Related papers: Code C# for chaos analysis of relativistic many-bo…
We enquire into the quasi-many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on ladder geometry, where different types of anyonic defects carry different masses induced by…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by Random Matrix Theory. We demonstrate it by…
A remarkable feature of chaos in many-body quantum systems is the existence of a bound on the quantum Lyapunov exponent. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
We devote our studies to the subject of weakly nonintegrable dynamics of systems with a macroscopic number of degrees of freedom. Our main points of interest are the relations between the timescales of thermalization and the timescales of…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
We demonstrate that the long-time dynamics of an observable associated with a single lattice site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, a widely used…
We consider a non-interacting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model) - a generic model of single-particle quantum chaos. We study the corresponding…
The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the…
The use of numerical simulations in science is ever increasing and with it the computational size. In many cases single processors are no longer adequate and simulations are run on multiple core machines or supercomputers. One of the key…
The nuclear many-body problem at the limits of stability is considered in the framework of the Continuum Shell Model that allows a unified description of intrinsic structure and reactions. Technical details behind the method are highlighted…
Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions,…
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…
We investigate the structure of the invariant measure of space-time chaos by adopting an "open-system" point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the…
This paper presents a fortran program to solve diverse few-body problems with the stochastic variational method. Depending on the available computational resources the program is applicable for $N=2-3-4-5-6-...$-body systems with $L=0$…
A new system of library code is proposed and initiated. It is emphasized that the same terminologies as we find in our textbooks should be used for class names in the library code. The language C# invented by Microsoft is adopted in this…