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.

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.

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.

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.

QUALITATIVE THEORY OF THE KUKLES SYSTEMS:(Ⅰ) NUMBER OF CRITICAL POINTS

We study the global qualitative properties of the well-known Kukles systems (1) below. Firstly, the number of critical points in case (1) has a center or a fine focus.

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.

Variational quantum simulation of the quantum critical regime

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.

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.

ON A BI-HARMONIC EQUATION INVOLVING CRITICAL EXPONENT: EXISTENCE AND MULTIPLICITY RESULTS

In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is a smooth domain in R n , n 5, and p ＋ 1 = 2 n n 4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.

EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A HARMONIC EQUATION WITH CRITICAL NONLINEARITY

This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).

On a Heuristic Point of View about the Generalization of Curie Law to Cosmic Higgs Fields with the Casimir Effect

Condensed state physics demonstrates that the Curie temperature is the point at which spontaneous magnetization drops to zero, marking the critical transition where ferromagnetic or ferrimagnetic materials transform into paramagnetic substances. Below the Curie temperature, a material remains ferromagnetic;above it, the material becomes paramagnetic, with its magnetic field easily influenced by external magnetic fileds. For example, the Curie temperature of iron (Fe) is 1043 K, while that of neodymium magnets ranges from 583 to 673 K. From both physics and mathematics perspectives, examining the temperature properties of materials is essential, as it provides valuable insights into their electromagnetic and thermodynamic behaviors. This paper makes a bold assumption and, for the first time, carefully verifies the existence of a Casimir temperature at 0.00206 K under conditions of one-atomic spacing.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

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.

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.

Study on Critical Properties for CO_2+Cosolvent Binary System and Ternary System

The performance of supercritical fluid (SCF) as a solvent can be greatly affected by addition of anentrainer to the system. In this study, a constant volume visual method is used to measure the critical point ofCO2+n-butyraldehyde, CO2+ i-butyraldehyde and CO2+alcohol binary systems and CO2+entrainer+trisodiumsalt of tri-(m-sulfonphenyl)phosphine (TPPTS) ternary systems, which provides us good theoretical basis for super-critical extraction and chemical reaction. The relationship between critical point and concentration of the entrainerare discussed. The phase behavior of binary system and that of ternary system are compared. The relationshipbetween the concentration of TPPTS and critical point of binary systems are also discussed.

A numerical study of fluid injection and mixing under near-critical conditions

Nitrogen injection under conditions close vicinity of the liquid-gas critical point is studied numerically. The fluid thermodynamic and transport properties vary drasti- cally and exhibit anomalies in the near-critical regime. These anomalies can cause distinctive effects on heat-transfer and fluid-flow characteristics. To focus on the influence of ther- modynamics on the flow field, a relatively low injection Reynolds number of 1 750 is adopted. For comparisons, a reference case with the same configuration and Reynolds number is simulated in the ideal gas regime. The model accommodates full conservation laws, real-fluid thermody- namic and transport phenomena. Results reveal that the flow features of the near-critical fluid jet are significantly differ- ent from their counterpart. The near-critical fluid jet spreads faster and mixes more efficiently with the ambient fluid along with a more rapidly development of the vortex pairing pro- cess. Detailed analysis at different streamwise locations in- cluding both the flat shear-layer region and fully developed vortex region reveals the important effect of volume dilata- tion and baroclinic torque in the near-critical fluid case. The former disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing pro- cess

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.

EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.