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.

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.

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 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.

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.

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.

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.

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.

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.

Emergent symmetry in quantum phase transition:From deconfined quantum critical point to gapless quantum spin liquid

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena,i.e.,the deconfined quantum critical point(DQCP)and the quantum spin liquid(QSL)state.Via large-scale tensor network simulations,we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic(AFM)model,namely the J1x-J1y-J2 model,which contains anisotropic nearestneighbor couplings J1x,J1y and the next nearest neighbor coupling J2.For small J1y/J1x,by tuning J2,a direct continuous transition between the AFM and valence bond solid phase is observed.With growing J1y/J1x,a gapless QSL phase gradually emerges between the AFM and VBS phases.We observe an emergent O(4)symmetry along the AFM–VBS transition line,which is consistent with the prediction of DQCP theory.Most surprisingly,we find that such an emergent O(4)symmetry holds for the whole QSL–VBS transition line as well.These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view,and strongly constrain the quantum field theory description of the QSL phase.The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.

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.

An Analytic Equation of State Based on SAFT-CP for Binary Non-Polar Alkane Mixtures Across the Critical Point

The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.

Critical point symmetry for odd-odd nuclei and collective multiple chiral doublet bands

A critical point symmetry(CPS) for odd-odd nuclei is built in the core-particle coupling scheme with the even-even core assumed to follow the spherical to triaxially deformed shape phase transition. It is shown that the model Hamiltonian can be approximately solved with the solutions being expressed in terms of the Bessel functions of irrational orders. In particular, the CPS predicts that collective multiple chiral doublets may exist in transitional odd-odd systems.

Search for QCD critical point by transverse velocity dependence of anti-deuteron to deuteron ratio

We propose the transverse velocity(β_T) dependence of the anti-deuteron to deuteron ratio as a new observable to search for the QCD critical point in heavy-ion collisions.The QCD critical point can attract the system evolution trajectory in the QCD phase diagram,which is known as the focusing effect.To quantify this effect,we employ the thermal and hadronic transport model to simulate the dynamical particle emission along a hypothetical focusing trajectory near the critical point.We found that the focusing effect can lead to anomalous β_T dependence on ■/p,■/d and ■/~3 He ratios.We examined the β_T dependence of ■/p and ■/d ratios of central Au+Au collisions at ■=7.7 to 200 GeV measured by the STAR experiment at RHIC.Surprisingly,we only observe a negative slope in β_T dependence of ■/d ratio at ■=19.6 GeV,which indicates the trajectory evolution has passed through the critical region.In the future,we could constrain the location of the critical point and/or width of the critical region by conducting precise measurements on the β_T dependence of the ■/d ratio at different energies and rapidity.

Three Solutions of p-Laplacian Equations Via a Critical Point Theorem of Ricceri

In this paper,we consider the following quasilinear diferential equation（p（u′））′＋λf（t,u）=0subject to one of the two boundary conditions：u（0）=u′（1）=0,u′（0）=u（1）=0.After transforming them into a problem of symmetrical solutions,the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri.An example is given to demonstrate our main result.

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.