Critical Point Of Phase Transition Research Articles

Pattern formation of Brusselator in the reaction-diffusion system

<p style='text-indent:20px;'>Time delay profoundly impacts reaction-diffusion systems, which has been considered in many areas, especially infectious diseases, neurodynamics, and chemistry. This paper aims to investigate the pattern dynamics of the reaction-diffusion model with time delay. We obtain the condition in which the system induced the Hopf bifurcation and Turing instability as the parameter of the diffusion term and time delay changed. Meanwhile, the amplitude equation of the reaction-diffusion system with time delay is also derived based on the Friedholm solvability condition and the multi-scale analysis method near the critical point of phase transition. We discussed the stability of the amplitude equation. Theoretical results demonstrate that the delay can induce rich pattern dynamics in the Brusselator reaction-diffusion system, such as strip and hexagonal patterns. It is evident that time delay causes steady-state changes in the spatial pattern under certain conditions but does not cause changes in pattern selection under certain conditions. However, diffusion and delayed feedback affect pattern formation and pattern selection. This paper provides a feasible method to study reaction-diffusion systems with time delay and the development of the amplitude equation. The numerical simulation well verifies and supports the theoretical results.</p>

Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty

We develop the neural network based “learning from regression uncertainty” approach for the automatic detection of phases of matter in nonequilibrium active systems. Taking the flocking phase transition of self-propelled active particles described by the Vicsek model for example, we find that after training a neural network for solving the inverse statistical problem, i.e. for performing the regression task of reconstructing the noise level from given samples of such a nonequilibrium many-body complex system’s steady state configurations, the uncertainty of regression results obtained by the well-trained network can actually be utilized to reveal possible phase transitions in the system under study. The noise level dependence of regression uncertainty is assumed to be in a non-trivial M-shape, and its valley appears at the critical point of the flocking phase transition. By directly comparing this regression-based approach with the widely-used classification-based “learning by confusion” and “learning with blanking” approaches, we show that our approach has practical effectiveness, efficiency, good generality for various physical systems across interdisciplinary fields, and a greater possibility of being interpretable via conventional notions of physics. These approaches can complement each other to serve as a promising generic toolbox for investigating rich critical phenomena and providing data-driven evidence on the existence of various phase transitions, especially for those complex scenarios associated with first-order phase transitions or nonequilibrium active systems where traditional research methods in physics could face difficulties.

Bifunctional sensing based on an exceptional point with bilayer metasurfaces.

Exceptional points (EPs), the critical phase transition points of non-Hermitian parity-time (PT) systems, exhibit many novel physical properties and associated applications, such as ultra-sensitive detection of perturbations. Here, a bilayer metasurface with two orthogonally oriented split-ring resonators (SRRs) is proposed and a phase transition of the eigenpolarization states is introduced via changing the conductivity of vanadium dioxide (VO2) patch integrated into the gap of one SRR. The metasurface possesses a passive PT symmetry and an EP in polarization space is observed at a certain conductivity of the VO2. Two sensing schemes with the metasurface are proposed to achieve high-sensitivity sensing of temperature and refractive index in the terahertz (THz) range. The metasurface is promising for applications in THz biosensing and polarization manipulation.

Critical quantum sensing based on the Jaynes-Cummings model with a squeezing drive

Quantum sensing improves the accuracy of measurements of relevant parameters by exploiting the unique properties of quantum systems. The divergent susceptibility of physical systems near a critical point for quantum phase transition enables criticality-enhanced quantum sensing. The quantum Rabi model (QRM), composed of a single qubit coupled to a single bosonic field, represents a good candidate for realizing such critical enhancement for its simplicity, but it is experimentally challenging to achieve the ultrastrong qubit-field coupling required to realize the critical phenomena. In this work, we explore an alternative to construct the analog of the QRM for the sensing, exploiting the criticality appearing in the Jaynes-Cummings (JC) model whose bosonic field is parametrically driven, not necessitating the ultrastrong coupling condition, thus to some extent relaxing the requirement for practical implementation.

Universal characteristics of one-dimensional non-Hermitian superconductors

We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone. The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points. If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be the Z 2 skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitian p- and s-wave topological superconductors. In terms of Majorana Pfaffian, a Z 2 non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence for the non-Hermitian topological superconductors.

Quantum thermometry with a dissipative quantum Rabi system

Dissipative quantum Rabi system, a finite-component system composed of a single two-level atom interacting with an optical cavity field mode, exhibits a quantum phase transition, which can be exploited to greatly enhance the estimation precision of unitary parameters (frequency and coupling strength). Here, using the quantum Langevin equation, standard mean field theory and adiabatic elimination, we investigate the quantum thermometry of a thermal bath surrounding the atom with quantum optical probes. With the increase in coupling strength between the atom and the cavity field, two kinds of singularities can be observed. One type of singularity is the critical point (CP) of phase transition from the normal to superradiant phase. The other type of singularity is the exceptional point (EP) in the anti-parity-time (anti-\(\mathcal{P}\mathcal{T}\)) symmetrical cavity field. In many previous jobs, the optimal measurement precision can appear around EPs. However, we show that the optimal measurement precision occurs at the CP, instead of the EP. And the direct photon detection represents an excellent proxy for the optimal measurement near the CP. In the case where the thermal bath to be tested is independent of the extra thermal bath interacting with the cavity field, the estimation precision of the temperature always increases with the coupling strength. Oppositely, if the thermal bath to be tested is in equilibrium with the extra thermal bath interacting with the cavity field, noises that suppress the information of the temperature will be introduced when increasing the coupling strength unless it is close to the CP.

Finite-size correlation behavior near a critical point: A simple metric for monitoring the state of a neural network.

In this article, a correlation metric κ_{c} is proposed for the inference of the dynamical state of neuronal networks. κ_{C} is computed from the scaling of the correlation length with the size of the observation region, which shows qualitatively different behavior near and away from the critical point of a continuous phase transition. The implementation is first studied on a neuronal network model, where the results of this new metric coincide with those obtained from neuronal avalanche analysis, thus well characterizing the critical state of the network. The approach is further tested with brain optogenetic recordings in behaving mice from a publicly available database. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.

Error-mitigated deep-circuit quantum simulation of open systems: Steady state and relaxation rate problems

Deep-circuit quantum computation, like Shor's algorithm, is undermined by error accumulation, and near-future quantum techniques are far from adequate for full-fledged quantum error correction. Instead of resorting to shallow-circuit quantum algorithms, recent theoretical research suggests that digital quantum simulation (DQS) of closed quantum systems are robust against the accumulation of Trotter errors, as long as local observables are concerned. In this paper, we investigate digital quantum simulation of open quantum systems. First, we prove that the deviation in the steady state obtained from digital quantum simulation depends only on the error in a single Trotter step, which indicates that error accumulation may not be disastrous. By numerical simulation of the quantum circuits for the DQS of the dissipative XYZ model, we then show that the correct results can be recovered by quantum error mitigation as long as the error rate in the DQS is below a sharp threshold. We explain this threshold behavior by the existence of a dissipation-driven quantum phase transition. Finally, we propose a new error-mitigation technique based on the scaling behavior in the vicinity of the critical point of a quantum phase transition. Our results expand the territory of near-future available quantum algorithms and stimulate further theoretical and experimental efforts in practical quantum applications.

An Improved Optimal Routing Strategy on Scale-Free Networks

Traffic dynamics have drawn more and more attention from physical and engineering field recently. In this brief, we focus on the traffic capacity that can be measured by the critical point of phase transition from free flow to congestion, and propose a routing strategy by constructing a cost function based on the ratio of degree to closeness centrality to improve the transportation efficiency of scale-free network. The maximum node betweenness, average path length and traffic load are investigated with simulations. Moreover, load reduction rate, load mean, and load variance are introduced to analyse the traffic distribution. Remarkable improvement of traffic capacity and more even load distribution can be achieved with our strategy, which is much better than the efficient routing (ER) strategy.

Octupole shape phase transitions and critical points in neutron rich actinides

The evolution of octupole shapes and shape phase transitions in neutron rich actinides is studied within the covariant density functional framework. Octupole constrained energy surfaces, and spectroscopic observables of four isotopic chains of: Cm, Cf, Fm and No with neutron numbers 186le N le 200 are analysed using a collective quadrupole–octupole Hamiltonian (QOCH). The parameters of the Hamiltonian are determined by axially reflection-asymmetric relativistic Hartree–Bogoliubov calculations based on the energy density functional DD-PC1, and a finite-range pairing interaction. The results suggest quantum phase transitions from non-octupole to octupole deformed shapes and to octupole vibrations with increasing neutron number. ^{288}Cm is possibly close to the critical point of a simultaneous phase transition from spherical to prolate deformed and from non-octupole to stable octupole deformed configurations.

Addressing skepticism of the critical brain hypothesis.

The hypothesis that living neural networks operate near a critical phase transition point has received substantial discussion. This “criticality hypothesis” is potentially important because experiments and theory show that optimal information processing and health are associated with operating near the critical point. Despite the promise of this idea, there have been several objections to it. While earlier objections have been addressed already, the more recent critiques of Touboul and Destexhe have not yet been fully met. The purpose of this paper is to describe their objections and offer responses. Their first objection is that the well-known Brunel model for cortical networks does not display a peak in mutual information near its phase transition, in apparent contradiction to the criticality hypothesis. In response I show that it does have such a peak near the phase transition point, provided it is not strongly driven by random inputs. Their second objection is that even simple models like a coin flip can satisfy multiple criteria of criticality. This suggests that the emergent criticality claimed to exist in cortical networks is just the consequence of a random walk put through a threshold. In response I show that while such processes can produce many signatures criticality, these signatures (1) do not emerge from collective interactions, (2) do not support information processing, and (3) do not have long-range temporal correlations. Because experiments show these three features are consistently present in living neural networks, such random walk models are inadequate. Nevertheless, I conclude that these objections have been valuable for refining research questions and should always be welcomed as a part of the scientific process.

Phase transition grade and microstructure of AdS black holes in massive gravity

Considering that under the framework of the massive gravity theory, the interaction between the mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, the phase transition process caused by this scalar charge is investigated in this analysis. The phase transition grade and microstructure of those BHs are investigated from both macroscopic and microscopic points of view. From the macroscopic point of view, it is found that Ehrenfest equations are satisfied at the phase transition critical point, which implies that the phase transition grade of those BHs is second-order. Based on the BH molecules model and Landau continuous phase transition theory, the phase transition of those BHs from the microcosmic point of view is analyzed. The critical exponents obtained from the two perspectives are consistent. By investigating the Ruppeiner geometry, the microstructure feature of those BHs is revealed. These results suggest that the phase transition of BH in massive gravity is a standard second-order phase transition at the critical point, and the microscopic details of those BHs are different from the Reissner–Nordström AdS BH in standard Einstein gravity.

Robust orbital diamagnetism in correlated Dirac fermions

We study orbital diamagnetism at zero temperature in (2 + 1)-dimensional Dirac fermions with a short-range interaction which exhibits a quantum phase transition to a charge density wave (CDW) phase. We introduce orbital magnetic fields into spinless Dirac fermions on the π-flux square lattice, and analyze them by using infinite density matrix renormalization group. It is found that the diamagnetism remains intact in the Dirac semimetal regime, while it is monotonically suppressed in the CDW regime. Around the quantum critical point of the CDW phase transition, we find a scaling behavior of the diamagnetism characteristic of the chiral Ising universality class. Besides, the scaling analysis implies that the robust orbital diamagnetism at weak magnetic fields in a Dirac semimetal regime would hold not only in our model but also in other interacting Dirac fermion systems as long as scaling regions are wide enough. The scaling behavior may also be regarded as a quantum, magnetic analogue of the critical Casimir effect which has been widely studied for classical phase transitions.

Effect of volume energy density on selective laser melting NiTi shape memory alloys: microstructural evolution, mechanical and functional properties

Equi-atomic NiTi shape memory alloy (SMA) samples were manufactured by selective laser melting (SLM) with different laser volume energy densities via synchronously varying laser power and scanning speed. The processing quality, phase transformation, and microstructural evolution were investigated to explore the mechanisms that are responsible for mechanical and functional properties. The results showed scattered micro-sized spherical gaseous defects inside the deposit. One-stage phase transformation occurred without intermediate R-phase transition, and the temperature of both endothermic and exothermic peaks was lower than that of the ingot. The microstructure initially grew along the building direction, but displayed different crystal orientations between coarse columnar grains and refined irregular sub-grains. The micro-hardness mapping revealed that homogenous anti-indentation properties were acquired independent of location variations. While the anisotropic behavior in tensile properties occurred due to the passive effect of columnar B2 austenitic grains, a synergistic effect of strength and plasticity was acquired primarily due to the combined effect of sub-grain refinement strengthening and transformation-induced plasticity. The pre-deformed NiTi samples recovered to their original shape when heated above its critical phase transition point. This work demonstrated that the crack-free NiTi SMA with exceptional comprehensive performances could be fabricated by SLM through the control of energy density.

AdS Black Holes in the Framework of Nonlinear Electrodynamics, Thermodynamics, and Joule–Thomson Expansion

The thermodynamics and phase transitions of magnetic Anti-de Sitter black holes were studied. We considered extended-phase-space thermodynamics, with the cosmological constant being a thermodynamic pressure and the black hole mass being treated as a chemical enthalpy. The extended-phase-space thermodynamics of black holes mimic the behavior of a Van der Waals liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It was demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation hold. The Joule–Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of the inversion temperature are found.

The liquid–gas phase transition in a variational approach and the role of three-body force

The thermal properties of hot baryonic matter and its isospin dependence for a wide range of densities and temperatures have been investigated within the lowest order constrained variational (LOCV) approach by employing the bare two-body interaction AV18 with the inclusion of a phenomenological three-body force (3BF) UIX as well as relativistic corrections (RC). The critical temperature and the liquid–gas (LG) phase transition have been calculated with and without the inclusion of 3BF both in the LOCV and its relativistic expansion, namely (RLOCV) approach. Our results have been compared with other predictions. It turns out that the 3BF gives a repulsive contribution to the equation of state (EOS) which is stronger at higher density and as a consequence reduces the critical temperature of LG phase transition while RC has no special effect on the critical point. The temperature dependence and the isospin dependence of other physical quantities, such as the specific heat capacity, latent heat, entropy, critical exponents, symmetry free energy, incompressibility and the role of UIX 3BF on these quantities have also been studied. At a given temperature, we find a reduction in critical temperature, latent heat, critical asymmetry parameter, and incompressibility when 3BF is added to the bare interaction, while 3BF has no effect on entropy and specific heat capacity, as expected. We observed that the stiffness of density-dependence of symmetry free energy affects on the critical point of LG phase transition. Stiffer symmetry free energy has a smaller critical temperature. Also, by including 3BF, the critical point is obtained in KBT=17.1MeV at 0.06 fm−3 , and the maximum value of latent heat is found in the range ∼31.8MeV.

Steady-state susceptibility in continuous phase transitions of dissipative systems

In this work, we explore the critical behaviors of fidelity susceptibility and trace distance susceptibility associated to the steady states of dissipative systems at continuous phase transitions. We investigate on two typical models, one is the dissipative spin-1/2 XYZ model on two-dimensional square lattice and the other is a driven-dissipative Kerr oscillator. We find that the susceptibilities of fidelity and trace distance exhabit singular behaviors near the critical points of phase transitions in both models. The critical points, in thermodynamic limit, extracted from the scalings of the critical controlling parameters to the system size or nonlinearity agree well with the existed results.

Finite-Size Scaling on a Digital Quantum Simulator Using Quantum Restricted Boltzmann Machine

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occurring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g., in the Quantum Rabi Model (QRM). Since these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic structure configurations of atomic and molecular systems. We calculate the critical point for the quantum phase transition of the QRM using this approach. We also provide a protocol to implement this method on a digital quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our work opens up a new direction in the study of quantum phase transitions on quantum devices.

Quantum and temperature effects on the crystal structure of superhydride LaH10 : A path integral molecular dynamics study

By classical and path-integral molecular dynamics simulations, we study the pressure-temperature ($P$-$T$) phase diagram of LaH$_{10}$ to clarify the impact of temperature and atomic zero-point motions. We calculate the XRD pattern and analyze the space group of the crystal structures. For 125 GPa $\leq P\leq$ 150 GPa and $T=300$ K, we show that a highly symmetric $Fm\bar{3}m$ structure, for which superconductivity is particularly favored, is stabilized only by the temperature effect. On the other hand, for $T=200$ K, the interplay between the temperature and quantum effects is crucial to realize the $Fm\bar{3}m$ structure. For $P=$100 GPa and $T=$300 K, we find that the system is close to the critical point of the structural phase transition between the $Fm\bar{3}m$ structure and those with lower symmetries.

Analytical results for the unusual Grüneisen ratio in the quantum Ising model with Dzyaloshinskii-Moriya interaction

The Gr\"uneisen ratio (GR) has emerged as a superb tool for the diagnosis of quantum phase transitions, which diverges algebraically upon approaching critical points of continuous phase transitions. However, this paradigm has been challenged recently by observations of a finite GR for self-dual criticality and divergent GR at symmetry-enhanced first-order transitions. To unveil the fascinating GR further, we exemplify the idea by studying an exactly solvable quantum Ising model with Dzyaloshinskii-Moriya interaction, which harbors a ferromagnetic phase, a paramagnetic phase, and a chiral Luttinger liquid. Although the self-dual criticality of the ferromagnetic--paramagnetic transition is undermined by the Dzyaloshinskii-Moriya interaction, we find that the GR at the transition is still finite albeit with an increasing value, signifying a proximate self-dual relation. By contrast, the GR at the transition between the gapped ferromagnetic phase and the gapless Luttinger liquid diverges and changes its sign when crossing the first-order transition. This implies that the GR could also probe the first-order transition between the gapped and gapless phases.