Dynamical Phase Diagram Research Articles

Nonequilibrium magnetic properties of the mixed spin (1/2, 1) Ising nanowire with core-shell structure

Abstract The nonequilibrium magnetic properties (phase transition temperatures, phase diagrams, hysteresis loop areas and correlations) are investigated in the kinetic mixed spin (1/2, 1) Ising nanowire system under the time varying magnetic field. The Glauber-type stochastic dynamics are employed to construct the set of mean field dynamic equations. The time variation of the core/shell magnetizations and the thermal behavior of the dynamic core/shell magnetizations are examined, extensively. The dynamic core/shell magnetizations, hysteresis loop areas and correlations are studied as a function of temperature in order to characterize the nature (continuous or discontinuous) of the phase transitions as well as to find the dynamic phase transition temperatures. The dynamic phase diagrams are presented in the magnetic field amplitude and temperature plane. The dynamic phase diagrams exhibit paramagnetic (p), ferrimagnetic (i), nonmagnetic (nm) phases, three mixed regions, (i + nm), (i + p) and (nm + p). The dynamic phase diagrams contain a dynamic tricritical point and reentrant phenomena, which strongly depend on interaction parameters.

Time crystals in a shaken atom-cavity system

We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of cavity photons and order parameters at noninteger multiples of the driving period, which signals the appearance of an incommensurate time crystal. The subharmonic oscillatory motion corresponds to dynamical switching between symmetry-broken states, which are nonequilibrium bond ordered density wave states. Employing a semiclassical phase-space representation for the driven-dissipative quantum dynamics, we confirm the rigidity and persistence of the time crystalline phase. We identify experimentally relevant parameter regimes for which the time crystal phase is long-lived, and map out the dynamical phase diagram. We compare and contrast the incommensurate time crystal with the commensurate Dicke time crystal in the amplitude-modulated case.

Dynamical phase diagram of a quantum Ising chain with long-range interactions

We investigate the effect of short-range correlations on the dynamical phase diagram of quantum many-body systems with long-range interactions. Focusing on Ising spin chains with power-law decaying interactions and accounting for short-range correlations by a cluster mean field theory we show that short-range correlations are responsible for the emergence of a chaotic dynamical region. Analyzing the fine details of the phase diagram, we show that the resulting chaotic dynamics bears close analogies with that of a tossed coin.

Period-n Discrete Time Crystals and Quasicrystals with Ultracold Bosons.

We investigate the out-of-equilibrium properties of a system of interacting bosons in a ring lattice. We present a Floquet driving that induces clockwise (counterclockwise) circulation of the particles among the odd (even) sites of the ring which can be mapped to a fully connected model of clocks of two counterrotating species. The clocklike motion of the particles is at the core of a period-n discrete time crystal where L=2n is the number of lattice sites. In the presence of a "staircaselike" on-site potential, we report the emergence of a second characteristic timescale in addition to the period n-tupling. This new timescale depends on the microscopic parameters of the Hamiltonian and is incommensurate with the Floquet period, underpinning a dynamical phase we call "time quasicrystal." The rich dynamical phase diagram also features a thermal phase and an oscillatory phase, all of which we investigate and characterize. Our simple, yet rich model can be realized with state-of-the-art ultracold atoms experiments.

Two-dimensional Fermi liquid dynamics with density-density and quadrupolar interactions

We consider a Fermi liquid model with density-density as well as quadrupolar forward scattering interactions parametrized by the Landau parameters $F_0$ and $F_2$. Using bosonization and a decimation technique, we compute collective modes and spectral functions for a huge range of interactions, ranging from strong repulsion to strong attraction in either angular momentum channels. We present a dynamical phase diagram showing a region of parameters where the collective modes structure changes abruptly, possibly signaling a dynamical phase transition.

Motion of Newtonian drops deposited on liquid-impregnated surfaces induced by vertical vibrations

We have studied the motion of drops on inclined liquid-impregnated surfaces (LISs) subject to vertical vibrations. The liquid drops comprise distilled water and different aqueous solutions of glycerol of increasing viscosity. The use of weak pinning LISs strongly affects the dynamical phase diagram. First of all, there is no trace of the dominant static region at low oscillating amplitudes reported for oscillating solid surfaces characterized by contact angle hysteresis. On the contrary, at sufficiently low oscillating amplitudes, the drops always move downwards with a velocity that depends only on the drop viscosity. Further increasing the oscillating amplitude may drive the drop upwards against gravity, as reported for dry surfaces. The use of more viscous drops widens this climbing region. Arguably, the main novelty of this work concerns the observation of two distinct descending regimes where the downhill speed differs by a factor of five or more. Fast-rate videos show that the evolution of the drop profile is diverse in the two regimes, likely because the vertical oscillations reduce the effect of the oil meniscus surrounding the drop at high accelerations.

Dynamical criticality and domain-wall coupling in long-range Hamiltonians

Dynamical quantum phase transitions hold a deep connection to the underlying equilibrium physics of the quench Hamiltonian. In a recent study [J.~C.~Halimeh \textit{et al.}, arXiv:1810.07187], it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here, we consider transverse-field Ising chains with power-law and exponentially decaying interactions, and show that by removing domain-wall coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with long-range hopping and pairing, anomalous dynamical criticality is no longer present. This indicates that bound domain walls are necessary for anomalous cusps to appear in the Loschmidt return rate. We also calculate the dynamical phase diagram of the Kitaev chain with long-range hopping and pairing, which in the case of power-law couplings is shown to exhibit rich dynamical criticality including a doubly critical dynamical phase.

Emergent limit cycles and time crystal dynamics in an atom-cavity system

We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant atomic resonance. By mapping out the dynamical phase diagram, we identify regions in parameter space showing stable limit cycle dynamics. Since the model describing the system is time-independent, the emergence of a limit cycle phase indicates the breaking of continuous time translation symmetry. Employing a semiclassical analysis to demonstrate the robustness of the limit cycles against perturbations and quantum fluctuations, we establish the emergence of a time crystal.

Crackling to periodic dynamics in granular media.

We study the local and global dynamics of sheared granular materials in a stick-slip experiment, using a slider and a spring. The system crackles, with intermittent slip avalanches, or exhibits irregular or periodic dynamics, depending on the shear rate and loading stiffness. The global force on the slider during shearing captures the transitions from the crackling to the periodic regime. We deduce a dynamic phase diagram as a function of the shear rate and the loading stiffness and associated scaling laws. Using photoelastic particles, we also capture the grain-scale stress evolution, and investigate the microscopic behavior in the different regimes.

Dynamic magnetic properties the spin-1 Ising model with bilinear and biquadratic interactions within the path probability method

Dynamic magnetic properties the spin-1 Ising model with bilinear and biquadratic interactions under the oscillating magnetic field are studied by using the path probability method. The influences of the reduced temperature, angular frequency, biquadratic exchange interaction and rate constants on the dynamic magnetic properties of the system, such as magnetizations, phase diagrams, hysteresis behaviors, coercivity fields, remanent magnetizations, are examined. New and interesting phase dynamic phase diagrams and a number of characteristic hysteresis loop behaviors, such as triple loops, type I, and type III behaviors, are observed. The results are qualitatively consistent with those of some theoretical and experimental studies.

Dynamics of skyrmion in disordered chiral magnet of thin film form

Magnetic skyrmion is a topological spin texture characterized by the mapping from the two dimensional real space to the unit sphere. It is realized in chiral magnets under an external magnetic field in the plane perpendicular to it. In thin film samples, which are most relevant to the applications, the thickness of the system parallel to the magnetic field is finite, and a skyrmion turns into a skyrmion string, which is often assumed to be a straight rod. There are phenomena related to the internal degrees of freedom along the string, e.g., the monopole and anti-monopole creation/annihilation, corresponding to the change in the skyrmion number. However, the role of this finite thickness in the topological stability and dynamics has not been explored yet. Here we study theoretically the current-driven dynamics of a skyrmion string under disorder potential by systematically changing the thickness of the sample to reveal the dynamical phase diagram in the plane of current density and thickness. We found the three regions, i.e., (i) pinned skyrmion string, (ii) moving depinned skyrmion string, and (iii) annihilation of skyrmion string, for thin and thick limits while (iii) is missing in the intermediate case. This indicates that there is the optimal range of thickness for the topological stability of skyrmion string enhanced compared with a two-dimensional skyrmion. This result provides a way to design and control skyrmions in thin films and interfaces of finite thickness.

Thermodynamic mechanism of selective cocrystallization explored by MD simulation and phase diagram analysis

AbstractThe thermodynamic mechanism of selective cocrystallization was investigated by combination of molecular dynamics (MD) simulations and phase diagram analysis, using system of urea and cresol isomers as model compounds. Hansen solubility parameters (HSPs) models were utilized to predict miscibility and cocrystal formation. Thermodynamic phase diagrams of cresol isomers and urea were measured with the help of process analysis technology. MD simulations were performed to investigate the intermolecular interactions between m‐ and/or p‐cresol and urea, by calculating the solvation free energies (SFEs) and analysing radial distribution functions (RDFs). The simulation and experimental results indicate that the solubility data of urea are apparently affected by the SFEs, which are linearly related with the concentration of urea. Moreover, it was also found that the type of O‐H···O=C hydrogen bond plays a critical role in the contribution of intermolecular interactions and is also a key factor for selective cocrystallization.

Dynamic Phase Diagram of Catalytic Surface of Hexagonal Boron Nitride under Conditions of Oxidative Dehydrogenation of Propane.

Partially oxidized surfaces of hexagonal boron nitride (hBN) and several metal borides are unexpectedly excellent catalysts for oxidative dehydrogenation of alkanes to olefins, but the nature of the active site(s) on these B-containing interfaces remains elusive. We characterize the surface of the partially oxidized B-rich hBN surface under reaction conditions from first principles. The interface has thermal access to multiple different stoichiometries and multiple structures of each stoichiometry. The size of the thermal ensemble is composition-dependent. The phase diagram of the interface constructed on the basis of the statistical ensembles of many accessible states is very different from the one based on global minima. Phase boundaries shift and blur, and phases consist of several stoichiometries and structures. The BO layer transiently exposes the reactive -B═O motifs in the metastable states. The fluxionality and structural diversity emerging under reaction conditions must be taken into account in theoretically descriptions of the catalytic interface.

Floquet superconductor in holography

We study nonequilibrium steady states in a holographic superconductor under time periodic driving by an external rotating electric field. We obtain the dynamical phase diagram. Superconducting phase transition is of first or second order depending on the amplitude and frequency of the external source. The rotating electric field decreases the superconducting transition temperature. The system can also exhibit a first order transition inside the superconducting phase. It is suggested this transition exists all the way down to zero temperature. The existence of nonequilibrium thermodynamic potential for such steady solutions is also discussed from the holographic point of view. The current induced by the electric field is decomposed into normal and superconducting components, and this makes it clear that the superconducting one dominates in low temperatures.

Dynamical criticality in open systems: Nonperturbative physics, microscopic origin, and direct observation

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the open weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a $\mathbb{Z}_2$ symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations, confirming our macroscopic and microscopic results.

Theoretical Investigation of Transcriptional Bursting: A Multistate Approach.

Variability in gene expression causes genetically identical cells to exhibit different phenotypes. One probable cause of this variability is transcriptional bursting, where the synthesis of RNA molecules randomly alternates with periods of silence in the transfer of genetic information. Yet, the molecular mechanisms behind this variability remain unclear. Experiments indicate that multiple biochemical states might be involved in the production of RNA molecules. Stimulated by these observations, we developed a theoretical framework to investigate the mechanisms of transcriptional bursting. It is based on a multistate stochastic approach that provides a full quantitative description of the dynamic properties in the system. We found that the degree of stochastic fluctuations during transcription directly correlates with the number of biochemical states. This explains experimentally observed variability and fluctuations in the quantities of the produced RNA molecules. The procedure to estimate the number of relevant biochemical states participating in the transcription is outlined and applied for analysis of experimental results. We also developed a general dynamic phase diagram for the transcription process. The presented theoretical method clarifies physical-chemical aspects of the transcriptional bursting and presents a minimal chemical-kinetic description of the process.

Theory for the dynamics of glassy mixtures with particle size swaps

We present a theory for the dynamics of a binary mixture with particle size swaps. The theory is based on a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. The theory shows that, in accordance with physical intuition, particle size swaps open up an additional channel for the relaxation of density fluctuations. Thus, allowing swaps speeds up the dynamics and moves the dynamic glass transition towards higher densities and/or lower temperatures. We calculate an approximate dynamic glass transition phase diagram for an equimolar binary hard sphere mixture. We find that in the presence of particle size swaps, with increasing ratio of the hard sphere diameters the dynamic glass transition line moves towards higher volume fractions, up to the ratio of the diameters approximately equal to 1.2, and then saturates. We comment on the implications of our findings for the theoretical description of the glass transition.

Molecular search with conformational change: One-dimensional discrete-state stochastic model.

Molecular search phenomena are observed in a variety of chemical and biological systems. During the search, the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic modes. To understand the mechanisms of molecular search with alternating dynamics, we investigate the search dynamics with stochastic transitions between two conformations in a one-dimensional discrete-state stochastic model. It is explicitly analyzed using the first-passage time probability method to obtain a full dynamic description of the search process. A general dynamic phase diagram is developed. It is found that there are several dynamic regimes in the molecular search with conformational transitions, and they are determined by the relative values of the relevant length scales in the system. Theoretical predictions are fully supported by Monte Carlo computer simulations.

Dynamical Quantum Phase Transitions: A Geometric Picture.

The Loschmidt echo is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model as an example, we show that this indeed is not the case and that a simple semiclassical approximation to systems well described by mean-field theory is, in fact, in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the postquench dynamics provided in Supplemental Material visualize this new point of view.

The Application of CALPHAD Calculations to Uranium-Based Metallic Nuclear Fuels

The thermodynamic calculation and optimization on the binary and ternary systems consisting of Mo, Pu, Th, Ti, U, V and Zr used in metallic nuclear fuel are systematically reviewed. By combining the optimized systems in literatures and present assessment of U-Mo-Zr ternary system, the thermodynamic databases of U-Mo-based and U-Zr-based nuclear fuels were established based on the Calculation of Phase Diagram (CALPHAD) method. The stable phase diagrams and dynamical phase diagrams under irradiation were reviewed based on the database. As the examples for the application of the two thermodynamic databases, the effect of alloying elements on the stability of bcc (γU) phase in different ternary and multicomponent alloys were discussed, which can provide essential theoretical guidance for the design Uranium-based metallic nuclear fuels.