Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

Linear numerical calculation method for obtaining critical point,pore fluid,and framework parameters of gas-bearing media

Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, pore fluid-related parameters, or framework-related parameters. So in this article, we provide a method for calculating these elastic parameters and use this method to analyze gas-bearing samples. We first derive three linear equations for numerical calculations. They are the equation of density p versus porosity Ф, density times the square of compressional wave velocity p Vp^2 versus porosity, and density times the square of shear wave velocity pVs^2 versus porosity. Here porosity is viewed as an independent variable and the other parameters are dependent variables. We elaborate on the calculation steps and provide some notes. Then we use our method to analyze gas-bearing sandstone samples. In the calculations, density and P- and S-velocities are input data and we calculate eleven relative parameters for porous fluid, framework, and critical point. In the end, by comparing our results with experiment measurements, we prove the viability of the method.

SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.

Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC： an overview

Fluctuations of conserved quantities, such as baryon, electric charge, and strangeness number, are sensitive observables in relativistic heavy-ion collisions to probe the QCD phase transition and search for the QCD critical point. In this paper, we review the experimental measurements of the cumulants(up to fourth order) of event-byevent net-proton(proxy for net-baryon), net-charge and netkaon(proxy for net-strangeness) multiplicity distributions Au+Au collisions at sNN^(1/2) 7:7; 11:5; 14:5; 19:6; 27;39; 62:4; 200 Ge V from the first phase of beam energy scan program at the relativistic heavy-ion collider(RHIC). We also summarize the data analysis methods of suppressing the volume fluctuations, auto-correlations, and the unified description of efficiency correction and error estimation.Based on theoretical and model calculations, we will discuss the characteristic signatures of critical point as well as backgrounds for the fluctuation observables in heavy-ion collisions. The physics implications and the future secondphase of the beam energy scan(2019–2020) at RHIC will also be discussed.

NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.

ASYMPTOTIC EXPANSION OF DIRAC-TYPE DISTRIBUTION ASSOCIATED WITH A CLASS OF HYPERSURFACES WITH DEGENERATED CRITICAL POINTS

In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.

Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach

The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pioneer as well as in more recent literature to exhibit all kinds of distinct critical points. Its response is thoroughly discussed, the effect of all parameters involved is extensively examined, including imperfection sensitivity, and the results obtained lead to the important conclusion that the model is possibly associated with the butterfly singularity, a fact which will be validated by the contents of a companion paper, based on catastrophe theory.

Distinction between critical current effects and intrinsic anomalies in the point-contact Andreev reflection spectra of unconventional superconductors

In this work,we discuss the origin of several anomalies present in the point-contact Andreev reflection spectra of（Li1-xFex）OHFeSe,LiTi2O4,and La2-xCexCuO4.While these features are similar to those stemming from intrinsic superconducting properties,such as Andreev reflection,electron-boson coupling,multigap superconductivity,d-wave and p-wave pairing symmetry,they cannot be accounted for by the modified Blonder–Tinkham–Klapwijk（BTK） model,but require to consider critical current effects arising from the junction geometry.Our results point to the importance of tracking the evolution of the dips and peaks in the differential conductance as a function of the bias voltage,in order to correctly deduce the properties of the superconducting state.

Experimental research on critical point hy- pothesis

According to the critical point hypothesis (CPH), energy release would accelerate in power law before occurrence of large earthquakes or failure of brittle materials. In the paper, CPH was studied by acoustic emission experiments of large-scale rock samples. Three kinds of rock samples were used in the experiments. The tri-axial loading con- dition was applied under different loading histories. The released elastic energy (Acoustic emission) was recorded with acoustic emission technique as microcracks emerged and developed inside the rock samples. The experimen- tal results gave a further verification on the CPH. The elastic energy release of rock samples would accelerate be- fore the failure even under different experimental conditions. Primary studies were also made on medium-term earthquake prediction by using accelerating energy release (AER) in the paper.

BIFURCATION PROBLEM OF CRITICAL POINTSFOR QUADRATIC DIFFERENTIAL SYSTEMS

In this paper foe bifurcation of critical points for the quadratic systems of type(II)and (III) is investigated. and an answer to the problem given in[1] is given.

ON THE CRITICAL POINTS OF THE MAP F_p:X→‖AXB-C‖_p^p

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.

Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator

One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.

Dynamical signatures of the one-dimensional deconfined quantum critical point

We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.

Signature of Critical Point in Momentum Profile of Trapped Ultracold Bose Gases

We present a new method to identify the critical point for the Bose-Einstein condensation （BEC） of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature, and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point. More importantly, the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point, which can be used to determine the critical temperature. These predictions are also confirmed by our BEC experiment for magnetically trapped ST Rb gases.

ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.

Critical point quantities and integrability conditions for a class of quintic systems

For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given. The technique employed is essentially different from usual ones. The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations. Some results show an interesting contrast with the related results on quadratic systems.

Limit Cycle Containing Nine Critical Points in its Interior for a Class of Cubic Systems

Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.

Analysis of Microbial Contamination Factors and Critical Control Points in the Process of Hog Slaughter and Production

In order to provide a reference for the further study of microbial contamination in the pork production process. Microbial contamination of pigs came from three slaughterhouses were detected, and critical control points in the progress of hog slaughter and processing were analyzed. The results showed that microbial con- taminatian existed in the entire slaughter and processing progress, including shower and assassination bloodletting, separation of the internal organs, chopping boards, workshop environment, personal hygiene of the operators, etc. , which should be paid more attention to. The results indicated that reasonable protection measures should be carried out, disinfection awareness of the operators should be improved, and regular disinfection should be ruled under the condition of continu- ous operation.

Quark Number Susceptibility around the Chiral Critical End Point

We calculate the quark number susceptibility （QNS） around the chiral critical end point （CEP）. The CEP is found to be located at （μc,Tc）= （80 MeV, 148 MeV） where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60MeV≤ μ ≤ 110MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.

On Properties of p-critical Points of Convex Bodies

Properties of the p-measures of asymmetry and the corresponding affine equivariant p-critical points, defined recently by the second author, for convex bodies are discussed in this article. In particular, the continuity of p-critical points with respect to p on （1, ＋∞） is confirmed, and the connections between general p-critical points and the Minkowski-critical points （∞-critical points） are investigated. The behavior of p-critical points of convex bodies approximating a convex bodies is studied as well.