Breaking Phenomena Research Articles

Replica symmetry breaking in random non-Hermitian systems

Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a $PT$-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: the elliptic Ginibre ensemble of random matrices and a non-Hermitian Sachdev-Ye-Kitaev (SYK) model. The free energy of the Ginibre model is temperature independent in the low-temperature phase. The SYK model has similar behavior for sufficiently low temperature, and then it experiences a possible continuous phase transition to a phase with a temperature-dependent free energy before the first-order transition takes place at a higher temperature. We identify the order parameter of the first-order phase transition and obtain analytical expressions for the critical temperature. The mechanism behind the transition is the existence of replica symmetry breaking configurations coupling left and right replicas that control the low-temperature limit of the partition function. We speculate that quantum chaos may be necessary for the observed dominance of off-diagonal replica symmetry breaking configurations in the low-temperature limit.

Rigid Bay-Conjugated Perylene Bisimide Rotors: Solvent-Induced Excited-State Symmetry Breaking and Resonance-Enhanced Two-Photon Absorption

Intramolecular charge transfer and excited-state symmetry breaking have a significant effect on the nonlinear optical properties of multipolar chromophores. Rigid and nonplanar perylene bisimide derivatives (PBIs) functionalized at bay positions were comparatively and comprehensively investigated. In apolar solvents, two quadrupolar molecular rotors showed an obvious decrease of the A0-0/A0-1 ratios, suggesting strong exciton coupling with the adjacent PBI units initiated by the π-π stacking. The vanishment of the preferable dimer emission in polar solvents supported the plausible phenomena of excited-state symmetry breaking, thanks to the facile rotation around the rigid linkers. Comparative femtosecond transition absorption studies confirmed their notable differences in relaxation dynamics and the generation of radical anions (PBI•-) and cations (PBI•+). The maxima two-photon absorption (2PA) wavelengths obtained for the molecular rotors were slightly red-shifted to 670 nm with intrinsic resonance-enhanced characteristics, reflecting the synergistic effect of functional positions and molecular architectures. Meanwhile, the obvious increase of significant 2PA cross-section values in polar solvents illustrated the stabilization of the symmetry-broken dipolar states. Further femtosecond Z-scan also manifested the contribution of excited-state dynamics on the nonlinear optical properties of multipolar chromophores.

Experimental Demonstration of Self-Oscillation Microcomb in a Mode-Splitting Microresonator

Self-oscillation and bifurcation as many-body dynamics solutions in a high-Q microresonator have induced substantial interest in nonlinear optics and ultrafast science. Strong mode coupling between clockwise (CW) wave and counterclockwise (CCW) wave induces mode-splitting and optical self-oscillation in the optical cavity. This study experimentally demonstrates the self-oscillation microcomb formation in a microresonator with strong backward Rayleigh scattering. When a pump laser sweeps across a resonance, both spontaneous symmetry breaking (SSB) and self-oscillation phenomenon are observed. The breathing soliton and stable soliton state can switch to each other through careful tuning of the pump detuning. Our experiments provide a reliable scheme for breather soliton microcomb generation. Meanwhile, the rich physics process enhances the comprehension of nonlinear optics in a cavity.

Formation of the undular bores in shallow water generalized Kaup–Boussinesq model

The formation of undular bores in Riemann problems of the good generalized Kaup–Boussinesq equation is investigated by Whitham modulation theory. Firstly, the Whitham equations associated with the one-phase and two-phase periodic wave solutions are given by the finite-gap averaging method. Secondly, the basic structures of rarefaction wave and dispersive shock wave are discussed by considering the self-similar solutions of the Whitham equations. Then we propose a complete classification of all possible wave patterns for the initial discontinuity of the good generalized Kaup–Boussinesq equation, in which it has been shown that the theoretical results from Whitham modulation theory are in good agreement with the full numerical simulations. The correspondences between the soliton frontiers of the dispersive shock waves and the exact soliton solution of the good generalized Kaup–Boussinesq equation are considered, and exotic undular bores are found. Finally, the dam break problem and piston problem are explored to show the important physical applications of the theoretical results, from which certain inspiring phenomena of wave breaking are discovered for the first time.

Ice load prediction of a podded propulsor under the dynamic azimuthing condition

In the process of cutting an ice layer by dynamic azimuthing of a podded propulsor, the unsteady and high pulsation characteristics of the ice load may compromise the safety and structural strength of podded propulsors. In this study, the failure criterion of simulated materials for the ice-breaking problem and the ice load calculation method were derived based on the peridynamics and the idea of panel division. The contact judgment method between the propeller and ice under the dynamic azimuthing condition of the podded propulsor was proposed. A numerical calculation model of the milling action of the ice–podded propulsor was established, and a numerical simulation of the ice–propeller milling process under the dynamic azimuthing conditions of the podded propulsor was realized. Moreover, numerical simulations under different ice layer moving velocities, propeller rotational speeds, podded propulsor azimuthing rates, and azimuth angles were carried out, and the ice layer breaking phenomenon and the variation characteristics of the propeller ice load under the dynamic azimuthing condition of the podded propulsor were obtained. The research results can guide technical support for the load evaluation, structural safety analysis, mechanism research of load components, and the selection of polar navigation steering strategies for ice-class podded propulsors.

Characterization of two-way coupled thermovibrationally driven particle attractee

Following the recent identification of a new category of thermovibrationally driven particle attractors in dilute fluid–particle systems [M. Lappa, “The patterning behaviour and accumulation of spherical particles in a vibrated non-isothermal liquid,” Phys. Fluids 26(9), 093301 (2014); M. Lappa, “On the formation and morphology of coherent particulate structures in non-isothermal enclosures subjected to rotating g-jitters,” Phys. Fluids 31(7), 073303 (2019); and M. Lappa and T. Burel, “Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures,” Phys. Fluids 32(5), 053314 (2020)], some effort is provided here to develop an integrated framework able to encompass earlier discoveries and account for new effects in a single treatment. In particular, we examine the alterations (“corrugation”) that can be induced in the geometrically perfect particle structures pertaining to this class of phenomena as the percentage of dispersed solid mass is progressively increased. The related dynamics are explored within the framework of a two-way coupled model with respect to several parameters (solid mass load, density ratio, frequency, and amplitude of the imposed vibrations). Ensuing results are interpreted by separating instantaneous and time-averaged contributions and using some ideas borrowed from the companion theory of bifurcations. We show that the back influence of particles on the carrier flow can lead to a variety of possible paths of evolution. While in some cases the original attractee can be overshadowed by particle-induced turbulence, in other circumstances new aggregates with heretofore unseen morphology show up.

Exact solutions for the shallow water equations in two spatial dimensions: A model for finite amplitude rogue waves

Exact solutions for the shallow water equations in two spatial dimensions are obtained from a matrix formulation of the governing system. These fully nonlinear long waves exhibit linear velocity and quadratic free surface displacement fields in the spatial variables. No breaking phenomenon is observed. A special moving boundary can be defined where a fixed mass of fluid inside this circular region may display a rogue wave type behavior. The fluid first converges towards the center of a domain, and the amplitude of the free surface will attain a finite maximum. Subsequently, the fluid reverses paths and rushes away from the center. The kinetic and potential energy of the rogue wave can be computed analytically for all time. As the shallow water equations are employed, these rogue waves are fully nonlinear. There is no restriction on the amplitude, quite unlike the weakly nonlinear assumptions of the nonlinear Schrödinger and Korteweg—de Vries theories. Furthermore, the maximum is truly localized in two spatial dimensions horizontally and the wave is not a ‘long-crested’ one.

Simulating quantum mechanics with a θ -term and an ’t Hooft anomaly on a synthetic dimension

A topological $\theta$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical. Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future. In the near term, it is interesting to study simpler models that retain some of the physical phenomena of interest and their implementation on quantum hardware. For example, dimensionally-reducing gauge theories on small spatial tori produces quantum mechanical models which, despite being relatively simple to solve, retain interesting vacuum and symmetry structures from the parent gauge theories. Here we consider quantum mechanical particle-on-a-circle models, related by dimensional reduction to the 1+1d Schwinger model, that possess a $\theta$-term and realize an 't Hooft anomaly or global inconsistency at $\theta = \pi$. These models also exhibit the related phenomena of spontaneous symmetry breaking and instanton-anti-instanton interference in real time. We propose an experimental scheme for the real-time simulation of a particle on a circle with a $\theta$-term and a $\mathbb{Z}_n$ potential using a synthetic dimension encoded in a Rydberg atom. Simulating the Rydberg atom with realistic experimental parameters, we demonstrate that the essential physics can be well-captured by the experiment, with expected behavior in the tunneling rate as a function of $\theta$. Similar phenomena and observables can also arise in more complex quantum mechanical models connected to higher-dimensional nonabelian gauge theories by dimensional reduction.

The Phase Structure of Two Color QCD and Charged Pion Condensation Phenomenon

The phase structure of dense quark matter in the two color case has been investigated with nonzero baryon $${{\mu }_{{\text{B}}}}$$ , isospin $${{\mu }_{{\text{I}}}}$$ and chiral isospin $${{\mu }_{{{\text{I5}}}}}$$ chemical potentials. It has been shown in the mean-field approximation that there exist three dualities, one of them between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case. The other two dual symmetries between the phase with condensation of charged pions and the phase with diquark condensation and between chiral symmetry breaking and diquark condensation phenomena. It has been demonstrated that due to the duality properties the phase diagram is extremely symmetric and the whole phase diagram in two color case can be obtained just by dualities from the phase structure of three color case. This shows that the dualities are rather usefull tool. It is shown that chiral imbalance generates charged pion condensation phenomenon in conditions of matter in neutron stars, i. e. electrically neutral and $$\beta $$ -equilibrated dense quark matter. And that diquark condensation does not prohibit the generation of the charged PC phase by chiral imbalance at least in the two color case.

Turbulent Parameters in the Middle Atmosphere: Theoretical Estimates Deduced from a Gravity Wave–Resolving General Circulation Model

Abstract We present a scaling analysis for the stratified turbulent and small-scale turbulent regimes of atmospheric flow with emphasis on the mesosphere. We distinguish rotating-stratified macroturbulence turbulence (SMT), stratified turbulence (ST), and small-scale isotropic Kolmogorov turbulence (KT), and we specify the length and time scales and the characteristic velocities for these regimes. It is shown that the buoyancy scale (Lb) and the Ozmidov scale (Lo) are the main parameters that describe the transition from SMT to KT. We employ the buoyancy Reynolds number and horizontal Froude number to characterize ST and KT in the mesosphere. This theory is applied to simulation results from a high-resolution general circulation model with a Smagorinsky-type turbulent diffusion scheme for the subgrid-scale parameterization. The model allows us to derive the turbulent root-mean-square (rms) velocity in the KT regime. It is found that the turbulent RMS velocity has a single maximum in summer and a double maximum in winter months. The secondary maximum in the winter MLT we associate with a secondary gravity wave–breaking phenomenon. The turbulent rms velocity results from the model agree well with full correlation analyses based on MF-radar measurements. A new scaling for the mesoscale horizontal velocity based on the idea of direct energy cascade in mesoscales is proposed. The latter findings for mesoscale and small-scale characteristic velocities support the idea proposed in this research that mesoscale and small-scale dynamics in the mesosphere are governed by SMT, ST, and KT in the statistical average. Significance Statement Mesoscale dynamics in the middle atmosphere, which consists of atmospheric turbulence and gravity waves, remains a complex problem for atmospheric physics and climate studies. Due to its high nonlinearity, the mesoscale dynamics together with the small-scale turbulence is the primary source of uncertainties and biases in high-altitude general circulation models (GCM) in the middle atmosphere. We use the stratified turbulence theory and the gravity wave–resolving GCM to characterize different scaling regimes and to define various length, time, and velocity scales, that are relevant for the mesoscale and small-scale dynamical regimes. Our results highlight the importance of stratified turbulence in the mesosphere and lower-thermosphere region.

Reynolds stress turbulence modelling of surf zone breaking waves

Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\omega$turbulence closure model for this purpose, where$\omega$is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\omega$model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\omega$model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\omega$model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.

The effects of smoothing length on the onset of wave breaking in smoothed particle hydrodynamics (SPH) simulations of highly directionally spread waves

Ocean wave breaking is a difficult-to-model oceanographic process, which has implications for extreme wave statistics, the dissipation of wave energy, and air–sea interaction. Numerical methods capable of reliably simulating real-world directionally spread breaking waves are useful for investigating the physics of wave breaking and for the design of offshore structures and floating bodies. Smoothed particle hydrodynamics is capable of modelling highly steep and overturning free surfaces, which makes it a promising method for simulating breaking waves. This paper investigates the effect of smoothing length on simulated wave breaking in both following and crossing seas. To do so, we reproduce numerically the experiments of highly directionally spread breaking waves in McAllister et al. (J Fluid Mech 860:767–786, 2019. https://doi.org/10.1017/jfm.2018.886) using a range of normalised smoothing lengths: \(h/d_p=1.4\), 1.7, 2.0, 2.3, with h smoothing length and \(d_p\) particle spacing. The smallest smoothing length we use appears to adversely affect the fidelity of the simulated surface elevation, so that the tallest wave crest observed in experiments is not fully reproduced (coefficient of determination \(r^2\approx 0.7\)). For smoothing lengths \(h/d_p=1.7\), 2.0, and 2.3, the experiments are well reproduced (\(r^2\ge 0.88\)); in these simulations smoothing length predominantly affects the spatial extent and duration of breaking. Qualitative and quantitative comparison of our simulations shows that values of \(h/d_p\) in the range \(1.7{-}2\) best reproduce the wave breaking phenomena observed in experiments.

A discussion of numerical wave absorption using sponge layer methods

The short communication reports a discussion of numerical wave absorption using sponge layer methods. Two issues are discussed. The first issue is whether it is necessary to introduce a damping source to the volume fraction equation, and the second issue is whether a vertically uneven sponge layer is more effective than a conventional (namely, vertically uniform) sponge layer. With respect to the first issue, it is found that introducing a damping source to the volume fraction equation results in a wave breaking phenomenon inside sponge layers. For the monochromatic wave simulated, the wave breaking phenomenon makes the reflection coefficient increase by approximately 60% and prolongs the simulation by approximately 5–6 times (when adaptive time steps are adopted). For the solitary wave simulated, the wave breaking phenomenon helps to dissipate the extra mass brought about by the solitary wave, significantly diminishing the reflection coefficient. With respect to the second issue, a vertically uneven sponge layer is derived and then tested over various wave types. Overall, the vertically uneven and conventional sponge layers perform comparably. Therefore, in the authors’ opinion, it might be unnecessary to conduct further investigations into the effectiveness of vertically uneven sponge layers.

Dark‐State Induced Quantum Nonreciprocity

AbstractWith the development of quantum technologies and their broad applications, the phenomenon of reciprocity breaking has been evolving from an effective tool in classical wave optics and electrodynamics to a promising instrument also for the field of quantum computing and quantum information processing. In this work, nonreciprocal wave phenomena that arise in atom‐like quantum systems are studied. Different approaches to isolation and nonreciprocity in quantum systems are reviewed, with a focus on a specific class of passive devices where nonreciprocity is induced by the system nonlinearity, without the need of an external bias. It is then discussed how to model these effects and what their underlying physics is, outlining how the existence of a slowly‐decaying subradiant state is critical to obtain large nonreciprocal responses. The susceptibility of these devices to changes in the environment is analyzed, together with the opportunities that come from including temporal modulations.

ISWFoam: a numerical model for internal solitary wave simulation in continuously stratified fluids

Abstract. A numerical model, ISWFoam, for simulating internal solitary waves (ISWs) in continuously stratified, incompressible, viscous fluids is developed based on a fully three-dimensional (3D) Navier–Stokes equation using the open-source code OpenFOAM®. This model combines the density transport equation with the Reynolds-averaged Navier–Stokes equation with the Coriolis force, and the model discrete equation adopts the finite-volume method. The k–ω SST turbulence model has also been modified according to the variable density field. ISWFoam provides two initial wave generation methods to generate an ISW in continuously stratified fluids, including solving the weakly nonlinear models of the extended Korteweg–de Vries (eKdV) equation and the fully nonlinear models of the Dubreil–Jacotin–Long (DJL) equation. Grid independence tests for ISWFoam are performed, and considering the accuracy and computing efficiency, the appropriate grid size of the ISW simulation is recommended to be 1/150th of the characteristic length and 1/25th of the ISW amplitude. Model verifications are conducted through comparisons between the simulated and experimental data for ISW propagation examples over a flat bottom section, including laboratory scale and actual ocean scale, a submerged triangular ridge, a Gaussian ridge, and slope. The laboratory test results, including the ISW profile, wave breaking location, ISW arrival time, and the spatial and temporal changes in the mixture region, are well reproduced by ISWFoam. The ISWFoam model with unstructured grids and local mesh refinement can effectively simulate the evolution of ISWs, the ISW breaking phenomenon, waveform inversion of ISWs, and the interaction between ISWs and complex topography.

Wave breaking phenomena and global existence for the weakly dissipative generalized Camassa-Holm equation

<p style='text-indent:20px;'>In this paper, we mainly study several problems on the weakly dissipative generalized Camassa-Holm equation. We first establish the local well-posedness of solutions by Kato's semigroup theory. We then derive the necessary and sufficient condition of the blow-up of solutions and a criteria to guarantee occurrence of wave breaking. Moreover, when the solution blows up, we obtain the precise blow-up rate. We finally show that the equation has a unique global solution provided the momentum density associated with their initial datum satisfies appropriate sign conditions.</p>

Replica symmetry breaking in the RKKY skyrmion-crystal system

We study the RKKY Heisenberg model on a three-dimensional stacked-triangular lattice under magnetic fields by extensive Monte Carlo simulations to get insight into the chiral-degenerate symmetric skyrmion crystal (SkX) in centrosymmetric metallic magnets. The triple-$q$ SkX state and the double-$q$ states are realized, together with the single-$q$ state. We find an unexpected phenomenon of the replica-symmetry breaking (RSB) well-known in glassy systems, although the Hamiltonian and the ordered state are entirely regular. In the RSB SkX phase, the triple-$q$ SkX state macroscopically coexists with the single-$q$ state, in spite of the fact that these ordered states cannot be transformed via any Hamiltonian-symmetry operation. In the thermodynamic limit, the free energies of these states are degenerate whereas the free-energy barrier between the states diverges, breaking the ergodicity. A similar RSB is observed also in the RSB double-$q$ phase where the double-$q$ state macroscopically coexists with the single-$q$ state. Experimental implications are discussed.

The Bardeen–Petterson effect in accreting supermassive black hole binaries: disc breaking and critical obliquity

ABSTRACT The inspiral of supermassive black hole (BH) binaries in a gas-rich environment is driven by the presence of an accretion disc and viscous interactions tend to align the spin of the BHs with the orbital angular momentum of the disc. Recent work introduced a new iterative approach to describe the alignment process and the resulting non-linear evolution of the surrounding warped accretion disc. Their model predicted that BH spins reach either full alignment or a ‘critical obliquity’ where solutions to the warp equations cease to exist. In this paper, we show that this critical region corresponds to the disc breaking phenomenon, where the disc is disrupted into two or more discrete sections. We use 3D hydrodynamical simulations to (i) recover the predictions of the semi-analytic model and (ii) unveil a richer phenomenology where the disc exhibits either unsuccessful, single and multiple breaks. We additionally identify hydrodynamic effects such as spiral arms that are able to stabilize the disc against breaking beyond criticality. Our results show that when disc breaking occurs, the ability of BHs and disc to align is compromised and in some cases even prevented as the binary inspirals.

Post-spontaneous-symmetry-breaking power-laws after a very strong earthquake: Indication for the preparation of a new strong earthquake or not?

It has recently been found that the evolution of the preparation of a strong earthquake (EQ), as it is monitored through fracture-induced electromagnetic emissions (EME) in the MHz band, presents striking similarity with the evolution of a thermal system as temperature drops, since distinct steps of the evolution of the phenomenon of spontaneous symmetry breaking (SSB) can be identified. Here, the study of fracture-induced EME in the MHz band in analogy to thermal systems is extended to the phase of local fracture structures that follow after the SSB (and the occurrence of the main EQ). By comparing fracture-induced MHz EME associated with the strongest EQs (MW=6.9) that occurred in Greece during the last twenty years with the 3D Ising model, a way to distinguish whether a possible identification of post-SSB power-laws immediately after a very strong EQ is a sign for the preparation of a new strong EQ or not is provided. In the suggested approach, the time series analysis method known as the method of critical fluctuations is used, enhanced by the autocorrelation function.

Controlling Resonator Nonlinearities and Modes through Geometry Optimization.

Controlling the nonlinearities of MEMS resonators is critical for their successful implementation in a wide range of sensing, signal conditioning, and filtering applications. Here, we utilize a passive technique based on geometry optimization to control the nonlinearities and the dynamical response of MEMS resonators. Also, we explored active technique i.e., tuning the axial stress of the resonator. To achieve this, we propose a new hybrid shape combining a straight and initially curved microbeam. The Galerkin method is employed to solve the beam equation and study the effect of the different design parameters on the ratios of the frequencies and the nonlinearities of the structure. We show by adequately selecting the parameters of the structure; we can realize systems with strong quadratic or cubic effective nonlinearities. Also, we investigate the resonator shape effect on symmetry breaking and study different linear coupling phenomena: crossing, veering, and mode hybridization. We demonstrate the possibility of tuning the frequencies of the different modes of vibrations to achieve commensurate ratios necessary for activating internal resonance. The proposed method is simple in principle, easy to fabricate, and offers a wide range of controllability on the sensor nonlinearities and response.