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Related papers: Variations on a Theme of Krylov

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We develop a new technique for establishing quantitative propagation of chaos for systems of interacting particles. Using this technique we prove propagation of chaos for diffusing particles whose interaction kernel is merely H\"older…

Analysis of PDEs · Mathematics 2016-12-09 Thomas Holding

We show that the intermittent and self-similar fluctuations displayed by a slow crack during the propagation in a heterogeneous medium can be quantitatively described by an extension of a classical statistical model for fracture. The model…

Disordered Systems and Neural Networks · Physics 2013-01-24 G. Pontuale , F. Colaiori , A. Petri

We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to…

Quantum Physics · Physics 2025-01-30 Philippe Suchsland , Roderich Moessner , Pieter W. Claeys

The Krylov subspace projection approach is a well-established tool for the reduced order modeling of dynamical systems in the time domain. In this paper, we address the main issues obstructing the application of this powerful approach to…

Mathematical Physics · Physics 2012-04-16 Vladimir Druskin , Rob Remis

We compute the circuit complexity of scalar curvature perturbations on FLRW cosmological backgrounds with fixed equation of state $w$ using the language of squeezed vacuum states. Backgrounds that are accelerating and expanding, or…

High Energy Physics - Theory · Physics 2020-08-24 Arpan Bhattacharyya , Saurya Das , S. Shajidul Haque , Bret Underwood

We introduce a ``spatial'' Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that…

chao-dyn · Physics 2009-10-31 M. Falcioni , D. Vergni , A. Vulpiani

Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a…

Quantum Physics · Physics 2023-09-20 Pietro Brighi , Marko Ljubotina , Maksym Serbyn

In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…

High Energy Physics - Theory · Physics 2023-06-09 Kiran Adhikari , Sayantan Choudhury

Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled…

Soft Condensed Matter · Physics 2018-07-04 Omer Gottesman , Jovana Andrejevic , Chris H. Rycroft , Shmuel M. Rubinstein

Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open…

General Relativity and Quantum Cosmology · Physics 2026-02-27 Shi-Cheng Liu , Lei-Hua Liu , Bichu Li , Hai-Qing Zhang , Peng-Zhang He

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…

Chaotic Dynamics · Physics 2011-09-14 Diego F. M. Oliveira , Marko Robnik , Edson D. Leonel

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

Statistical Mechanics · Physics 2026-02-23 Edson D. Leonel , Diego F. M. Oliveira

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level…

Statistical Mechanics · Physics 2023-08-23 D. Szász-Schagrin , B. Pozsgay , G. Takács

In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…

Statistical Mechanics · Physics 2024-11-26 Wen-Yu Su , Yu-Jing Liu , Nvsen Ma , Chen Cheng

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This…

Strongly Correlated Electrons · Physics 2018-09-26 Adolfo del Campo , Javier Molina Vilaplana , Lea F. Santos , Julian Sonner

A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…

chao-dyn · Physics 2009-10-28 A. Torcini , P. Grassberger , A. Politi

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…

Statistical Mechanics · Physics 2019-05-21 Bruno Bertini , Pavel Kos , Tomaz Prosen

We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…

Fluid Dynamics · Physics 2025-12-08 Mrinal Jyoti Powdel , Samriddhi Sankar Ray

The main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent Hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating…

Symplectic Geometry · Mathematics 2007-05-23 Paul Biran , Leonid Polterovich , Dietmar Salamon

The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…

Probability · Mathematics 2019-01-30 Marc Arnaudon , Pierre Del Moral