Related papers: Unsupervised Techniques to Detect Quantum Chaos
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
The low energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior…
Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The first type controls the early-time physics, e.g. the thermal relaxation and the sensitivity of the system to initial conditions. It can be traced back to the…
We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation…
We study a 2-spin quantum Turing architecture, in which discrete local rotations \alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. We show that a single chaotic parameter input \alpha_m leads to a chaotic…
Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
We analyze numerically ensembles of tight-binding Hamiltonians describing highly-symmetric graphene nanoflakes with weak diagonal disorder induced by random electrostatic potential landscapes. When increasing the disorder strength,…
A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK)…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their…