Gaussian Field Research Articles

Propagation behaviors of two-dimensional chirped finite-energy Pearcey beams in free space

Abstract We introduce a two-dimensional chirped finite energy Pearcey beams (FEPB) for the first time and investigate the propagation dynamics. First, we applied Huygens-Fresnel integral to derive an explicit analytical expression which is suitable for describing FEPB propagation in free space. It is interesting to find that FEPB will experience three typical propagation patterns, i.e., single-autofocusing case, dual-autofocusing case and non-autofocusing diffraction case, only depending on the value of the input asymmetric chirp. We further arrive at the critical condition of such three patterns analytically. However, another input symmetric chirp acts to strengthen or weaken the autofocusing intensity through changing the former sign, but does not affect the focal distance. Our findings denote that two-dimensional chirped FEPB can pave another prospective wave in controlling linear self-focusing and the optical particle manipulation, when compared with the corresponding Airy field or conventional Gaussian field.

From inflation to dark matter halo profiles: the impact of primordial non-Gaussianities on the central density cusp

It has recently been shown that local primordial non-Gaussianities (PNG) with significant amplitude (|f NL| ∼ 1000), at small (Mpc) scales, can help in forming simulated galaxies with more disky baryonic kinematics than in the Gaussian case, while generating matter power spectra that can differ by up to 20% from the Gaussian case at non-linear scales. Here, we explore in detail the consequences of such small-scale PNG on the dark matter halo profiles. We show in particular that, for negative f NL, dark matter halos formed in collisionless simulations are not always well described by the traditional Navarro-Frenk-White (NFW) profiles, as supported by their sparsity distribution. We conclude that NFW profiles are not as clear attractors for the density profiles of dark matter halos in the presence of PNG than in the case of a Gaussian contrast density field. We show how alternatives to the NFW profile can describe halos both in the Gaussian and non-Gaussian cases. From the combination of our sparsity analysis and the quality of the adjustments of the density profiles with a minimal extension to NFW, we conclude that z = 1 halos carry the most interesting information about PNG.

A central limit theorem for the number of excursion set components of Gaussian fields

A central limit theorem for the number of excursion set components of Gaussian fields

Percolation of strongly correlated Gaussian fields II. Sharpness of the phase transition

Percolation of strongly correlated Gaussian fields II. Sharpness of the phase transition

Extracting high-order cosmological information in galaxy surveys with power spectra

The reconstruction method was proposed more than a decade ago to boost the signal of baryonic acoustic oscillations measured in galaxy redshift surveys, which is one of key probes for dark energy. After moving the observed overdensities in galaxy surveys back to their initial position, the reconstructed density field is closer to a linear Gaussian field, with higher-order information moved back into the power spectrum. We find that by jointly analysing power spectra measured from the pre- and post-reconstructed galaxy samples, higher-order information beyond the 2-point power spectrum can be efficiently extracted, which generally yields an information gain upon the analysis using the pre- or post-reconstructed galaxy sample alone. This opens a window to easily use higher-order information when constraining cosmological models.

A Ray–Knight theorem for $$\nabla \phi $$ interface models and scaling limits

AbstractWe introduce a natural measure on bi-infinite random walk trajectories evolving in a time-dependent environment driven by the Langevin dynamics associated to a gradient Gibbs measure with convex potential. We derive an identity relating the occupation times of the Poissonian cloud induced by this measure to the square of the corresponding gradient field, which—generically—is not Gaussian. In the quadratic case, we recover a well-known generalization of the second Ray–Knight theorem. We further determine the scaling limits of the various objects involved in dimension 3, which are seen to exhibit homogenization. In particular, we prove that the renormalized square of the gradient field converges under appropriate rescaling to the Wick-ordered square of a Gaussian free field on $$\mathbb R^3$$ R 3 with suitable diffusion matrix, thus extending a celebrated result of Naddaf and Spencer regarding the scaling limit of the field itself.

The number of critical points of a Gaussian field: finiteness of moments

The number of critical points of a Gaussian field: finiteness of moments

Temperature field of non-Oberbeck–Boussinesq Rayleigh–Bénard convection in a low aspect ratio cell

A time-resolved experimental investigation was undertaken on the temperature evolution of Rayleigh–Bénard convection (RBC) in a slender convection cell with aspect ratio of Γ=0.1. Experiments were conducted for Rayleigh numbers of Ra=5.3×107, 7.6×107, and 9.5×107 and Prandtl number of Pr≈6 within the non-Oberbeck–Boussinesq (NOB) condition with a temperature difference variation in the range of 30 °C≤ΔT≤40 °C. Measurement of the temperature was by applying time-resolved two-color planar laser-induced fluorescence over the initial 2400 s. Experimental observations showed that the lateral confinement of the convection cell leads to the development of a single large-scale thermal plume instead of multiple plumes. Results showed that contrary to expectations, lateral confinement was found to be ineffective in suppressing temperature oscillations near thermal boundaries. Results also indicated that for Ra=5.3×107, 7.6×107, the temperature oscillations had a frequency of f≈0.028 Hz similar to the frequency of the oscillations in Oberbeck–Boussinesq (OB) RBC. For Ra=9.5×107, however, it was found that the frequency of the oscillations was much lower than the OB RBC with a relatively wide range of the oscillations in the vicinity of f≈0.006 Hz. It is also found that the lateral confinement and formation of singular high-energy thermal plumes leads to an increase in the nonsymmetrical temperature distribution of NOB RBC with a bimodal distribution of the temperature field, deviating significantly from the Gaussian distribution temperature field found in OB RBC.

Learning Networks from Gaussian Graphical Models and Gaussian Free Fields

Learning Networks from Gaussian Graphical Models and Gaussian Free Fields

Stochastic thermodynamics of a probe in a fluctuating correlated field

We develop a framework for the stochastic thermodynamics of a probe coupled to a fluctuating medium with spatio-temporal correlations, described by a scalar field. For a Brownian particle dragged by a harmonic trap through a fluctuating Gaussian field, we show that near criticality (where the field displays long-range spatial correlations) the spatially-resolved average heat flux develops a dipolar structure, where heat is absorbed in front and dissipated behind the dragged particle. Moreover, a perturbative calculation reveals that the dissipated power displays three distinct dynamical regimes depending on the drag velocity.

Azimuthal modulation of light propagation through 1DPCs via efficient nonlinear frequency mixing

The present study aims to investigate the transmitted and reflected light beams from a one-dimensional defect photonic crystal (1DPC) composed of a three-level ladder-type quantum system. The lower leg of the ladder scheme is driven by a weaker probe beam, while the upper leg is driven by a stronger control beam. Unlike natural atoms, this type of model with broken symmetry permits the generation of a sum-frequency signal beam between the majority of higher and lower quantum states, resulting in the formation of a cyclic closed-loop arrangement for the interaction between light and matter. The Laguerre Gaussian (LG) field with strong coupling and a weak probe light interact with the quantum system. A new weak signal light is produced as a result of the system’s symmetric breakdown, and the medium becomes azimuthal dependent. We investigate the spatial dependence of the transmitted and reflected light from a defect 1DPC by using azimuthal modulation of the LG light. Additionally, we will discuss how the absorption spectrum’s spatial modulation varies with winding numbers. We discover that in certain regions, the gain can be realized without population inversion under certain specified parametric parameters.

Smooth Matérn Gaussian random fields: Euler characteristic, expected number and height distribution of critical points

This paper studies Gaussian random fields with Matérn covariance functions with smooth parameter ν>2. Two cases of parameter spaces, the Euclidean space and N-dimensional sphere, are considered. For such smooth Gaussian fields, we have derived the explicit formulae for the expected Euler characteristic of the excursion set, the expected number and height distribution of critical points. The results are valuable for approximating the excursion probability in family-wise error control and for computing p-values in peak inference.

Damage recovery in composite laminates through deep learning from acoustic scattering of guided waves

We propose an innovative deep learning (DL) regression strategy combined with guided wave modes to address inverse acoustic scattering problems effectively. This approach allows for accurate recovery of heterogeneous defect fields at the interfaces of composite laminates. The neural network (NN) model’s training process employs stochastic Gaussian fields as output, which are linked to the interfacial defect fields of the physical problem. Our method assumes prior knowledge of the material geometrical properties of the constituent layers. To model the interfaces, we utilize the Quasi-Static Approximation, a technique generating position-dependent interfacial stiffness matrices containing uncoupled normal and tangential springs. We validate our approach by assessing its performance in handling noisy input data and reduced models, as well as accounting model errors at the composite interface. The obtained results show that the proposed method has a remarkable generalization capability, allowing it to recover diverse defect field profiles with accuracy. Moreover, it exhibits robustness concerning noisy data and model errors. Lastly, thanks to the guided wave modes approach, the presented methodology not only maintains its capability to recover heterogeneous defect fields potentially in real-time but also extends the range of inspection to encompass a significantly larger structural area.

The effect of misalignment on the coupling optics involving laser diode and single-mode triangular index fiber with an upside down tapered hyperbolic microlens on its tip

Abstract This article contains theoretical investigation of the performance of the coupler comprising laser diode and mono-mode circular core triangular index fiber (TIF), which contains on its tip an upside down tapered hyperbolic microlens (UDTHM). Here, we take care of probable angular and transverse mismatches. In our derivation, we use the refractive index distribution in the tapering area, the ray equation, and the relation involving refraction by hyperbolic microlens. We report analytical formulation of coupling efficiencies in the presence of specified types of misalignments using a relevant ABCD refraction matrix for a UDTHM in the vertical plane. In the fields of lasers and fibers, we use Gaussian field distribution in our analysis. Our research is based on two widely employed wavelengths, 1.3 µm and 1.5 µm. In this study, we used three TIF with V numbers of 4.380, 3.511, and 1.924, respectively. Little computation is required to execute the prescribed formulations. This study surfaces the sensitivity of the coupler in presence of the aforementioned types of offsets. The found results will prove valuable to manufacturers working in the domain of UDTHM.

The subadditivity of quantum entropy in Gaussian quantum systems

The entropy of a quantum state measures information or uncertainty contained in the quantum system and plays a crucial role in quantum information theory. Many entropic properties, such as the subadditivity, have been studied for the discrete system with a finite-dimensional state space, while much less is explored in the infinite-dimensional system. In this work, we study the entropic properties of the continuous system that models a collection of Gaussian modes or fields. In particular, we identify the parameter range for the Rényi, Tsallis, and Unified entropies of Gaussian states that they are additive, subadditive, and strong subadditive. We show that the Rényi entropies are subadditive, further giving rise to the subadditivity of the Tsallis and Unified entropies in certain parameter range. We also find that the Tsallis and Unified entropies are not strong subadditive, while the Rényi entropies with the order ranging from 1 to 2 are conjectured to admit the strong subadditivity. Our results are useful in studying quantum correlations and channel capacities in Gaussian systems.

Voltage-controlled two-dimensional Fresnel diffraction pattern in quantum dot molecules

This study explores the influence of inter-dot tunneling effects within a quantum dot molecule on the Fresnel diffraction phenomenon. Our findings indicate that the Fresnel diffraction of the output probe Gaussian field can be manipulated by adjusting the inter-dot tunneling parameter’s strength and the characteristics of the coupling field. The inter-dot tunneling effect establishes a closed-loop system, setting conditions for the interference of the applied fields. We specifically examine a Laguerre–Gaussian (LG) coupling field, investigating how its properties-such as strength, value, and sign of the orbital angular momentum (OAM)-impact the Fresnel diffraction of the output probe field. Increasing the inter-dot tunneling parameter and the coupling LG field’s strength allows for control over the spatial distribution of the Fresnel diffraction pattern. Notably, the inter-dot tunneling parameter can disturb the symmetry of the diffraction patterns. Additionally, considering a negative OAM for the coupling LG field transforms the diffraction pattern into its inverse shape. This suggests that, in the presence of the inter-dot tunneling effect, the Fresnel diffraction pattern is contingent on the direction of rotation of the helical phase front of the coupling LG field. Our results offer insights into quantum control of Fresnel diffraction patterns and the identification of OAM in LG beams, presenting potential applications in quantum technologies.

Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields

Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields

Anisotropic internal fields behavior in La[formula omitted]Sr[formula omitted]CuO4 ([formula omitted]): Precursor to the spin glass state revealed by muon spin relaxation

In this study, we conducted a zero-field muon spin experiment on slightly doped La2−xSrxCuO4 from 200 K down to near the spin glass temperature (TSG). Utilizing pulsed muon beams with longer time spectra, we investigated the interplay between dynamic and static fields, which influenced the lineshapes of the nuclear dipole field. Our results reveal the emergence and growth of a Lorentzian field associated with localized moments, coexisting with nuclear Gaussian field anisotropy, as the temperature approaches TSG. This behavior of the internal fields may serve as a precursor to the spin glass state. The findings are consistent with a theoretical model that describes the electric field gradient required to characterize the spin glass state.

Asymptotic distribution of nodal intersections for ARW against a surface

We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal intersection length against a fixed regular reference surface. Expectation and variance have been addressed by Maffucci [Ann. Henri Poincaré 20(11), 3651–3691 (2019)] who found that the expected length is proportional to the square root of the eigenvalue times the area of the surface, while the asymptotic variance only depends on the geometry of the surface, the projected lattice points being equidistributed on the two-dimensional unit sphere in the high-energy limit. He also noticed that there are “special” surfaces, so-called static, for which the variance is of smaller order; however he did not prescribe the precise asymptotic law in this case. In this paper, we study second order fluctuations of the nodal intersection length. Our first main result is a Central Limit Theorem for “generic” surfaces, while for static ones, a sphere or a hemisphere e.g., our main results are a non-Central Limit Theorem and a precise asymptotic law for the variance of the nodal intersection length, conditioned on the existence of so-called well-separated sequences of Laplacian eigenvalues. It turns out that, in this regime, the nodal area investigated by Cammarota [Trans. Am. Math. Soc. 372(5), 3539–3564 (2019)] is asymptotically fully correlated with the length of the nodal intersections against any sphere. The main ingredients for our proofs are the Kac-Rice formula for moments, the chaotic decomposition for square integrable functionals of Gaussian fields, and some arithmetic estimates that may be of independent interest.

Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative

Focusing on the redshift space observations with plane-parallel approximation and relying on the rotational dependency of the general definition of excursion sets, we introduce the so-called conditional moments of the first derivative (cmd) measures for the smoothed matter density field in three dimensions. We derive the perturbative expansion of cmd for the real space and redshift space where peculiar velocity disturbs the galaxies’ observed locations. Our criteria can successfully recognize the contribution of linear Kaiser and Finger-of-God effects. Our results demonstrate that the cmd measure has significant sensitivity for pristine constraining the redshift space distortion parameter β = f/b and interestingly, the associated normalized quantity in the Gaussian linear Kaiser limit has only β dependency. Implementation of the synthetic anisotropic Gaussian field approves the consistency between the theoretical and numerical results. Including the first-order contribution of non-Gaussianity perturbatively in the cmd criterion implies that the N-body simulations for the Quijote suite in the redshift space have been mildly skewed with a higher value for the threshold greater than zero. The non-Gaussianity for the perpendicular direction to the line of sight in the redshift space for smoothing scales R ≳ 20 Mpc h −1 is almost the same as in the real space. In contrast, the non-Gaussianity along the line-of-sight direction in the redshift space is magnified. The Fisher forecasts indicate a significant enhancement in constraining the cosmological parameters Ω m , σ 8, and n s when using cmd + cr jointly.