Nonequilibrium Phase Transition Research Articles

Random process with a turbulent power spectrum

Random processes with large fluctuations are simulated by a system of nonlinear stochastic equations describing coupled nonequilibrium phase transitions. It is shown that under the action of white noise a critical state can arise, which is characterized by a turbulent spectrum and a scale-invariant probability density function. Under the action of a periodic force on a random process with a turbulent spectrum, a resonant response of scale-invariant functions arises. The lumped system is generalized to the spatially distributed case. To study the sustainability and stationarity of a random process, the principle of maximum entropy is used.

Efficient quantum information probes of nonequilibrium quantum criticality

Quantum information-based approaches, in particular the fidelity, have been flexible probes for phase boundaries of quantum matter. A major hurdle to a more widespread application of fidelity and other quantum information measures to strongly correlated quantum materials is the inaccessibility of the fidelity susceptibility to most state-of-the-art numerical methods. This is particularly apparent away from equilibrium where, at present, no general critical theory is available and many standard techniques fail. Motivated by the usefulness of quantum information-based measures we show that a widely accessible quantity, the single-particle affinity, is able to serve as a versatile instrument to identify phase transitions beyond Landau’s paradigm. We demonstrate that it not only is able to signal previously identified nonequilibrium phase transitions but also has the potential to detect hitherto unknown phases in models of quantum matter far from equilibrium.

Ultrafast Martensitic Phase Transition Driven by Intense Terahertz Pulses

We report on an ultrafast nonequilibrium phase transition with a strikingly long-lived martensitic anomaly driven by above-threshold single-cycle terahertz pulses with a peak field of more than 1 MV/cm. A nonthermal, terahertz-induced depletion of low-frequency conductivity in Nb 3 Sn indicates increased gap splitting of high-energy Γ 12 bands by removal of their degeneracies, which induces the martensitic phase above their equilibrium transition temperature. In contrast, optical pumping leads to a Γ 12 gap thermal melting. Such light-induced nonequilibrium martensitic phase exhibits a substantially enhanced critical temperature up to ∼100 K, i.e., more than twice the equilibrium temperature, and can be stabilized beyond technologically relevant, nanosecond time scales. Together with first-principle simulations, we identify a compelling terahertz tuning mechanism of structural order via Γ 12 phonons to achieve the ultrafast phase transition to a metastable electronic state out of equilibrium at high temperatures far exceeding those for equilibrium states.

Full quantum theory of nonequilibrium phonon condensation and phase transition

Fr\"olich condensation is a room-temperature nonequilibrium phenomenon which is expected to occur in many physical and biological systems. Though predicted theoretically a half century ago, the nature of such condensation remains elusive. In this Letter, we derive a full quantum theory of Fr\"ohlich condensation from the Wu-Austin Hamiltonian and present for the first time an analytical proof that a second-order phase transition induced by nonequilibrium and nonlinearity emerges in the large-$D$ limit with and without decorrelation approximation. This critical behavior cannot be witnessed if external sources are treated classically. We show that the phase transition is accompanied by large fluctuations in the statistical distribution of condensate phonons and that the Mandel-Q factor which characterizes fluctuations becomes negative in the limit of excessive external energy input. In contrast with the cold atom equilibrium BEC, the Fr\"ohlich condensate is a result of the nonequilibrium driving where the pump plays a role of setting the number of particles, and the medium plays a role of setting the temperature. Hence, BEC can either arise by reducing the medium temperature at fixed pump (equilibrium case), or by increasing the pump at fixed medium temperature (nonequilibrium case).

Microbial biofilms are shaped by the constant dialogue between biological and physical forces in the extracellular matrix.

Microbial biofilms are shaped by the constant dialogue between biological and physical forces in the extracellular matrix.

Quantum statistical theory for an exciton-polariton condensate: Fluctuations and coherence

A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.

Nonclassical correlated optical multistability at low photon level for cavity electromagnetically induced transparency

We study the nonequilibrium dynamic behaviors in a driven-dissipative single-atom cavity electromagnetically induced transparency. The optical bistability and multistability beyond a Kerr nonlinearity are observed utilizing the optical Stark shift induced strong nonlinearity. We show that the nonequilibrium dynamical phase transition between bistability and multistability is highly tunable by the system parameters in a large parameter region. The first-order dissipative optical bistability (multistability) always corresponds to the photon-bunching quantum statistics, which indicates that the quantum fluctuations and correlations play important roles in nonequilibrium dynamics. Interestingly, bistability and multistability with photon-bunching quantum statistics occurring at extremely low steady-state cavity photon number are observed, even under a very strong cavity driven field. Furthermore, we demonstrate that the unique cavity steady-state solution of the full quantum calculation is excellently consistent with the lowest solution based on the semiclassical mean-field approach in bistability and multistability regimes when the cavity photon number is much less than unity, albeit these nonclassical quantum states should possess strong quantum fluctuations in this parameter regime. Our results pave the way to exploring nonclassical correlated optical multistability in quantum regime, which may bring exciting opportunities for potential applications from quantum information processing to quantum metrology.

Entropy production and its large deviations in an active lattice gas

Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase separation. Exploiting a recent formulation of the exact fluctuating hydrodynamics for this model, we provide analytical results for its entropy production statistics in both typical and atypical (biased) regimes. This complements previous studies of the large deviation statistics of entropy production in off-lattice active particle models that could only be addressed numerically. Our analysis uncovers an unexpectedly intricate phase diagram, with five different phases arising (under bias) within the parameter regime where the unbiased system is in its homogeneous state. Notably, we find the concurrence of first order and second order nonequilibrium phase transition curves at a bias-induced tricritical point, a feature not yet reported in previous studies of active systems.

Kibble-Zurek Mechanism for Dynamical Ordering in a Driven Vortex System.

The Kibble-Zurek mechanism describes the formation of topological defects in systems crossing a continuous symmetry-breaking phase transition at a finite quench rate. While this mechanism has been extensively studied for equilibrium transitions, its applicability to nonequilibrium transitions has not yet been fully examined. Recent simulation has shown the applicability of the Kibble-Zurek mechanism to dynamical ordering transitions in particlelike assemblies, including superconducting vortices, driven over random disorder. Here, we experimentally study the configurational order of vortices in the course of dynamical ordering with various quench rates. We verify a power-law scaling of the defect density with the quench rate and an impulse-adiabatic crossover on the ordered side of the transition, which are key predictions of the Kibble-Zurek mechanism. Our results suggest the applicability of the Kibble-Zurek mechanism to other nonequilibrium phase transitions.

Dynamic phase transitions on the kagome Ising ferromagnet.

We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.

Machine learning of pair-contact process with diffusion

The pair-contact process with diffusion (PCPD), a generalized model of the ordinary pair-contact process (PCP) without diffusion, exhibits a continuous absorbing phase transition. Unlike the PCP, whose nature of phase transition is clearly classified into the directed percolation (DP) universality class, the model of PCPD has been controversially discussed since its infancy. To our best knowledge, there is so far no consensus on whether the phase transition of the PCPD falls into the unknown university classes or else conveys a new kind of non-equilibrium phase transition. In this paper, both unsupervised and supervised learning are employed to study the PCPD with scrutiny. Firstly, two unsupervised learning methods, principal component analysis (PCA) and autoencoder, are taken. Our results show that both methods can cluster the original configurations of the model and provide reasonable estimates of thresholds. Therefore, no matter whether the non-equilibrium lattice model is a random process of unitary (for instance the DP) or binary (for instance the PCP), or whether it contains the diffusion motion of particles, unsupervised learning can capture the essential, hidden information. Beyond that, supervised learning is also applied to learning the PCPD at different diffusion rates. We proposed a more accurate numerical method to determine the spatial correlation exponent nu _{perp }, which, to a large degree, avoids the uncertainty of data collapses through naked eyes.

Emergent quantum correlations and collective behavior in noninteracting quantum systems subject to stochastic resetting

We investigate the dynamics of a non-interacting spin system, undergoing coherent Rabi oscillations, in the presence of stochastic resetting. We show that resetting generally induces long-range quantum and classical correlations both in the emergent dissipative dynamics and in the non-equilibrium stationary state. Moreover, for the case of conditional reset protocols -- where the system is reinitialized to a state dependent on the outcome of a preceding measurement -- we show that, in the thermodynamic limit, the spin system can feature collective behavior which results in a phenomenology reminiscent of that occurring in non-equilibrium phase transitions. The discussed reset protocols can be implemented on quantum simulators and quantum devices that permit fast measurement and readout of macroscopic observables, such as the magnetisation. Our approach does not require the control of coherent interactions and may therefore highlight a route towards a simple and robust creation of quantum correlations and collective non-equilibrium states, with potential applications in quantum enhanced metrology and sensing.

Collective excitations at non-equilibrium phase transition in metabolically active red blood cells

Collective excitations of superconductors and superfluids have been extensively studied in condensed matter physics, while recent experimental advances have made it possible to study the non-equilibrium dynamics of human blood. Here, we show that some dynamic quantitative metrics calculated for the ion fluxes of two isolated peripheral blood droplets that were spatially separated by the presence of a semiconductor exhibited the characteristic features of a quasi-particle (or collective excitation) at a critical point. In the experiment, the spontaneous peak, which indicates order, appeared at a physiological (hereafter: critical) temperature of 36 °C in the human blood. The ordering effect, which was still present in the weak magnetic field of 350 mT, disappeared above the critical magnetic field of approximately 500 mT, suggesting a dynamic Meissner effect in the system (henceforth “dynamic” means derived from the “time series” – a series of real numbers). Moreover, a superconducting gap ratio of approx. 2.91 was found below the upper limit (4) of the BCS theory for weak coupling. Both these effects indicate the existence of a “superconducting” (ion) environment that is conducive to the emergence of quasiparticles. While the dynamic structure of the time series is substantially isotropic at temperatures beyond the phase transition, the system undergoes symmetry breakdown and non-equilibrium phase transition at a critical state. The designated series of dynamic variables can be used in medicine, inter alia, in screening tests as new indicators describing the patient's health.

Decoupled ultrafast electronic and structural phase transitions in photoexcited monoclinic VO2.

Photoexcitation has emerged as an efficient way to trigger phase transitions in strongly correlated materials. There are great controversies about the atomistic mechanisms of structural phase transitions (SPTs) from monoclinic (M1-) to rutile (R-) VO2 and its association with electronic insulator-metal transitions (IMTs). Here, we illustrate the underlying atomistic processes and decoupling nature of photoinduced SPT and IMT in nonequilibrium states. The photoinduced SPT proceeds in the order of dilation of V-V pairs and increase of twisting angles after a small delay of ~40 fs. Dynamic simulations with hybrid functionals confirm the existence of isostructural IMT. The photoinduced SPT and IMT exhibit the same thresholds of electronic excitations, indicating similar fluence thresholds in experiments. The IMT is quasi-instantaneously (<10 fs) generated, while the SPT takes place with time a constant of 100 to 300 fs. These findings clarify some key controversies in the literature and provide insights into nonequilibrium phase transitions in correlated materials.

Mathematical Model of the Process of Non-Equilibrium Hydrate Formation in a Porous Reservoir during Gas Injection

Increasing the efficiency of natural gas storage in geological formations is possible by transferring gas from a free state to a gas hydrate state, since gas hydrates have a number of unique properties. For example, 1 m3 of methane hydrate contains 164 m3 of gas under normal conditions. It is possible to store a sufficiently large amount of gas in a small volume at a relatively low pressure. To study the regularities of the process of formation of underground gas hydrate gas storage, this article presents a mathematical model of the process of methane injection into a natural reservoir saturated with methane and water, accompanied by the formation of gas hydrate. Unlike previous works, the constructed mathematical model additionally takes into account a number of factors: the filtration flow of water, the real gas properties, the Joule–Thomson effects and adiabatic compression. The process of gas hydrate formation is considered as a non-equilibrium phase transition. Numerical solutions of the problem are constructed that describe the distributions of parameters (temperature, pressure, phase saturations) in a reservoir. Dependences are obtained that reveal the regularities of the process of non-equilibrium formation of gas hydrate in a natural reservoir during gas injection. The influence of gas injection pressure and temperature, as well as reservoir porosity and permeability, on the distributions of pressure, temperature, water saturation and hydrate saturation in the reservoir, as well as on the dynamics of changes in these parameters and the mass of gas hydrate formed in the reservoir over time, are analyzed.

Enhanced pion-to-proton ratio at the onset of the QCD phase transition

The pion-to-proton ratio is identified as a potential signal for a non-equilibrium first-order chiral phase transition in heavy-ion collisions, as the pion multiplicity is directly related to entropy production. To showcase this effect, a non-equilibrium Bjorken expansion starting from realistic initial conditions along a Taub adiabat is used to simulate the entropy production. Different dynamical criteria to determine the final entropy-per-baryon number are investigated and matched to a hadron resonance gas model along the chemical freeze out curve to obtain the final pion and proton numbers. We detect a strong enhancement of their multiplicity ratio at the energies where the system experiences a strong phase transition as compared to a smooth crossover which shows almost no enhancement.

Experimental validation of the Kibble-Zurek mechanism on a digital quantum computer

The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system’s critical exponents at equilibrium and the quenching rate. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution, on an open access IBM quantum computer (IBM-Q). We find that for this simple one-qubit model, experimental data validates the central KZM assumption of the adiabatic-impulse approximation for a well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies, separately elucidating the role of crosstalk between qubits and the increasing decoherence effects associated with the quantum circuit depth on the KZM predictions. Our results strongly suggest that increasing circuit depth acts as a decoherence source, producing a rapid deviation of experimental data from theoretical unitary predictions.

Criticality and entanglement in nonunitary quantum circuits and tensor networks of noninteracting fermions

Entanglement dynamics in nonunitary quantum systems have been found to exhibit novel nonequilibrium quantum phase transitions and have attracted tremendous attention with connections to various aspects of quantum information theory. This work establishes, for systems of noninteracting fermions, an exact three-way correspondence between (i) nonunitary (as well as unitary) quantum circuits dynamics in $d$ spatial dimensions; (ii) ($d$+1)-dimensional Gaussian tensor networks, and (iii) fermion systems in ($d$+1) spatial dimensions subject to unitary evolution with static Hamiltonians. Through this correspondence, $d$-dimensional random quantum circuits are connected with the classic subject area of Anderson localization in ($d$+1) spatial dimensions and consequently follow the ``tenfold way'' Altland-Zirnbauer classification. Selected examples of quantum circuits exhibiting entanglement phases and criticalities are used to illustrate these general principles.

Study of nonequilibrium phase transitions mechanisms in exclusive network and node model of heterogeneous assignment based on real experimental data of KIF3AC and KIF3CC motors

Study of nonequilibrium phase transitions mechanisms in exclusive network and node model of heterogeneous assignment based on real experimental data of KIF3AC and KIF3CC motors

Noise-induced sustainability of cooperation in Prisoner's Dilemma game

Based on the concept of stochastic Prisoner’s Dilemma (SPD) game in experimental economics proposed by Bereby-Meyer and Roth (Am Econ Rev 96 (2006) 1029–1042) (see also H. Kunreuther et al., Judgm. Decis. Mak. 4 (5) (2009) 363–384), the dynamical properties of the SPD game is investigated in this paper. For the non-repeated SPD game, we can see that the increase of noise intensity will not only lead to loss of the stochastic stability of the boundary state corresponding to defection but also the non-equilibrium phase transition of the quasi-stationary distribution of the system, and that the fixation probability of cooperation will increase with the increase of noise intensity. However, for the stochastic TFT-AllD game, the increase of noise intensity will lead to the loss of the stochastic stability of the two boundaries corresponding to cooperation and defection respectively, but will not lead to the non-equilibrium phase transition of the quasi-stationary distribution of the system. Moreover, as a special case of the stochastic TFT-AllD game (i.e., (m−1)(b−c)=2c), we show that the fixation probability of TFT will increase (decrease) with the increase of noise intensity if the initial frequency of TFT is less (or larger) than 1/2.