Higher-dimensional chaotic features and random matrix signatures following a local quench

• URL: http://arxiv.org/abs/2607.05512v1
• Date: Mon, 06 Jul 2026 18:00:06 GMT
• Title: Higher-dimensional chaotic features and random matrix signatures following a local quench
• Abstract summary: We study the multidimensional structure of correlation functions produced by local operator quenches in free massive field theory.<n>We analyze extrema by the multidimensional diagnostics recently introduced for chaotic scatterings and related problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the multidimensional erratic structure of correlation functions produced by local operator quenches in finite-volume free massive scalar field theory in dimensions 2 and 3. The basic observable is the subtracted equal-time two-point function in the locally excited state and its spatiotemporal patterns of extrema. We analyze these extrema by the multidimensional diagnostics recently introduced for chaotic scattering amplitudes and related problems: all-pair distance distributions, nearest-neighbor spacings, greedy-path spacing ratios, and the extrema form factor. For the $1+1$-dimensional local quench we find that, in the regime of small Euclidean smearing, the fitted extremum statistics move close to the $β=1$ random-matrix benchmark, while increasing the smearing scale softens the effective repulsion and moves the distributions away from the GOE-like value. For the $2+1$-dimensional local quench we find that the nearest-neighbor statistics of the refined extrema are close to, or above, the $β=1$ benchmark, and the greedy-path ratio statistics are described by even larger effective $β$ values. Finally we studied the all-pair extrema spatial form factor and found that, in the one-, two-, and three-dimensional cases, its main structure is controlled by the corresponding uniform interval, rectangle, or cuboid geometry of the extrema cloud and found the dip-ram-plateau structure in the last two cases. Thus the form factor provides a complementary global diagnostic of how the extrema fill their effective metric support, while the genuinely nontrivial local and mesoscopic organization is carried by the nearest-neighbor and greedy-path statistics.

Related papers

• Riemannian ascent--descent for nonconvex nonconcave minimax landscapes: convergence to basin saddle points and applications to distributionally robust optimization [1.0195618602298684]
  We study minimax problems over a gradient of a geodesicean space and a Buresian manifold.<n>Because no globally convergent order first method is known to be available, we instead introduce the notion of a emphbasin saddle point.
  arXiv  Detail & Related papers  (2026-09-12T20:42:11Z)
• Complex spacing ratio statistics in the partially open asymmetric quantum baker map [36.94429692322632]
  We study the complex eigenvalue statistics of the asymmetric quantum baker map with partial projective openings.<n>We find a smooth crossover from a quasi-1D spectral regime, where eigenvalues cluster near the unit circle and the phase distribution of $z$ is peaked.<n>Both the number of open channels $M$ and the reflectivity $$ modulate this crossover, and $$ provides an additional continuous control even at fixed opening size.
  arXiv  Detail & Related papers  (2026-07-08T19:24:35Z)
• Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical $k$-Spin Complexity [0.6627152091494143]
  This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale random field on the sphere.<n>It applies it to two problems: Spiked PCA and the landscape of the spherical $k$-spin model.
  arXiv  Detail & Related papers  (2026-06-16T08:27:25Z)
• Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds [61.14405512940818]
  We show that Score-based generative models are trained in high-dimensional ambient spaces.<n>We use a ReLU implementation of nearest-projection coordinates via finite intrinsic anchors and Gauss Newton.
  arXiv  Detail & Related papers  (2026-05-15T10:20:05Z)
• Faster 3D Gaussian Splatting Convergence via Structure-Aware Densification [52.517763621139956]
  3D Gaussian Splatting has emerged as a powerful scene representation for real-time novel-view synthesis.<n>Standard adaptive density control relies on screen-space positional gradients.<n>We present a structure-aware densification framework for 3D Gaussian Splatting.
  arXiv  Detail & Related papers  (2026-04-30T15:37:20Z)
• Curvature-Aligned Probing for Local Loss-Landscape Stabilization [0.7090165638014331]
  Local loss-landscape stabilization under sample growth is typically measured either pointwise or through isotropic averaging in the full parameter space.<n>We recast stabilization as an observational problem and introduce a unified family of criteria parameterized by an aggregation order and a probing distribution.<n>We derive scalable estimators based on Hessian-vector products, subspace Monte Carlo, and a closed-form-moment proxy.
  arXiv  Detail & Related papers  (2026-04-16T11:01:48Z)
• Dimension-Independent Convergence of Underdamped Langevin Monte Carlo in KL Divergence [50.719298242863744]
  Underdamped Langevin dynamics (ULD) is a widely-used sampler for Gibbs distributions $propto e-V$.<n>We prove the first dimension-free KL divergence bounds for discretized ULD.
  arXiv  Detail & Related papers  (2026-03-02T22:14:38Z)
• Multiscale scattered data analysis in samplet coordinates [0.0]
  We study multiscale data scattered schemes for globally supported radial basis functions with focus on the Mat'ern class.<n>We prove that the condition numbers of the the diagonal blocks of the corresponding multiscale system remain bounded independently of the particular level.<n>We exploit this fact to derive a general error estimate bounding the consistency error issuing from a numerical approximation of the multiscale system.
  arXiv  Detail & Related papers  (2024-09-23T08:07:47Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
  localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet. We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
  arXiv  Detail & Related papers  (2022-05-29T16:53:20Z)
• Universality in Anderson localization on random graphs with varying connectivity [0.0]
  We show that there should be a non-ergodic region above a given value of disorder $W_E$. Although no separate $W_E$ exists from $W_C$, the length scale at which fully developed ergodicity is found diverges like $|W-W_C|-1$. The separation of these two scales at the critical point allows for a true non-ergodic, delocalized region.
  arXiv  Detail & Related papers  (2022-05-29T09:47:39Z)
• Mean-Square Analysis with An Application to Optimal Dimension Dependence of Langevin Monte Carlo [60.785586069299356]
  This work provides a general framework for the non-asymotic analysis of sampling error in 2-Wasserstein distance. Our theoretical analysis is further validated by numerical experiments.
  arXiv  Detail & Related papers  (2021-09-08T18:00:05Z)
• The role of regularization in classification of high-dimensional noisy Gaussian mixture [36.279288150100875]
  We consider a high-dimensional mixture of two Gaussians in the noisy regime. We provide a rigorous analysis of the generalization error of regularized convex classifiers. We discuss surprising effects of the regularization that in some cases allows to reach the Bayes-optimal performances.
  arXiv  Detail & Related papers  (2020-02-26T14:54:28Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.