Location Of Critical Point Research Articles

Detecting Quantum Topologic Phase Transitions Through The C-Function

Topological Quantum Field Theory or TQFT is a quantum field theory that calculates topological invariance in measurement theory and mathematical physics. In recent years, several attempts have been made to find efficient observations to determine the TQFT of quasiparticle properties. In this paper, we propose a different and very effective way to detect the critical points of TQFT by considering the system functions. We suggest the C-Function as a novel probe that is accurate for detecting the location of critical points on topological quantum. The C-function uses a holographic model to show a topological quantum phase transition between a simple topological isolation phase and a gapless Weyl semimetal. The quantum tipping point displays a strong Lifshitz-like anisotropy in the spatial direction, and a quantum phase transition that does not follow the standard Landau paradigm. The C-function precisely shows the global features of quantum criticality and distinguishes very accurately between two separate zero-temperature phases. Considering the C-function relationship with entanglement entropy can detect quantum phase transitions and can be applied outside the holographic framework.
 Keywords: quantum topologic, phase transitions, c-function

The effect of smooth parametrizations on nonconvex optimization landscapes

AbstractWe develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good guarantees) or for theoretical purposes (e.g., to reveal that the landscape satisfies a strict saddle property). In both cases, the central question is: how do the landscapes of the two problems relate? More precisely: how do desirable points such as local minima and critical points in one problem relate to those in the other problem? A key finding in this paper is that these relations are often determined by the parametrization itself, and are almost entirely independent of the cost function. Accordingly, we introduce a general framework to study parametrizations by their effect on landscapes. The framework enables us to obtain new guarantees for an array of problems, some of which were previously treated on a case-by-case basis in the literature. Applications include: optimizing low-rank matrices and tensors through factorizations; solving semidefinite programs via the Burer–Monteiro approach; training neural networks by optimizing their weights and biases; and quotienting out symmetries.

Mapping the critical equation of state by resummations

Determining the existence and the location of the QCD critical point remains a major goal in the heavy-ion collision experiments. A crucial theoretical input for achieving this goal is mapping the QCD equation of state in the presence of baryon chemical potential (μ) which at the moment is limited to small values of μ, away from the critical point. We present a new framework for reconstructing the equation of state from a truncated Taylor series expansion for small μ by using novel resummation techniques. We show how this resummation method can be used to (i) determine the location of the critical point and (ii) constrain the form of the critical contribution to the QCD equation of state which has a direct impact on the shape of the experimental signatures of the critical point. Using the recent lattice data from the HotQCD collaboration we estimate that Tc ≈ 100 MeV, μc ≈ 580 MeV, the crossover slope at the critical point α1 ≈ 9°, and further constrain the non-universal mapping parameters between the Ising model and QCD (scaling) equations of state.

QCD at finite temperature and density: Criticality

We overview recent theoretical developments in the search for QCD critical point at finite temperature and density, including from lattice QCD, effective QCD theories, and proton number cumulants in heavy-ion collisions. We summarize the available constraints and predictions for the critical point location and discuss future challenges and opportunities.

Location of the QCD critical point predicted by holographic Bayesian analysis

We present results for a Bayesian analysis of the location of the QCD critical point constrained by first-principles lattice QCD results at zero baryon density. We employ a holographic Einstein-Maxwell-dilaton model of the QCD equation of state, capable of reproducing the latest lattice QCD results at zero and finite baryon chemical potential. Our analysis is carried out for two different parametrizations of this model, resulting in confidence intervals for the critical point location that overlap at one sigma. While samples of the prior distribution may not even predict a critical point, or produce critical points spread around a large region of the phase diagram, posterior samples nearly always present a critical point at chemical potentials of μBc ∼ 550 − 630 MeV.

Bi-circular model with test particle variable mass

This paper presents the effects of the perturbations on the motion of the test particle variable mass in the bi-circular Sun perturbed oblate Earth-Moon system where primary is taken as oblate Earth, secondary is taken as Moon and the third body is assumed as Sun. These three bodies are moving in the same plane around barycenter. The fourth and smallest body (test particle is assumed to be having variable mass with time) is moving in the space under the perturbations such as gravitational forces of the primaries, the solar radiation pressure, the coriolis and centrifugal forces. Then we determine the equations of motion, the locations of critical points, their stability and periodic orbits.

A new approach for correlating Paris parameters with fatigue life of aircraft fuselage panels

This work presents a numerical technique that establishes a relationship between the C and m parameters of the Paris Law and the number of fatigue life cycles. This relationship is particularly important for determining the material's ability to withstand a specified number of cycles in an aircraft fuselage design. The methodology is based on a multiscale problem and comprises two stages: the macro model, which focuses on internal stresses and critical point location, and the micro model, which considers the critical fatigue life cycle number (n) across a "grid" of C and m parameters, resulting in the optimal curve N(C,m). To validate the adopted methodology, the academic program BemCracker2D has been used to calculate the internal stress fields, simulate cracks, and estimate fatigue life. Three case studies were conducted, and the results indicated that the range of C and m values obtained depends on the configuration of the macro model, the physical parameters of the material, and the defined number of cycles in the design. Ultimately, this computational technique allows for generalization to any fuselage damage analysis model, providing C and m Paris parameter data to mitigate fatigue damage.

Physical analysis of Rastall PFRF black hole through accretion process

The adiabatic accretion onto the charged black hole surrounded by perfect fluid radiation field (PFRF) in Rastall gravity is addressed in this manuscript. For this purpose, mass accretion rate M˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{M}$$\\end{document}, critical horizon radius and some other flow parameters are being determined in the presence of polytropic fluid. Overall the process is being done analytically. The location of critical points, polytropic gas compression ratios and temperature profiles are also being investigated for different versions of polytropic equation of state. We also give the comparison of the location of critical points with case of Schwarzschild black hole in which critical points lies out side the horizon. Through above scenario, it is found that charge Q and Rastall parameter Nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{r}$$\\end{document} have deep effects on the accretion process. It is also mentioned here that under some constraints on parameters, our results reduce to Schwarzschild and charged black holes results.

Machine learning renormalization group for statistical physics

We develop a machine-learning renormalization group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the c-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

Nuclear Shape-Phase Transition From Spherical U(5) to Deformed gamma-Unstable O(6) Dynamical Symmetries of Interacting Boson Model Applied to Ru, Pd, and Xe Isotopic Chains

The shape transition from spherical vibrator U(5) to gamma-unstable deformed rotor O(6) in even-even Ru, Pd, and Xe isotopic chains are studied in framework of sd interacting boson model (IBM1) using the coherent state formalism to obtain the potential energy surfaces (PES’s). The location of critical points in the transition are identified by analysis the PES’s in terms of the deformation parameter beta and by using the catastrophe theory in terms of the two essential parameters (r_1, r_2). By using the most general IBM1 Hamiltonian in Casimir form with neglecting the U(5) and SU(3) quadratic Casimir operators and introducing only one control parameter the PES leads to the same energy surface as the Q-consistent IBM Hamiltonian at gamma =0. For the studied isotopic chains, the chi ^2-test is used to perform the fitting between the experimental and the corresponding calculated IBM for some selected energy levels and electric quadrupole transition probabilities B(E2) values using a simulated search program. A good agreement is produced for both energies and B(E2) transition rates. The present model calculations suggest that ^{100}Ru, ^{102}Pd and ^{130}Xe nuclei are good candidates for the E(5) critical point symmetry.

Three-dimensional critical points and flow patterns in pulmonary alveoli with rhythmic wall motion

The dynamics of airflow in the pulmonary acini are of broad interest in understanding respiratory diseases and the fate of inhaled particles. This study investigates the three-dimensional (3d) alveolar flows with rhythmic cavity wall motion, using a finite element method based computational fluid dynamics. This study reports the new research findings on the critical points and associated flow patterns. The locations of critical points are found based on the Brouwer degree theory and Broyden’s method. The phase portrait is used to evaluate the flow patterns around the critical points and the stability (repelling/attracting property) of the critical points on the symmetry plane of the alveolus. Based on the Poincare–Bendixson theorem, the closed orbits on the symmetry plane are found which have the capability to alter the spiral direction of the spiral streamlines. In the 3d space, the alveolar flow is symmetric about the geometric symmetry plane of the alveolus. Different types of 3d critical points, including saddle, spiral, and spiral saddle, are revealed. There are only one saddle point and at least one spiral point or spiral saddle in the alveolar flow. Spiral points and spiral saddles are located on the vortex core line and their number is dependent on the Reynolds number and varies with time. The study of critical points and their evolution helps us to understand the mechanism of irreversible transport of particle tracers from a new perspective.

The escape transition in a self-avoiding walk model of linear polymers

A linear polymer grafted to a hard wall and underneath an atomic force microscopy tip can be modeled in a lattice as a grafted lattice polymer (self-avoiding walk) compressed underneath a piston near the wall. As the piston approaches the wall the increasingly confined polymer escapes from the confined region to explore conformations beside the piston. This conformational change is believed to be a phase transition in the thermodynamic limit, and has been argued to be first order, based on numerical results in the literature. In this paper a lattice self-avoiding walk model of the escape transition is constructed. It is proven that this model has a critical point in the thermodynamic limit corresponding to the escape transition of compressed grafted linear polymers. This result relies on the analysis of self-avoiding walks in slits and slabs in the square and cubic lattices. Additionally, numerical estimates of the location of the escape transition critical point is reported based on Monte Carlo simulations of self-avoiding walks in slits and in slabs.

Deciphering Methylation Effects on S2(ππ*) Internal Conversion in the Simplest Linear α,β-Unsaturated Carbonyl.

Chemical substituents can influence photodynamics by altering the location of critical points and the topography of the potential energy surfaces (electronic effect) and by selectively modifying the inertia of specific nuclear modes (inertial effects). Using nonadiabatic dynamics simulations, we investigate the impact of methylation on S2(ππ*) internal conversion in acrolein, the simplest linear α,β-unsaturated carbonyl. Consistent with time constants reported in a previous time-resolved photoelectron spectroscopy study, S2 → S1 deactivation occurs on an ultrafast time scale (∼50 fs). However, our simulations do not corroborate the sequential decay model used to fit the experiment. Instead, upon reaching the S1 state, the wavepacket bifurcates: a portion undergoes ballistic S1 → S0 deactivation (∼90 fs) mediated by fast bond-length alternation motion, while the remaining decays on the picosecond time scale. Our analysis reveals that methyl substitution, generally assumed to mainly exert inertial influence, is also manifested in important electronic effects due to its weak electron-donating ability. While methylation at the β C atom gives rise to effects principally of an inertial nature, such as retarding the twisting motion of the terminal -CHCH3 group and increasing its coupling with pyramidalization, methylation at the α or carbonyl C atom modifies the potential energy surfaces in a way that also contributes to altering the late S1-decay behavior. Specifically, our results suggest that the observed slowing of the picosecond component upon α-methylation is a consequence of a tighter surface and reduced amplitude along the central pyramidalization, effectively restricting the access to the S1/S0-intersection seam. Our work offers new insight into the S2(ππ*) internal conversion mechanisms in acrolein and its methylated derivatives and highlights site-selective methylation as a tuning knob to manipulate photochemical reactions.

Hamming distance and the onset of quantum criticality

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Our approach charts a path to circumvent inherent limitations imposed by the SP, allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations.

Multi-task super resolution method for vector field critical points enhancement

<p>It is a challenging task to handle the vector field visualization <span style="font-family: 'Times New Roman';">at</span> local critical points. Generally, topological based methods firstly divide critical regions into different categories, and then process the different types of critical regions to improve the effect, which pipeline is complex. In the paper, a learning based multi-task super resolution (SR) method is proposed to improve the refinement of vector field, and enhance the visualization effect, especially at the critical region. In detail, the multi-task model consists of two important <span style="font-family: 'Times New Roman';">des</span>igns on task branches: one task is to simulate the interpolation of discrete vector fields based on an improved super-resolution network; and the other is a classification task to identify the types of critical vector fields. It is an efficient end-to-end architecture for both training and inferencing stages, which simplifies the pipeline of critical vector field visualization and improves the visualization effect. In experiment, we compare our method with both traditional interpolation and pure SR network on both simulation data and real data, and the reported results indicate our method lower the error and improve PSNR significantly.</p>

Multi-task super resolution method for vector field critical points enhancement

<p>It is a challenging task to handle the vector field visualization <span style="font-family: 'Times New Roman';">at</span> local critical points. Generally, topological based methods firstly divide critical regions into different categories, and then process the different types of critical regions to improve the effect, which pipeline is complex. In the paper, a learning based multi-task super resolution (SR) method is proposed to improve the refinement of vector field, and enhance the visualization effect, especially at the critical region. In detail, the multi-task model consists of two important <span style="font-family: 'Times New Roman';">des</span>igns on task branches: one task is to simulate the interpolation of discrete vector fields based on an improved super-resolution network; and the other is a classification task to identify the types of critical vector fields. It is an efficient end-to-end architecture for both training and inferencing stages, which simplifies the pipeline of critical vector field visualization and improves the visualization effect. In experiment, we compare our method with both traditional interpolation and pure SR network on both simulation data and real data, and the reported results indicate our method lower the error and improve PSNR significantly.</p>

Three studies in high-Tc cuprates

We investigate three fundamental issues in the physics of high-Tc cuprates, from the perspective of a recently proposed comprehensive theory for these materials. (a) Orbital ordering × superconductivity. The first issue is the detailed microscopic mechanism that produces an attractive interaction between holes in high-Tc cuprates. (b) Dispersion relation × pseudogap order parameter. The second issue refers to the existence of a pseudogap order parameter, which would be different from zero all over the pseudogap phase and would vanish elsewhere. (c) Chemical potential × quantum critical point location. The third issue concerns the debate as to whether the quantum critical point, located where the pseudogap transition line T*(x) meets the T = 0 axis is inside the superconducting dome or at its boundary. We obtain clearcut solutions for the three issues.

Topological phases and entanglement in real space for 1D SSH topological insulator: effects of first and second neighbor-hoppings

The hybrid atoms-cell site entanglement in a one-dimensional Su-Schrieffer-Heeger (SSH) topological insulator with first and second neighbor hopping in space representation of finite chains is analyzed. The geometrical phase is calculated by the Resta electric polarization and the entanglement in the atomic basis by the Schmidt number. A relation between entanglement and the topological phase transitions (TPT) is given since the Schmidt number has local critical points of maximal entangled (ME) states in the singularities of the geometrical phase. States with second neighbors have higher entanglement than first-neighbors hopping. The general conditions to produce ME hybrid Bell states and the localization-entanglement relation are given.

Uniform Ray Description of Physical Optics Scattering by Finite Locally Periodic Metasurfaces

This article presents a uniform ray description of electromagnetic wave scattering by locally periodic metasurfaces of polygonal shape. The model is derived by asymptotically evaluating the critical-point contributions of a physical optics (PO) scattering integral. It is valid for metasurfaces whose bulk scattering coefficients are periodic functions of a phase parameter, which, in turn, is a continuous and smooth function of surface coordinates. The scattered field is expressed in terms of reflected, transmitted, and diffracted rays that do not generally obey conventional geometrical constraints (i.e., Snell’s law and the Keller cone). An iterative technique is presented to determine the locations of critical points on one or multiple interacting metasurfaces. Numerical results demonstrating the utility and accuracy of the asymptotic PO model are also provided.

A parallel high-precision critical point detection and location for large-scale 3D flow field on the GPU

A parallel high-precision critical point detection and location for large-scale 3D flow field on the GPU