω→0. Published by the American Physical Society 2024

SPINAS: spinor amplitude subroutines for constructive diagram evaluations

SPINAS is a C++ package created for the implementation and numerical computation of phase-space points of constructive amplitudes in particle physics. This package contains a suite of classes and methods for handling particles, propagators, spinor products, and processes. SPINAS is structured to offer straightforward usability while ensuring maximum efficiency. This is achieved through a design that emphasizes the storage and reuse of intermediate results within amplitude calculations for each phase-space point. We include a user guide describing how to use the components, a complete example of how to use SPINAS for a scattering amplitude, a discussion of the design and implementation useful for those wishing to contribute, and a discussion of our validation of this package, including both a validation of individual components of the package and a comparison of a complete set of Standard Model processes with Feynman diagrams.

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.

Symmetry-based study and dynamics of casual bulk viscous matter-dominated universe

The dynamics of cosmological expansion is studied for a spatially flat matter-dominated universe filled with barotropic casual bulk viscous fluid. The evolution equation for the Hubble parameter is derived using Friedmann equations and conservation law for the viscous fluid, in which the viscous pressure is modeled by truncated version of the full Israel-Stewart theory of bulk viscosity. We use a Lie symmetry-based approach to study the evolution of the expansion rate of the Universe. The model equation possesses eight-parameter Lie symmetry generators and gives two different analytic group invariant solutions for the Hubble parameter. Expressions for various important cosmological parameters are obtained and values are estimated analytically for the explanation of the evolution dynamics of the Universe. The interesting features of the obtained symmetry-based solutions are that, one satisfies the present acceleration of the Universe, while the other could not support present accelerating phase, rather represents a universe dominated by non-viscous stiff fluid. We make useful checks on the observational constraints on the model parameters from the latest released observational data. The accelerating phase of the current universe is investigated using observational bounds and compared the model under investigation with the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model. The evolutionary cosmic phases obtained from the analysis of the Lie symmetry-based solutions correspond to the association with the critical points in the equivalent phase space. These interesting features are investigated and analyzed using dynamical systems approach.

Colloid and nanoparticle-driven phase behavior in weakly perturbed nematic liquid crystals

We study theoretically weakly colloidal particle or nano-particle perturbed nematic liquid crystal (LC) order. We consider cases where the particles are essentially homogeneously dispersed in LC matrix. A mesoscopic Landau-de Gennes approach is used where we focus on the temperature variations in the amplitude order parameter field for different particle volume concentrations ϕ. In the dilute regime, we describe the nematic order in terms of interface and volume amplitude order fields. This modeling suggests that the temperature-driven order-disorder crossover exhibits a two-step transformation. In the case that particles locally support LC order, on decreasing temperature firstly the interface order is established, followed by the build-up of volume order. The latter appears via the 1st order phase transition. On the other hand, the interface order growth is formed either gradually or via the 1st order interfacial transition. In the regime of relatively high values of ϕ the system can be effectively described in terms of a single amplitude order parameter field. In this case, the temperature-driven phase behaviour is qualitatively similar to the interface order temperature response in the diluted regime. We analytically express phase transition temperatures and determine critical points in the temperature-interface interaction phase space. Key novelties of the paper are the determination of conditions for particle-LC interface-driven discontinuous change of nematic ordering and nanoparticle-enabled critical point condition in pressure-driven order-disorder phase transformations. Experimental evidences supporting the predicted phase behavior are presented.

On committor functions in milestoning.

As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions.

Twofold Machine-Learning and Molecular Dynamics: A Computational Framework

Data science and machine learning (ML) techniques are employed to shed light into the molecular mechanisms that affect fluid-transport properties at the nanoscale. Viscosity and thermal conductivity values of four basic monoatomic elements, namely, argon, krypton, nitrogen, and oxygen, are gathered from experimental and simulation data in the literature and constitute a primary database for further investigation. The data refers to a wide pressure–temperature (P-T) phase space, covering fluid states from gas to liquid and supercritical. The database is enriched with new simulation data extracted from our equilibrium molecular dynamics (MD) simulations. A machine learning (ML) framework with ensemble, classical, kernel-based, and stacked algorithmic techniques is also constructed to function in parallel with the MD model, trained by existing data and predicting the values of new phase space points. In terms of algorithmic performance, it is shown that the stacked and tree-based ML models have given the most accurate results for all elements and can be excellent choices for small to medium-sized datasets. In such a way, a twofold computational scheme is constructed, functioning as a computationally inexpensive route that achieves high accuracy, aiming to replace costly experiments and simulations, when feasible.

Tropical Feynman integration in the Minkowski regime

We present a new computer program, feyntrop, which uses the tropical geometric approach to evaluate Feynman integrals numerically. In order to apply this approach in the physical regime, we introduce a new parametric representation of Feynman integrals that implements the causal iε prescription concretely while retaining projective invariance. feyntrop can efficiently evaluate dimensionally regulated, quasi-finite Feynman integrals, with not too exceptional kinematics in the physical regime, with a relatively large number of propagators and with arbitrarily many kinematic scales. We give a systematic classification of all relevant kinematic regimes, review the necessary mathematical details of the tropical Monte Carlo approach, give fast algorithms to evaluate (deformed) Feynman integrands, describe the usage of feyntrop and discuss many explicit examples of evaluated Feynman integrals. Program summaryProgram title:feyntrop.CPC Library link to program files:https://doi.org/10.17632/k6r62hdgvd.1Developer's repository link:https://github.com/michibo/feyntrop.Licensing provisions: MIT License.Programming language: The tropical Monte Carlo code is written in C++. The high-level interface is written in python.Supplementary material: The repository includes installation and usage instructions (README.md), a jupyter notebook tutorial (tutorial_2L_3pt.ipynb), the collection of examples presented in section 6 (see the folder /examples), and a test suite to ensure a successful installation (see the folder /tests).Nature of problem: Sufficiently fast numerical integration of (dimensionally regularized) Feynman integrals (also in the Minkowski regime of phase space).Solution method: Tropical Monte Carlo integration of a manifestly iε-free parametric representation of Feynman integrals.Additional comments: The program feyntrop is based on previous code available at https://github.com/michibo/tropical-feynman-quadrature, which was published as a proof-of-concept with, Michael Borinsky, ‘Tropical Monte Carlo quadrature for Feynman integrals’, Ann. Inst. Henri Poincaré Comb. Phys. Interact. (in press)[1]. This previous code did not have features which are required for phenomenological studies in high-energy physics. In particular, it only allowed for phase space points in the Euclidean regime, and only computed the leading term in the ϵ expansion.Restrictions: The Feynman integral must be quasi-finite and the momentum configuration must be sufficiently generic. Numerators of Feynman integrals are not implemented. ReferencesEigen3[2]. The xoshiro256+ pseudo-random-number generator [3]. python[4]. pybind11[5]. sympy[6].

Imaging feature-based clustering of financial time series.

Timeseries representation underpin our ability to understand and predict the change of natural system. Series are often predicated on our choice of highly redundant factors, and in fact, the system is driven by a much smaller set of latent intrinsic keys. It means that a better representation of data makes points in phase space clearly for researchers. Specially, a 2D structure of timeseries could combine the trend and correlation characters of different periods in timeseries together, which provides more clear information for top tasks. In this work, the effectiveness of 2D structure of timeseries is investigated in clustering tasks. There are 4 kinds of methods that the Recurrent Plot (RP), the Gramian Angular Summation Field (GASF), the Gramian Angular Differential Field (GADF) and the Markov Transition Field (MTF) have been adopted in the analysis. By classifying the CSI300 and S&P500 indexes, we found that the RP imaging series are valid in recognizing abnormal fluctuations of financial timeseries, as the silhouette values of clusters are over 0.6 to 1. Compared with segment methods, the 2D models have the lowest instability value of 0. It verifies that the SIFT features of RP images take advantage of the volatility of financial series for clustering tasks.

Wigner function for the quantum mechanics on a sphere

The Wigner quasiprobability function for a particle on a sphere is introduced and its properties investigated. In opposition to alternative approaches this Wigner function depends on the points of the classical phase space, that is the cotangent bundle T∗S2.

Improving metrology with quantum scrambling

Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.

Two-loop master integrals for a planar and a non-planar topology relevant for single top production

We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential Equations approach is employed for their analytic solution. The necessary boundary terms are computed in closed form in the dimensional regulator, allowing us to obtain analytic results in terms of multiple polylogarithms of arbitrary transcendental weight. We provide explicit solutions of all two-loop master integrals up to transcendental weight six and discuss their numerical evaluation for Euclidean and physical phase-space points.

Phase-Space Geometry and Optimal State Preparation in Quantum Metrology with Collective Spins

We revisit well-known protocols in quantum metrology using collective spins and propose a unifying picture for optimal state preparation based on a semiclassical description in phase space. We show how this framework allows for quantitative predictions of the timescales required to prepare various metrologically useful states, and that these predictions remain accurate even for moderate system sizes, surprisingly far from the classical limit. Furthermore, this framework allows us to build a geometric picture that relates optimal (exponentially fast) entangled probe preparation to the existence of separatrices connecting saddle points in phase space. We illustrate our results with the paradigmatic examples of the two-axis countertwisting and twisting-and-turning Hamiltonians, where we provide analytical expressions for all the relevant optimal timescales. Finally, we propose a generalization of these models to include p-body collective interaction (or p-order twisting), beyond the usual case of p=2. Using our geometric framework, we prove a no-go theorem for the local optimality of these models for p>2.Received 8 November 2022Revised 1 February 2023Accepted 28 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020314Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum metrologyQuantum sensingTechniquesPhase space dynamicsQuantum InformationNonlinear DynamicsAtomic, Molecular & Optical

INTERNAL TIME OF A MECHANICAL SYSTEM

One of the most urgent unsolved problems of modern science is the extension of the second law of thermodynamics to conservative mechanical systems that are in a state far from thermodynamic equilibrium. How does the collective motion of the material points of the system, each of which is described by time-reversible equations, become irreversible? Thus, the increase in entropy of an ideal gas in a state close to equilibrium indicates the irreversible nature of the evolution of a conservative mechanical system, which is definitely an ideal gas. That is, entropy acts as internal time and sets the direction to the future or the "arrow of time". The paper deals with obtaining a characteristic of a conservative mechanical system that would have the properties of entropy. The goal is to extend the second law of thermodynamics to conservative mechanical systems that are in a state far from equilibrium. Analytical methods were used to analyze the differential equations of motion of a phase liquid particle as an image of a mechanical system in a multidimensional space. The evolution of the distribution of the probability of a particle of a phase fluid staying on a hypersurface of equal energy is considered. For a conservative mechanical system, a value is introduced whose properties allow us to apply the term "internal time" to it. Its growth determines the difference between future events and past events, which is an inherent property of subjective time. When approaching the state of equilibrium, internal time slows down, and physical time, accordingly, accelerates relative to internal time. Internal time is as universal as physical time, in the sense that it is determined for each system by a universal formula. The proposed approach made it possible to solve the fundamental problem of replacing the averaging of the probability density in the phase space by averaging in time along the trajectory of the point in the phase space. We used the fact that the equation of motion of a conservative system can be obtained as the equation of motion of a particle of a phase liquid, using the law of conservation of matter. The equations of motion of a particle were transferred to the motion of a point. In contrast, when using the traditional approach, the equation of motion of a point in phase space was taken as the basic law of nature. An understanding of internal time allows us understand the emergence of dissipative structures in the future.

Husimi Dynamics Generated by non-Hermitian Hamiltonians.

The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics for generic initial states shows surprising features. Here we analyze the dynamics of the Husimi distribution in a semiclassical limit, illuminating the foundations of the full quantum evolution. The classical Husimi evolution is composed of two factors: (i)the initial Husimi distribution evaluated along phase-space trajectories and (ii)the final value of the norm corresponding to each phase-space point. Both factors conspire to lead to intriguing dynamical behaviors. We demonstrate how the full quantum dynamics unfolds on top of the classical Husimi dynamics for two instructive examples.

Brief review of the development of theories of robustness, roughness and bifurcations of dynamic systems

The development issues of theories of robustness, roughness and bifurcations of dynamic systems are considered. In the modern theory of dynamic systems and automatic control systems, researches of the properties of roughness and robustness of systems are becoming more and more important. The work considers methods of research and ensuring robust stability of interval dynamic systems of both algebraic and frequency directions of robust stability. The main results of the original algebraic method of robust stability for continuous and discrete time are given. In the frequency direction of robust stability, the issues of a frequency-robust method to the analysis and synthesis of robust multidimensional control systems based on the use of the frequency condition number of the transfer matrix of the “input-output” ratio are considered. The main provisions of the theory and method of topological roughness of dynamic systems based on the concept of roughness according to Andronov-Pontryagin are presented with the introduction of a measure of roughness of systems in the form of a condition number of matrices of reduction to a diagonal (quasi-diagonal) basis at special points of phase space. Criteria for dynamic systems bifurcations are formulated. Applications of the topological roughness method to synergetic systems and chaos have been used to investigate many systems, such as Lorenz and Rössler attractors, Belousov-Jabotinsky, Chua systems, “predator-prey” and “predator-prey-food”, Hopf bifurcation, Schumpeter and Caldor economic systems, Henon mapping, and others. For research of weakly formalized and non-formalized systems, the use of the approach of analogies of theoretical-multiple topology and the abstract method to such systems is proposed. Further research suggests the development of roughness and bifurcation theories for complex nonlinear dynamical systems.

Qubit control using quantum Zeno effect: Action principle approach

We employ the stochastic path-integral formalism and action principle for continuous quantum measurements – the Chantasri–Dressel–Jordan (CDJ) action formalism Chantasri et al., (2013; 2015) – to understand the stages in which quantum Zeno effect helps control the states of a simple quantum system. The detailed dynamics of a driven two-level system subjected to repeated measurements unravels a myriad of phases, so to say. When the detection frequency is smaller than the Rabi frequency, the oscillations slow down, eventually coming to a halt at an interesting resonance when measurements are spaced exactly by the time of transition between the two states. On the other hand, in the limit of large number of repeated measurements, the dynamics organizes itself in a rather interesting way about two hyperbolic points in phase space whose stable and unstable directions are reversed. Thus, the phase space flow occurs from one hyperbolic point to another, in different ways organized around the separatrices. We believe that the systematic treatment presented here paves the way for a better and clearer understanding of quantum Zeno effect in the context of quantum error correction.

Using chaotic dynamics to characterize the complexity of rough surfaces.

In this work, we use the basic ingredients of chaotic dynamics (stretching and folding of phase space points) for the characterization of the complexity of microscopy images of rough surfaces. The key idea is to use an image as the initial condition of a chaotic discrete dynamical system, such as the Arnold cat map, and track its transformations during the first iterations of the map. Since the basic effects of the Arnold map are the stretching and folding of image texture, the application of the map leads to an enhancement of the high frequency content of images along with an increase of discontinuities in pixel intensities. We exploit these effects to quantify the complexity of S type (lying between homogeneity and randomness) of the image texture since the first (enhancement of high frequencies) can be used to quantify the distance of texture from randomness and noise and the second (the proliferation of discontinuities) the distance from order and homogeneity. The method is validated in synthetic images which are generated from computer generated surfaces with controlled correlation length and fractal dimension and it is applied in real images of nanostructured surfaces obtained from a scanning electron microscope with very interesting results.