Inertia triggers nonergodicity of fractional Brownian motion

How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared displacement (MSD) to the time-averaged MSD (TAMSD) of overdamped or massless FBM, but also concurrently dramatically alter the values of the ergodicity breaking parameter (EB). Our theoretical results for the behavior of EB for underdamped ot massive FBM for varying particle mass m, Hurst exponent H, and trace length T are in excellent agreement with the findings of extensive stochastic computer simulations. The current results can be of interest for the experimental community employing various single-particle-tracking techniques and aiming at assessing the degree of nonergodicity for the recorded time series (studying e.g. the behavior of EB versus lag time). To infer FBM as a realizable model of anomalous diffusion for a set single-particle-tracking data when massive particles are being tracked, the EBs from the data should be compared to EBs of massive (rather than massless) FBM.

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does the process of stochastic resetting impact nonergodicity? These are the main questions addressed in this study. Specifically, we examine, both analytically and by stochastic simulations, the implications of resetting on the MSD-and TAMSD-based spreading dynamics of fractional Brownian motion (FBM) with a long-time memory, of heterogeneous diffusion processes (HDPs) with a power-law-like space-dependent diffusivity D(x) = D0 |x| γ, and of their “combined” process of HDP-FBM. We find, i.a., that the resetting dynamics of originally ergodic FBM for superdiffusive choices of the Hurst exponent develops distinct disparities in the scaling behavior and magnitudes of the MSDs and mean TAMSDs, indicating so-called weak ergodicity breaking (WEB). For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD, and additionally observe a new trimodal form of the probability density function (PDF) of particle’ displacements. For all three reset processes (FBM, HDPs, and HDP-FBM) we compute analytically and verify by stochastic computer simulations the short-time (normal and anomalous) MSD and TAMSD asymptotes (making conclusions about WEB) as well as the long-time MSD and TAMSD plateaus, reminiscent of those for “confined” processes. We show that certain characteristics of the reset processes studied are functionally similar, despite the very different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity breaking parameter EB as a function of the resetting rate r. For all the reset processes studied, we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB ∼ (1/r)-decay at large r values. Together with the emerging MSD-versus-TAMSD disparity, this pronounced r-dependence of the EB parameter can be an experimentally testable prediction. We conclude via discussing some implications of our results to experimental systems featuring resetting dynamics.

ABJ correlators with weakly broken higher spin symmetry

We consider four-point functions of operators in the stress tensor multiplet of the 3d $$ \mathcal{N} $$ N = 6 U(N)k× U(N + M)−k or SO(2)2k× USp(2 + 2M)−k ABJ theories in the limit where M and k are taken to infinity while N and λ ∼ M/k are held fixed. In this limit, these theories have weakly broken higher spin symmetry and are holographically dual to $$ \mathcal{N} $$ N = 6 higher spin gravity on AdS4, where λ is dual to the bulk parity breaking parameter. We use the weakly broken higher spin Ward identities, superconformal Ward identities, and the Lorentzian inversion formula to fully determine the tree level stress tensor multiplet four-point function up to two free parameters. We then use supersymmetric localization to fix both parameters for the ABJ theories in terms of λ, so that our result for the tree level correlator interpolates between the free theory at λ = 0 and a parity invariant interacting theory at λ = 1/2. We compare the CFT data extracted from this correlator to a recent numerical bootstrap conjecture for the exact spectrum of U(1)2M× U(1 + M)−2M ABJ theory (i.e. λ = 1/2 and N = 1), and find good agreement in the higher spin regime.

Atomic-layer Rashba-type superconductor protected by dynamic spin-momentum locking

Spin-momentum locking is essential to the spin-split Fermi surfaces of inversion-symmetry broken materials, which are caused by either Rashba-type or Zeeman-type spin-orbit coupling (SOC). While the effect of Zeeman-type SOC on superconductivity has experimentally been shown recently, that of Rashba-type SOC remains elusive. Here we report on convincing evidence for the critical role of the spin-momentum locking on crystalline atomic-layer superconductors on surfaces, for which the presence of the Rashba-type SOC is demonstrated. In-situ electron transport measurements reveal that in-plane upper critical magnetic field is anomalously enhanced, reaching approximately three times the Pauli limit at T = 0. Our quantitative analysis clarifies that dynamic spin-momentum locking, a mechanism where spin is forced to flip at every elastic electron scattering, suppresses the Cooper pair-breaking parameter by orders of magnitude and thereby protects superconductivity. The present result provides a new insight into how superconductivity can survive the detrimental effects of strong magnetic fields and exchange interactions.

Novel thick brane solutions with U(1) symmetry breaking

In this work, using two scalar fields ($$\phi $$ ϕ , $$\psi $$ ψ ) coupled to 4 + 1 dimensional gravity, we construct novel topological brane solutions through an explicit U(1) symmetry breaking term. The potential of this model is constructed so that two distinct degenerate vacua in the $$\phi $$ ϕ field exist, in analogy to the $$\phi ^{4}$$ ϕ 4 potential. Therefore, brane solutions appear due to the vacuum structure of the $$\phi $$ ϕ field. However, the topology and vacuum structure in the $$\psi $$ ψ direction depends on the symmetry breaking parameter $$\beta ^{2}$$ β 2 , which leads to different types of branes. As a result, one can interpret the present model as a combination of a $$\phi ^{4}$$ ϕ 4 brane with an auxiliary field, which leads to deviations from the $$\phi ^{4}$$ ϕ 4 system with the brane achieving a richer internal structure. Furthermore, we analyse in detail the behaviour of the superpotentials, the warp factors, the Ricci and Kretschmann scalars and the Einstein tensor components. In addition to this, we explore the stability of the brane in terms of the free parameters of the model. The analysis presented here complements previous work and is sufficiently novel to be interesting.

The Primary Breaking Pattern of Main Roof Above the First Working Face Based on Main Bending Moment

Scientific mining is based on breaking regularity of roof above underground working face in coal mine. In order to explore the primary breaking pattern of main roof above the first working face, on account of theory of thin elastic plate, development of the breaking in each region of main roof is analyzed and the breaking sequence of each region is explored in virtue of main bending moment taken as the breaking parameter. The results indicate that the first broken point of main roof is midpoint of the long side. The breaking, which occurs on the top surface of main roof, is caused by the second main bending moment. The fracture in long side region starts from midpoint of the long side and develops along the length direction of the working face. The fracture in middle region starts from the center of main roof and develops along the length direction of the working face. The fracture in short side region starts from midpoint of the short side and develops along advance direction of the working face. There always is an extreme value order of control moment in each region, Mc > Mz > Md, when a single parameter is within a reasonable range. Due to this, the breaking sequence is the long side region, the middle region and the short side region although they end up with the same breaking pattern O-X. Mc, Mz and Md depend on the advance distance of working face and increase linearly with transverse loading. Besides, the short side of main roof becomes stable with the increase of the length of working face. Revealing the primary breaking pattern of main roof above the first working face contributes to learning breaking behavior of main roof and providing theoretical support for design of the working face and roof management.

Vacuum energy of the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion

By employing the $1/N$ expansion, we compute the vacuum energy $E(\delta\epsilon)$ of the two-dimensional supersymmetric (SUSY) $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ with $\mathbb{Z}_N$ twisted boundary conditions to the second order in a SUSY-breaking parameter $\delta\epsilon$. This quantity was vigorously studied recently by Fujimori et al. using a semi-classical approximation based on the bion, motivated by a possible semi-classical picture on the infrared renormalon. In our calculation, we find that the parameter $\delta\epsilon$ receives renormalization and, after this renormalization, the vacuum energy becomes ultraviolet finite. To the next-to-leading order of the $1/N$ expansion, we find that the vacuum energy normalized by the radius of the $S^1$, $R$, $RE(\delta\epsilon)$ behaves as inverse powers of $\Lambda R$ for $\Lambda R$ small, where $\Lambda$ is the dynamical scale. Since $\Lambda$ is related to the renormalized ’t Hooft coupling $\lambda_R$ as $\Lambda\sim e^{-2\pi/\lambda_R}$, to the order of the $1/N$ expansion we work out, the vacuum energy is a purely non-perturbative quantity and has no well-defined weak coupling expansion in $\lambda_R$.

Wave and Hydrodynamic Processes in the Vicinity of a Rubble-Mound, Permeable, Zero-Freeboard Breakwater

A numerical study for the effect of crest width, breaking parameter, and trunk permeability on hydrodynamics and flow behavior in the vicinity of rubble-mound, permeable, zero-freeboard breakwaters (ZFBs) is presented. The modified two-dimensional Navier-Stokes equations for two-phase flows in porous media with a Smagorinsky model for the subgrid scale stresses were solved numerically. An immersed-boundary/level-set method was used. The numerical model was validated for the cases of wave propagation over a submerged impermeable trapezoidal bar and a low-crested permeable breakwater. Five cases of breakwaters were examined, and the main results are: (a) The size of the crest width, B, does not notably affect the wave reflection, vorticity, and currents in the seaward region of ZFBs, while wave transmission, currents in the leeward side, and mean overtopping discharge all decrease with increasing B. A non-monotonic behavior of the wave setup is also observed. (b) As the breaking parameter decreases, wave reflection, transmission, currents, mean overtopping discharge, and wave setup decrease. This observation is also verified by relevant empirical formulas. (c) As the ZFB trunk permeability decreases, an increase of the wave reflection, currents, wave setup, and a decrease of wave transmission and mean overtopping discharge is observed.

Wave and Hydrodynamic Processes in the Vicinity of a Rubble-mound, Permeable, Zero-freeboard Breakwater

A numerical study for the effect of crest width, breaking parameter and trunk permeability on hydrodynamics and flow behavior in the vicinity of rubble-mound, permeable, zero-freeboard breakwaters (ZFBs) is presented. The modified two dimensional Navier-Stokes equations for two-phase flows in porous media with a Smagorinsky model for the subgrid scale stresses were solved numerically. An immersed-boundary/level-set method was used. The numerical model was validated for the cases of wave propagation over a submerged impermeable trapezoidal bar and over a low-crested permeable breakwater. Five cases of breakwaters were examined, and the main results are: (a) The size of the crest width, B, does not notably affect the wave reflection, vorticity and currents in the seaward region of ZFBs, while wave transmission, currents in the leeward side, and mean overtopping discharge, all decrease with increasing B. A non-monotonic behavior of the wave setup is also observed. (b) As the breaking parameter decreases, wave reflection, transmission, currents, mean overtopping discharge, and wave setup decrease. This observation is also verified by relevant empirical formulas. (c) As the ZFB trunk permeability decreases, an increase of the wave reflection, currents, wave setup, and a decrease of wave transmission and mean overtopping discharge is observed.