Critical Point Of Phase Transition Research Articles

Quantum estimation of tripartite coupling in spin-magnon-mechanical hybrid systems

Tripartite interactions play a fundamental role in the quantum information processing and quantum technology. However, it is generally difficult to realize strong tripartite coupling. We investigate the estimation of a tripartite coupling strength in a hybrid setup composed of a single nitrogen-vacancy (NV) center and a micromagnet. A time-independent parametric drive can be utilized to increase the estimation precision of the tripartite coupling strength. By calculating the quantum Fisher information (QFI), we can obtain the optimal estimation precision by measuring the eigenstate of the tripartite system. At the critical position, the QFI is divergent due to that the preparation time of the eigenstate is divergent. When the system is subjected to a dissipation, the QFI near the critical point of the driven-dissipation phase transition is analytically obtained. The direct intensity measurement is the optimal measurement near the dissipation phase transition point. In addition, we quantify the robustness of an imperfect measurement operator by the measurement noise susceptibility based on the error propagation formula. We find that the direct intensity measurement is robust enough against small measurement disturbance from a coherent drive. But it can be disturbed by the nonlinear anti-harmonic measurement noise, especially near the critical point.

Topological phases and non-Hermitian topology in tunable nonreciprocal cyclic three-mode optical systems

We propose a method for simulating a 1D non-Hermitian Su-Schrieffer-Heeger model with modulated nonreciprocal hopping using a cyclic three-mode optical system. The current system exhibits different localization of topologically nontrivial phases, which can be characterized by the winding number. We find that the eigenenergies of such a system undergo a real-complex transition as the nonreciprocal hopping changes, accompanied by a non-Bloch parity-time symmetry breaking. We explain this phase transition by considering the evolution of saddle points on the complex energy plan and the ratio of complex eigenenergies. Additionally, we demonstrate that the skin states resulting from the non-Hermitian skin effect possess higher-order exceptional points under the critical point of the non-Bloch parity-time phase transition. Furthermore, we investigate the non-Hermitian skin phase transition by the directional mean inverse participation ratio and the generalized Brillouin zone. This work provides an alternative way to investigate the novel topological and non-Hermitian effects in nonreciprocal optical systems.

Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

By considering the concept of the modified Chaplygin gas (MCG) as a single fluid model unifying dark energy and dark matter, we construct a static, spherically charged black hole (BH) solution in the framework of General Relativity. The P–V criticality of the charged anti-de Sitter (AdS) BH with a surrounding MCG is explored in the context of the extended phase space, where the negative cosmological constant operates as a thermodynamical pressure. This critical behavior shows that the small/large BH phase transition is analogous to the van der Waals liquid/gas phase transition. Accordingly, along the P–V phase spaces, we derive the BH equations of state and then numerically evaluate the corresponding critical quantities. Similarly, critical exponents are identified, along with outcomes demonstrating the scaling behavior of thermodynamic quantities near criticality to a universal class. The use of geometrothermodynamic (GT) tools finally offers a new perspective on the discovery of the critical phase transition point. At this stage, we apply a class of GT tools, such as Weinhold, Ruppeiner, HPEM, and Quevedo classes I and II. The findings are therefore non-trivial, as each GT class metric captures at least either the physical limitation point or the phase transition critical point. Overall, this paper provides a detailed study of the critical behavior of the charged AdS BH with surrounding MCG.

Nonlocal Metasurface with Chiral Exceptional Points in the Telecom-Band.

The exceptional point (EP) is the critical phase transition point in parity-time (PT) symmetry systems, offering many unique physical phenomena, such as a chiral response. Achieving chiral EP in practical applications has been challenging due to the delicate balance required between gain and loss and complicated fabrication, limiting both working band and device miniaturization. Here, we proposed a nonlocal metasurface featuring orthogonal gold nanorods, where loss modulation is achieved through rod size and lattice pitch. By tuning the coupling strength, we experimentally observed the PT symmetry phase transition and chiral EP in the telecom-band. The experimental and simulated circular conversion dichroism at EP reach 0.79 and 0.99, respectively. We also demonstrated an abrupt phase flip of a specific component near EP theoretically. This work provides a feasible scheme for exploring EP in polarized space within the telecom-band, which may find applications in polarization control, wavelength division multiplexing, ultrasensitive sensing, imaging, etc.

Berry curvature dipole and its strain engineering in layered phosphorene

The emergence of the fascinating non-linear Hall effect intrinsically depends on the non-zero value of the Berry curvature dipole. In this work, we predict that suitable strain engineering in layered van der Waals material phosphorene can give rise to a significantly large Berry curvature dipole. Using symmetry design principles, and a combination of feasible strain and staggered on-site potentials, we show how a substantial Berry curvature dipole may be engineered at the Fermi level. We discover that monolayer phosphorene exhibits the most intense Berry curvature dipole peak near 11.8% strain, which is also a critical point for the topological phase transition in pristine phosphorene. Furthermore, we have shown that the necessary strain value to achieve substantial Berry curvature dipole can be reduced by increasing the number of layers. We have revealed that strain in these van der Waals systems not only alters the magnitude of Berry curvature dipole to a significant value but allows control over its sign. We are hopeful that our predictions will pave way to realize the non-linear Hall effect in such elemental van der Waals systems.

Application of the catastrophe theory to acoustoplasma research

In the paper the possibility of applying the mathematical theory of catastrophes to the processes occurring during the interaction of acoustic fields with plasma is considering. In particular, it is proposed to apply the theory to find out possible jumps in parameters and phase transitions in an acoustoplasmic medium. Based on the experimentally obtained database (in this case, for acoustoplasmic processes), a mathematical model of the process under study was constructed. And then, applying the theory of catastrophes, it is determined whether there are sudden changes in the values of control parameters in the area under consideration, critical points of unstable equilibrium and phase transitions, i.e. catastrophic parameter jumps. The choice of the equation describing the process is made based on the number of control parameters for this process. It is also proposed to use the methodology in various fields of science and technology, where similar conditions may arise.

Mechanics and topology of twisted hyperelastic filaments under prescribed elongations: Experiment, theory, and simulation

Soft filaments can be stretched, bent, and twisted, exhibiting complex configurations. When a filament undergoes large torsional deformation, it can display instabilities, and its post-buckling behavior and configuration evolution differs significantly from that observed under small deformation. We study the mechanics and topologically complex morphologies of twisted rubber filaments under prescribed elongation by combining experiment and finite strain theory. Based on the Mooney-Rivlin model, a finite strain theory of the hyperelastic filament under combined tension, bending, and torsion has been established, accounting for both geometrical and material nonlinearities. An experimental and theoretical morphological phase diagram is constructed as a function of the twist density and the initial elongation. The buckling and post-buckling behaviors of the twisted rubber filaments under prescribed elongation are well captured by the theory that considers geometrical nonlinearity and self-contact. By tracking the interconversion of link, twist, and writhe, we accurately determine the configuration and the critical points of phase transitions. The theoretical predictions agree closely with the measurements. This work sheds light on understanding the morphological complexity of the loaded hyperelastic rod.

Data-driven detection of critical points of phase transitions in complex systems

Detecting the critical points of phase transitions and their driver factors in complex systems from data is a very challenging task. In these regards, the dynamic network biomarker/marker (DNB) method derived from the bifurcation theory is currently very popular, but a unified criterion to pick the most appropriate DNBs is lacking. Here, we propose a giant-component-based DNB (GDNB) method inspired by the percolation theory, that directly selects the largest DNB as the transition core to reflect the progress of the transition. We test the effectiveness of this scheme to detect transitions on three distinct systems, differing in terms of interactions and transitions: Monte Carlo simulations of the 2D Ising model, molecular dynamics simulations of protein folding, and measured gene expression time course in mouse muscle regeneration. These results suggest that the GDNB method inherits all the advantages of the DNB method, while it improves the interpretability at a reduced computational complexity.

Transport theory and the founding of condensed matter physics

In 1966, Woon Siong Gan coined and invented the name transport theory in condensed matter physics. Today, transport theory is the backbone theory of condensed matter physics and the whole condensed matter physics can be represented by transport theory. His PhD thesis pioneered the application of statistical mechanics to ultrasound propagation in semiconductor in the presence of high magnetic fields and low temperatures with the phase transition from the spherical energy surface of metal to the warped energy surface of semiconductor. The usual treatment is using the many-body theory of quantum field theory. Phase transition is an important topic in condensed matter physics. Thus, his PhD thesis also played a role in the founding of condensed matter physics. In this paper, transport theory is applied to phase transition, an important topic in condensed matter physics. The advantages of using transport theory is its broad coverage of both particles interaction and description of the singularity characteristics of phase transition. An example for illustration is that of magnetization which has Ising model describing spins interaction and the Lee Yang theory describing the singularity behavior of the partition function at the critical point of phase transition.

Quantum phase transition and eigen microstate condensation in the quantum Rabi model

We introduce an eigen microstate approach (EMA) in the quantum system to describe the quantum phase transition without knowing the order parameter. Phases of a quantum system are determined by the so-called eigen microstates and their corresponding eigenvalues, which satisfy scaling relations in the critical regime. The quantum Rabi model (QRM) is taken as an example to demonstrate the validity of the EMA. Using both analytical and numerical calculations, we obtain the critical point, critical exponents, and scaling functions of the superradiant phase transition in the QRM. It suggests that a new phase emergency can be interpreted as a condensation of a specific eigen microstate. We expect that, in further studies, the EMA will be applied to more complex quantum phase transition problems in which order parameters cannot be easily defined.

The boundary phase transitions of the 2+1D ℤN topological order via topological Wick rotation

In this work, we show that a critical point of a 1d self-dual boundary phase transition between two gapped boundaries of the ℤN topological order can be described by a mathematical structure called an enriched fusion category. The critical point of a boundary phase transition can be viewed as a gappable non-chiral gapless boundary of the ℤN topological order. A mathematical theory of the gapless boundaries of 2d topological orders developed by Kong and Zheng (arXiv:1905.04924 and arXiv:1912.01760) tells us that all macroscopic observables on the gapless boundary form an enriched unitary fusion category, which can be obtained by a holographic principle called the “topological Wick rotation.” Using this method, we obtain the enriched fusion category that describes a critical point of the phase transition between the e-condensed boundary and the m-condensed boundary of the ℤN topological order. To verify this idea, we also construct a lattice model to realize the critical point and recover the mathematical data of this enriched fusion category. The construction further shows that the categorical symmetry of the boundary is determined by the topological defects in the bulk, which indicates the holographic principle indirectly. This work shows, as a concrete example, that the mathematical theory of the gapless boundaries of 2+1D topological orders is a powerful tool to study general phase transitions.

Microscopic analysis of octupole shape phase transitions and critical points in neutron rich actinides

Octupole constrained energy surfaces, and spectroscopic observables of four isotopic chains of: Cm, Cf, Fm and No with neutron numbers 186 N200 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 theoretical results suggest quantum phase transitions from non-octupole to octupole deformed shapes and to octupole vibrations with increasing neutron number. 288Cm 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.

Unrevealing the phase transition of high-performing high-nitrogen energetic material 1,5-diaminotetrazole-4: N-oxide via first-principles studies

The effect of pressure on crystal structures, electronic properties, hydrogen bonds, optical properties and mechanical features of high-performing energetic material 1,5-diaminotetrazole-4: N-oxide was investigated by high-precision DFT-D method. The results reveal that there exists a critical point of phase transition around 8 GPa, reflected in various properties of the crystal. Band gap decreases gradually as the pressure increases, illustrating electrons are easier to transit from occupied orbit to the empty. The DOS analysis indicates that C-NH2, N-NH2 and N = O bonds may play a role as a reaction channel for the initial decomposition under high pressures. The hydrogen bond analysis indicates that pressure can alter the distribution of hydrogen bond in the crystal and modify the physicochemical properties. The absorption spectra of the crystal under high-pressure conditions show several strong bands in UV–visible region. The analysis on mechanical properties reveals that pressure can effectively improve the rigidity, plasticity and ductility for the crystal. Our results clarify the effect of pressure on energetic materials and are conducive to find the new crystalline phases for energetic materials.

Renormalization of steered coherence and quantum phase transitions in the alternating Ising model

We explore net steered coherence defined with respect to the mutually unbiased bases. By using the quantum renormalization group method, we studied its scaling property for the ground state of two blocks of the alternating Ising model in the renormalized space. The results show that different patterns in the net steered coherence describe different phases of the model, and its susceptibility with respect to the magnetic field is divergent at the critical points of quantum phase transitions. As the net steered coherence exists for almost all bipartite states, it can serve as an alternative for exploring quantum criticality of the many-body systems in the parameter regions without entanglement and quantum discord.

Breaking of the universal nature of the central charge criticality in AdS black holes in Gauss-Bonnet gravity

In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($\Lambda$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($\alpha$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this universal nature breaks when such phase transition is considered for black holes in the Gauss-Bonnet gravity. Apart from this, treating the Gauss-Bonnet parameter as a thermodynamic variable as suggested in \cite{kastori} in light of the consistency between first law and the Smarr relation leads to modified thermodynamic volume (conjugate to variable cosmological constant), adding to a new understanding of the Van der Waals gas like behaviour of the black holes in higher dimensional and higher curvature gravity theories. Our analysis considers a general $D$ dimensional background. We have then imposed a greater focus in the analysis of the phase structure of the five dimensional Gauss-Bonnet spacetime. Our analysis also shows that the general universal nature of the critical value of the central charge (which was present in four dimensional $AdS$ spacetime), breaks down in case of five dimensional $AdS$ spacetime even in the absence of Gauss-Bonnet gravity. This finding indicates the universal nature of the central charge may be a special feature of the four dimensional $AdS$ spacetime only.

Perfect intrinsic squeezing at the superradiant phase transition critical point

Some of the most exotic properties of the quantum vacuum are predicted in ultrastrongly coupled photon–atom systems; one such property is quantum squeezing leading to suppressed quantum fluctuations of photons and atoms. This squeezing is unique because (1) it is realized in the ground state of the system and does not require external driving, and (2) the squeezing can be perfect in the sense that quantum fluctuations of certain observables are completely suppressed. Specifically, we investigate the ground state of the Dicke model, which describes atoms collectively coupled to a single photonic mode, and we found that the photon–atom fluctuation vanishes at the onset of the superradiant phase transition in the thermodynamic limit of an infinite number of atoms. Moreover, when a finite number of atoms is considered, the variance of the fluctuation around the critical point asymptotically converges to zero, as the number of atoms is increased. In contrast to the squeezed states of flying photons obtained using standard generation protocols with external driving, the squeezing obtained in the ground state of the ultrastrongly coupled photon–atom systems is resilient against unpredictable noise.

Collapse of Superradiant Phase and Unstable Macroscopic Vacuum State in An-Optomechanical-Dual-Cavity with a Bose-Einstein Condensate

Based on spin-coherent-state variational method, we mainly study the multiple stable macroscopic quantum states and quantum phase transitions of a Bose-Einstein Condensate in an optomechanical dual-cavity by modulating the dual-cavity interaction and the nonlinear phonon-photon interaction. Especially, the collapse of superradiant phase can be tuned in the existing nonlinear photon-phonon interaction, but the critical quantum phase transition point or boundary hasn’t been influenced. As a result, the system occurs an additional phase transition from the superradiant phase to the inversely atomic populated state. Moreover, when dual-cavity coupling interaction increases to a certain value, a new quantum phase transition from the normal phase to the inversely atomic populated state will appear. Finally, the superradiant phase completely collapses and the normal phase also collapses into an unstable macroscopic vacuum state for a strong dual-cavity coupling interaction.

Anomalous Phase Diagram and Conformational Behaviors of n-Hexane at High Temperatures and High Pressures

n-Hexane has been widely used in the fields of chemistry and energy sources, as well as in studies of ultrafast dynamics of quantum dots at high pressures/temperatures. Here, we report the solid–liquid phase diagrams of n-hexane from room temperature to 651 K within 10 GPa by using in situ Raman spectroscopy and microscopic photography techniques. An anomalous melting phenomenon has been observed in n-hexane, that is, the solid–liquid phase transition critical point at the same pressure is different in the processes of heating and cooling, and there is a great relaxation process. This may be attributed to that the temperature and pressure can affect the equilibrium of the internal conformation of n-hexane. As the pressure increases, the relaxation effect will gradually increase. In addition, the internal conformational database of n-hexane under control of temperature and pressure was obtained through Raman results.

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.