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Related papers: Lyapunov growth in quantum spin chains

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We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved…

Statistical Mechanics · Physics 2023-04-18 Naoyuki Shibata , Hosho Katsura

We study the spatiotemporal dynamics of random spatially distributed noninfinitesimal perturbations in one-dimensional chaotic extended systems. We find that an initial perturbation of finite size $\epsilon_0$ grows in time obeying the…

Chaotic Dynamics · Physics 2009-11-10 Juan M. Lopez , Cristina Primo , Miguel A. Rodriguez , Ivan G. Szendro

We demonstrate that a quantum field theory (QFT) in general two-dimensional curved spacetimes can be realized by a system of quantum spins or qubits. We consider a spin-1/2 model on a one-dimensional ring with spatially and temporally…

High Energy Physics - Theory · Physics 2025-05-28 Shunichiro Kinoshita , Keiju Murata , Daisuke Yamamoto , Ryosuke Yoshii

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase-space. A recent numerical study of spatially-extended systems…

Chaotic Dynamics · Physics 2013-12-02 Diego Pazó , Juan M. López , Antonio Politi

Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…

Chaotic Dynamics · Physics 2016-12-21 Kenji Shinoda , Kunihiko Kaneko

We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$…

Mathematical Physics · Physics 2022-01-25 Michael Aizenman , Hugo Duminil-Copin

The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…

Strongly Correlated Electrons · Physics 2026-03-17 Mandev Bhullar , Philip Richard , Hae-Young Kee

This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of…

chao-dyn · Physics 2009-10-28 Lapo Casetti , Cecilia Clementi , Marco Pettini

Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a…

Quantum Physics · Physics 2025-07-08 E. Medina-Guerra , I. V. Gornyi , Yuval Gefen

For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann and Jensen. We have…

High Energy Physics - Lattice · Physics 2009-11-10 P. Butera , M. Comi , A. J. Guttmann

We compute semi-analytic and numerical estimates for the largest Lyapunov exponent in a many-particle system with long-range interactions, extending previous results for the Hamiltonian Mean Field model with a cosine potential. Our results…

Statistical Mechanics · Physics 2020-06-24 Moisés F. P. Silva , Tarcísio M. Rocha Filho , Yves Elskens

All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It…

Disordered Systems and Neural Networks · Physics 2021-10-26 E. Can Artun , A. Nihat Berker

The scaling hypothesis for the coupled chotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum…

Chaotic Dynamics · Physics 2007-05-23 D. Volchenkov , R. Lima

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model,…

High Energy Physics - Theory · Physics 2023-11-02 Antonio M. García-García , Chang Liu , Jacobus J. M. Verbaarschot

In the spirit of classic works of Wilson on the renormalization group and operator product expansion, a new framework for the study of the theory space of euclidean quantum field theories has been introduced. This formalism is particularly…

High Energy Physics - Theory · Physics 2009-10-22 B. Mikhak , A. M. Zarkesh

We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, i.e., as the mesh…

Probability · Mathematics 2021-04-28 Dmitry Chelkak , Konstantin Izyurov , Rémy Mahfouf

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the…

Mathematical Physics · Physics 2025-02-13 Giulia Cava , Alessandro Giuliani , Rafael Leon Greenblatt

Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two…

Chaotic Dynamics · Physics 2016-03-07 N. V. Kuznetsov , T. A. Alexeeva , G. A. Leonov

We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling terms,…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Jeremy D. Schnittman , Frederic A. Rasio

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's…

Statistical Mechanics · Physics 2019-10-25 Daniel E. Parker , Xiangyu Cao , Alexander Avdoshkin , Thomas Scaffidi , Ehud Altman